I
SSOCIATION FOR MATHEMATI RIENNE POUR L'ENSEIGNEME . .. d< . · ·...• • CONTENTS tuis:r !�1rc0il w181a soArt <··· · i:r /•·•·•·•·•···•·•·•·•·•·•·•·•·•i •·•·•··lirfiRixt13• 11 ••/· i :phlirigt? · . ••·• ► Foreword/ 1 FitMk�fgi · I J ·· · ► · · . .. ..I ...... · President's Message/2 · . · · · · · .. . ·?·· · · ·. • ··· ·� E• Bri· wson. ··. ... . �A,P:u:keJ:>·. . . ··•·••·· ► ··· ··········· ································ · •· •····· ·············· ·· ·••..•·•.•.·••·••••••'.••·.··••.•.••••·••··••••.;.... .•.••.• •..•.. •.: • :•.••.••.••·. ..: .·... ..•.•.••.•.• ••••·•·.••··•••.•• .• ·•.•···.·•.•.·.••..•• ..•·••.•••.•••·.•.•·L. ·••.•••.•·••·•.•••••. .•••••••••.·..•.·•·•··•••·••./•••·:rr. t.g"P..•••••••···•···..•.•·•.. ·•.••·...... · · Letter to the Editor/3 St»tft,tti } ·· · · . ··· ··· ·· .. .··.. . ······ 1 .·• ► Iitiibt •. S@th ; •·.·•·•·•········ · · '.t'.Pitfuan X •>· A Short and Personal View of Our ·················•·••·····•·1·•······ ·· ••.••.·······.•·••.·E.••.•··· < · · · · ·····•·1·•.··· •······.·.·..••··· ··.•••·t•.·. . .j_.·•·•.·•.•. �c•··•·• ··••·• · · · · . ·. · JIP". · K · · . o·. erpe. ••·.·••.•·r•.. ·••.········••.·····••.\. es > . · . · · > · Roots/4 H ficWw
FROM THE ARCH IVIES JOHN C. EGSGARD ... SOME OF THE MAJOR SIX CHAPTERS OF OAME ACTIONS TAKEN... ► SouthwesternOntario Association for PUBLICATIONS ► Submitted a brief to the Minister of Mathematics Education (SWOAME) Education on the Qualificationsand COMMITTEE ► Grand Valley Mathematics Association ... With the completion of the terms of the Preparation of Teachers of Mathematics (GVMA) previous editors, Bill Eames and John Griffith K-8. ► NorthernOntario Mathematics Associa for the Gazette and Brock Rachar for the ► Conducted a leadership conference for tion (NOMA) Abacus, new e�itors were obtained. Arnold elementaryteachers of mathematics. Stormont Dundas Glengarry Prescott Harris was appointed as editor of the Gazette ► ► Established a Senior Cyclic Curriculum Russell and Andy Czempinski forthe Abacus ... Committee. Carleton Ottawa Mathematics Association Nominated Dr. Magee of the University ► ► REPORT OF of WesternOntario as a life member of THE PRESIDENT, VOLUMl;.14, NUMBER 1, OBA. SEPTEMBER 1975 LE'ITERTOTHEEDITOR
, 0 0 0 I! l!l! l'VT'F.H."lAnONA.t.£,,.. ~ ..... 01:: Ii i44:tM¥iHHU4i
Minister (416) 965-5277 Ministre Ministry of Education Ministere de January 1991 !'Education
On behalf of the Ministry of Education and the Government of Ontario, I extend to you my sincere best wishes on this the 100th anniversary of subject associations for mathematics education in the province of Ontario.
Through the past hundred years the mathematics education associations of Ontario have had a rich and commendable record of service to the educators and students within the province. The original mathematics association OATMP (Ontario Association of Teachers of Mathematics and Physics), the OATM (Ontario Association of Teachers of Mathematics) and the present OAME (Ontario Association for Mathematics Education) have made a significant contribution to mathematics education.
As you celebrate this important event in your history, please be assured that your past contributions have been appreciated and our educational partnership with your association will continue into the future. My best wishes to all members past, present, and future as you enter your centennial year and a new decade of education in Ontario.
Yours sincerely,
Marion Boyd Minister ASHORTAND (Teachers' College), who spoke on "Euclid as THE EARLY YEARS: THE a Textbook". He was concernedthat it had been Fl RST SO YEARS PERSONAL VIEW OF abandoned in continental Europe and the USA On 1891-01-18-10:00 the preliminary but not in Great Britain and Canada. (He fa meeting of thoseinterested in theformation of OURROOTS vored keeping it) a Mathematical Association for the Province fu 1879, Dr. Mclellan (President of the was held in the libraryof the Nonnal School. JACK LESAGE OEA) said: (Using theformula on page 24 of the Volume As I look back over the history of the "l think, then, that notwithstanding the 29, Number 1 issue of the Ontario Mathemat associations and think of my own mathematics dogmatic utterances of certain ics Gazette, I calculate that to be a Sunday.) education history, I realize thatthe person who Metaphysicians who were almost total ProfessorsLouden, Baker and McKay, and influenced me the most was Frank Kinlin. So I ly ignorant of Mathematics, and the Messrs. Kirkland, MacMurchy, McGowan, respectfully dedicatemy article to him. careless admissions of afev.• Mathemat Riddell, Grant, Dickson and Manley were This will be a series of significant dates, ical Metaphysicians who sacrificedthe present. They obviously decided to form an interesting quotes and some connecting com certainty and stability of Mathematics association that would encompass Physics - ments. Please do not confuse this with a for the aberrations of Psychology, which, of course, is Applied Mathematics! - scholarly history! I am gratefulfor two sources enough has been adduced to establish and the firstmeeting of the Mathematical and upon whichI have drawn heavily: the proposition that Mathematics are Physical Association of Ontario was held on ► Historical Highlights of The Ontario entitled to a high position as an Instru 1892-04-21. The charter President was A. Association of Teachers of Mathematics ment of Education." MacMurchy. There were 37 charter members and Physics, 1891-1960 by ErnieTotton The next day there was a talk on "The and the dues were $0.50. and Frank Asbury, Copp Clark Higher Education of Women". (For an inter Dr. J.A. McClellan - author of The Ele ► Highlights, Ontario Association for estingfootnotetothisseeJean Leppard'sarticle ments of Algebra, Canada Publishing, 1886 - Mathematics Education I Association on her introduction to "Higher Education" in spoke on "Mathematics as an Education" and Ontarienne pour L' Enseignement des 1928.) A Professor Young gave a talk on the Universityof Toronto ProfessorAlfred Baker's Mathematiques, 1973-1989 by Morley development of the brain and concluded that: talk was "The Introductionof Astronomy into and Mona MacGregor ► "kindergartenwas the best approach for5 our High Schools". (He was the author of: to 7-year olds, and Elementary Plane Geomehy, Inductive and PRE-HISTORY ► "the processes of arithmetic were the Deductive, lntroducto,y and Practical, $0.50; In1860 the OntarioTeachers Association, important matter, and that children should Geometly for Schools, Theoretical, $0.75; and later to become the Ontario Educational As not be tormented by being required to Analytical Geometly,for Beginners, $1; all by sociation (OEA) was formed. It eventually give the reasons forevery step." W.J. Gage in theearly 1900's.) became the umbrella forthe various specialized fu 1880 David Boyle (Headmasterof Aurora fu 1895, ProfessorA.T. DeLury (President) Sections: Public School) spoke on "TheNatural Sciences of the Universityof Toronto suggested: ► Subject oriented - Mathematics and in the Public Schools". He said: "A Committee of the Association might Physics "Children are rushing away to the cit report each year on all, or the more r important, textbooks appearing during ► Child oriented - Elementary School ies, f ightened from their schools by the yea,; (so that) teachers would have Teachers impractical and uninteresting instruc tion by teachers who regard it a sacred knowledge as to the character and im ► Administrationoriented - School dutyto tell just how many x's it takes to portance of the recent books on their Inspectors, School Trustees, etc. make a y; how fast one train, so many subjects." It wasn't until 1918 that the frrst Teachers' feet long, is going in one direction when He also suggested that teachers in any dis Federation was formed (OSSTF), so this it passes another train, twice or halfthe trict might organize themselves to prosecute association was the voice of Education in same length, going the opposite way, or some special studies, ... , by coming together Ontario.It would appear that the meetings were the same way, at such-and-such a rate; when possible or convenient, work on some held in August since at that time there was no or when the hands of an 8-day clock ... original investigations. So we see that, already, March Break (nor its predecessor, Easter Hol will next be togethe1� or at right angles, the concept of chapters was in its rudimentary idays). It is interesting to note that theEaster or in some other position .... At the same stages. A.H. McDougall of OttawaCollegiate Week Holiday was negotiated by the OEA so time the pupil doesn't need to know the stated that therehad been a decline of interest that teachers could come to Toronto for a differencebetween a cat and a cat-fish, in Mathematics and Arithmetic, blaming it on Teachers' Convention. or a sunflowerand an ear of corn,pro the: increase in the number of femaleteachers, The firstreference found concerning math vided always (that) he can solve some lowered Arithmetic requirements forthe first ematics was a talk in 1873 by Thomas Kirk crooked combination of figures by the class teaching certificate,the "Yankee idea" of land, Science Master at the Normal School unitary or any other method." solving difficultiesby leaving them out. "Our Public School Arithmetic has left "heartily approves of the work in Ge School Students. He lamented their weakness out everything in the shape of compli omet,y outlined for the Lower School in mental arithmetic, and in problem solving. cated fractional expressions ... a grow (Grades 9,10) in the dr
FROM THE GALI.ERV: A "MAKE AND FROM THE GALLERY: JOHN COLEMAN AND JOHN DELGRANDE TAKE" WORKSHOP EUROPE AND THE USA: ONTARIO: 1900TO 1960 1900TO 1960 ► 1904: TheAnalytic Geometryof the straight line and of the circle was re-introduced to ► 1892: Felix Klein gave his famous UpperSchool (Form V). lectures on "Elementary Mathematics ► 1937 (Grades 9, 10): A common programme forall levels of student (called General From an Advanced Standpoint" to Mathematics). It included: Arithmetic, Mensuration, Algebra, Euclid (Books I, II) Gymnasium teachers at Gottingen in ► 1937 (Grades 11, 12): Algebra, Euclid (Books ill,rv, V) 1908. He appealed forthe use of intuition and an emphasis on Analytic Geometry ► 1937 (Grade 13): Algebra, Analytic Geometry,Trigonometry and Statics and Transformations. (Editor: See the This programmestayed in place until the early 1960's. Ontario 1878 curriculum.) Editor: While this is a look at secondary sclwol cunicula, it is interestingto ,wte thata new cwriculum ► 1900/1920:Alfred North Whiteheadin for elementa,yschools was introducedin 1937. lfyouever get the challCe,read thepreamble. It stands England made a strongcase forteaching the test oftime as a philosoplry of education. the "great ideas" of mathematics. The programmesin France and Germany had Euclid plus heavy components of Analytic Geometry(and one presumes, of FROM THE ARCHIVES Algebra) and some Calculus. B-PROBLEMS In1957 - Sputnikwent up and, in the Draw the figures,describe the method of constructionand give proofs. USA at least, Mathematics became a 1. On astraight lineof given length make a parallelo am equal in area to a giventriangle matter of national prestige (survival?). gr and having an angle equal to a given angle. DEPARTMENT OF EDUCATION, ONTARIO ANNUAL EXAMINATIONS, 1929 MIDDLE SCHOOL GEOMETRY
FROM THE GALLERY: BOB TUCK, HM FENCOTT, BOB KOVATCH EUROPE AND THE USA: ONTARIO: THE SIXTIES AND SEVENTIES THE SIXTIES ► 1959 The Ontario MathematicsCommission was founded.Many changes followed. ► 1959: At theconference in Royaumont, EARLY SIXTIES France many of the best mathematics Mathematicswas to be offeredin three branches(Arts and Science; Science, Technology minds - and thebodies that contained and Trades; Business and Commerce) and at two levels - Four-Year (General) and Five them! - in the West discussed the future. Year (Advanced) in each of these branches. It was also to be offeredin theTwo-Year This is where Dieudonne's "Euclid must programme and in the Occupational programme (Grades 9, 10). go." was delivered! (Dieudonne was a Grades 9, 10 (all branches): Arithmetic,Euclid (I), Algebra (the usual and sets, relations, member of Bourbaki- see John ► number properties) Coleman's article.) Grades 11, 12: Euclid (Ill,IV), Algebra (the usual and functions),Trigonometry (including ► 1961: The Athens Conference was a ► some formerGrade 13 material), Analytic Geometry(straight line - formerlyGrade 13) follow-upto theRoyamount Conference. Grade 13: MathA (logic, functions, conics, trigonometry,transformations, calculus), Math Many new programmes were created. ► B (sets, combinatorics, probability, binomial theorem, vectors, vector equations, linear Differentcourses of action were taken in systems, transformations,complex numbers, polar coordinates, groups) the various countries.But, in many cases, theprogramme was overloaded when LATE SIXTIES new topics were added to the old. (This This was thesecond round of revision and was intended to consolidate theprevious was especially truein the UK, Germany changes. The Credit System was on the horizon. and the Nordic countries.)The term "New ► Grades 9, 10: Mainly thesame but group theory and number structurewas added to Grade Math"was coined. By thelate sixties 10. (Thiswas a major failure.) Morris Klinewas writing and speaking ► Grades 11, 12: Mainly the same but an attempt was made to add SyntheticTransforma about the "New Math disaster" in the tions to Grade 11. (This was a failure.) USA. He felt that there was too much theory and not enough attention to ► Grade 13: The material fromMath A and Math B was re-packaged into three courses applications,especially in Science. (He (Algebra, Calculus, Functions and Relations) was themain speaker at an OATMP Editor: Anwng other thi11gs, this made time-tabling easie1: This cha11ge was 11ot initiated bythe annual meeting in the mid-sixties.) Department of Educatiollbut was made ill response to demandsji-om the teachers. The guidelines were very flexible and allowed fora lot of teacher experimentation. During FROM THE ARCHIVES thisperiod, criticism of the curriculum startedto appear. The developing Faculty of Mathematicsat the University of Waterloo became a focalpoint forthe concerned EDITORIAL teachers. RALPHSTANTON Editor: /tis interesting to note that, while the seconda1yschool cwriculumseemed tofocusollcontent, . . . But it is time that the government re the new trendsill the Kinderga,ten to 6 cwriculum were Oil content (more geomelly, statistics) a11d ceived more information. It is time that this oil pivcess. We see PJJJ Mathematics, Livillg and Learnillg,Nuffield approach, The Formative political SHORTFALL ceased. Years, etc.. In conclusion, one bright note. One univer sity in the province seems to be receiving MID SEVENTIES adequate operating grants. According to the The new Grades 9 to 12 curriculumwas introducedunder the leadership of George FinancialPost of October 12, student popula Scroggie of the Ministry. This revision was important formany reasons, not the least of tion at York was 500 students. Theoperating which was thatit released the energy and opinions of practising teachers. They were grant at York was 1.3 million, an average of incensed at many of the proposals and demanded change. I remember leading a delegation 2600 dollars per student.At Queen's Universi to Queen's Park that represented theentire MetroTo ronto and York regions. We met with ty,for example, student population was 3792. George and an Assistant Deputy Minister (Editor: probably Frank Kinlin) to state our The operating grant at Queen's was 3.45 mil misgivings. The actual changes were minorbut it was a coming of age forMathematics lion, anaverage of910 dollars per student. The teachersin the Province as we cast offthe paternalinfluence of the Ministry. other universities were in the same range as Queen's ... Editor: A,wther i11terestillg aspect of the Intermediate curriculum revisioll is that the Minislly VOLUME 3, NUMBER 1, commissioned D,: Pallick Babin of the U of 0, who ill tum secondedPaul Pogue to produce FEBRUARY 1964 "Recommendatio11s for Intennediate Divisioll Mathematics ill Olltario" 1976. It still makes good readillg. EUROPE AND THE USA: ONTARIO: THE EIGHTIES THE EIGHTIES ► The 1985 revision was verydemocratic. Dave Alexander had a three-year mandate to issue ► Therewas disenchantment and the new white papersand collect reaction. Although many people did not think that they were buzzwords were "Back to the Basics" listened to as much as they would have liked and the opinion-poll-mentality did take over and "Be Accountable". Titlshas caused it was, I think,process a that worked remarkably well. Those who are now dissatisfied somemajor changes. should ask themselves, "Did I do my homeworkon the White Papers?". fu Waterloo ► One of the most obvious inNorth County we did a huge amount of work in 1983-84 and sent in well-researcheddocuments America is the massive effortby the to the committee. Many of our suggestions were accepted and many were not. The NCTMto produce the "Standards" importantpoint is that we had the opportunity document. Thebest part about this Editor: I can personally verifythis. I sent in manysuggestions. Thankfully! Most of themwen: not (Editor: excellent) work is that we see for accepted but/ hwwthat theywere considered.On another issue it is interesting to note that, by1980, the firsttime the Americans implement and moreexplicitly in 1985, wefinally see, in the Grades 7 to OAC cuniculum, an emphasison the ing what we did 30 years ago. (Our process componentsthat were introduced in the Kindergarten to 6 cuniculum in theearly '70's! younger mathematics teachers should knowthis!) ► One major criticism that has been advanced is the overloading of topics in Grades 11 to ► TheEuropean situation will be very much OAC and the lack of time to achieve appropriate levels of problem solving.Recall that the affectedby the massive political changes Coleman Report onthe Mathematical Sciences in Canada (1981) identifiedthe lack of that are takingplace. fu afew years we problemsolving skills as a major defect in our teaching of mathematics. will possibly see a Renaissance of ideas ► I think that the present Advanced Level programmehas a lot of merit,especially the Grade in Europe, especially Germanyand 12andOAC: EasternEurope. We are leaders in North America; We are no longer 40 yearsbehind Europe; FROM THIEARCHIVES Thechallenge forthe 1990's is to consolidate what we have and raise the level of problem solving. EDITORIAL Editor:This compa,isonis based on a very interesting summarythat Gord Nic/wllsof Preston HS ... It is both a pleasure and a privilege to sent to me. The summarywas, in tum, the basis for a week of lectures that Gord gave when he was introducean issue of the Gazette devoted en teaching in the Type B programme at FEUJin '73/74. Thecontent is. his, the wording is mine. tirely to Mathematics in the new Colleges of Applied Artsand Technology.Titls new system of Colleges is only in its second year of oper ation,yet already it shows tremendous vitality in attempting to meet the needs of the great number of high school graduates who require furthereducation in our complex society ... VOLUME 7, NUMBER 1, DECEMBER 1986
FROM THE CiALLERY:RON DUNKLEY, NEIL WILLIAMSON, FRANK EBOS, AND FRIENDS
J1:4 7, J;tEJ��E 'l �0E� "'s�Y� >M? a �--- / -� «"� �W --< SOMETHOUGHTS ONTHEPAST NORM SHARP I began my Ontario teaching career in September 1937. Those of you who were around at thattime mayrememberthatschool openings were delayed a fewweeks because of thepolio epidemic.Others may have differentreference points. This was before:the pill and thepopu lation explosion, TY, penicillin, polio shots, antibiotics, open-heart surgery (Editor: thanks for that!) hair transplants,frozen foods, nylon, Xerox, Kinsey, radar, fluorescent lights, credit cards, ballpoint pens, vitamins,disposable di apers, Jeeps, face lifts, instant coffee, decaf feinatedanything, FM,tape recorders, electric typewriters, word processors, electronicmusic and disco dancing. In those days our courses were based on FROM THE GALLERY: NORM SHARP texts written by such mathematicseducators as Another text for this course was by Jenkins. Lougheed and Workman,Levitt, Jackson, etc. for a long time and that influenced today's Texts were much smaller than those used today. Good reference texts that were on every courses. For a number of years courses and concepts teacher's desk were Advanced Geometry for Theimprovements in the elementary schools remained constant. Then some new ideas came High Sch�ols, McDougall and Higher Algebra, were in content and approaches. Many work across the border fromthe United States. This Halland Knight.The geometry course contained shops were given in which teachers were ex was the'new math' and many educators took such famous theorems as: Ceva, Menelaus, posed to the advantages of using concrete courses in the US to familiarize themselves Nine Point Circle, Simpson's Line, Ptolemy's materials and of teaching more geometry. It with thisturn of events. Beberman, University Theorem along withthe topics Medial Section, was still difficult for many teachers in the of Chicago, was a much sought afterspeaker at Harmonic Ranges and Pencils, the Complete elementary schools to convince themselves conferences. Emphasis was placed on names Quadrilateral, Poles and Polars. Many of the thatthere was anything other thanadd, subtract, more than ideas and, to many of us, it appeared problems in the texts would be stoppers on multiply and divide in mathematics. I think that that we would lose much of the work that we present-day Mathematics contests. we convinced them that a day per week on were teaching. Did it matter if we confused geometry would encourage many of those Editor: Don't forget that this comment comes number with numeral? Was it so important that having difficultywithari thmeticfactsthat there from a valuable member of the Canadian thebasic arithmetic be all proved from a few was still a lot of fun in thesubject. I can say from Mathematics Competitions problems com axioms. Ideas that we used naturally such as my experiencethat I learnedmuch more about mittee. commutative, associative, distributive and three-dimensional geometry than I had ever identities were now to be given centralbilling. experienced before. My earliest recollection of a mathematics Saner heads prevailed. In the late 50's there Probably themost dramatic changes in the meeting in Toronto was in (about) 1938. Gene was the Lakefield conference to which well mathematics curricula in thepast 20 years have Durrant was the speaker. He outlined a new knownmathematics educators fromacross the been the change to metricalong with the intro course in Geometry.It was completely analytic province were invited for a week's discussion. duction of the use of calculators and comput (straight line and conic sections). Previously The result was the formation of the Ontario ers. Imagine inserting data into either machines the Geometry course had three divisions; Mathematics Commission. Summerworkshops when the data comes frommeasurement using synthetic two-dimensional, synthetic three were established with new texts being written the Imperial system. I remember being in En dirnensional,analytic (straightline). Theteacher for testing and evaluating. The Commission gland several years ago and being amazed at could choose one of the first two and the did its work, sifting through allthe ideas being the facility of their cash registers in pounds, Provincial exam had three parts of which the forced upon school systems in Great Britain, shillings and pence. Yes, they can make a student selected two. The text for the new United States, France, Germany and different machine to do the converting but when the geometry course was written by Durrantand parts of Canada. The members selected the best converting is differentin linear measure thanit Kingston and later by Durrant, Sharp and Kerr. of the new to meld with the best of the old and is in capacity measure, from what it is in mass, prepared the courses that were to remain in use you realize the way our calculations have been As one settles into the comfortsof a senior ONTARIO PUBLIC streamlined. citizen the mind is not as active and the memory SCHOOL ARITHMETIC The opposition to the metric system has wanes Editor: I am 0,11a committee with Norm ( AUTHOR NOT INDICATED mainly disappeared but there is still some op and either he is lying or he is the exception to Why do we begin at the units' place in the position to calculators.It has taken a fewyears the rule!)so herearesomepeoplethatlhaven't addition and subtraction of numbers?Is it nec to realize the full potential of these small mentioned: essary to begin at the units' place in multiplica electronicunits. The proper use of calculators ► Edith B,ggs and GeoffreyMathews from tion? Why? has taken the emphasis fromcomputation and England who exerted a great, and good placed it in other areas. Now, much of the influence on us. Editor: Thisis a11 i11teresti11g problem. emphasis can be placed on problem solving ► Andy Elliott, Ruth Winters and Janet Iffor an ocean voyage the cost of a steerage and students who can not memorize their tables Black, who along with me learned so as well as others can devote their time and much on our visit to England (sponsored ticket is ¾ that ofa second-class ticket, and the effortsto the applications of mathematics. More by OMC and the OntarioCurriculum cost of a second-class ticket is ½ that of the emphasis is placed on approximatio� validity Institute). first-class,frnd the amount saved by travelling of answers and frnding new ways to solve ► Wynne Bates, Jack McKnight, John Del steerage instead of second-class on a boat for problems. It is most fascinating to see.theways Grande and Joe Perrell,who along with which a first-classticket will cost $135. the mindsof students operate and where the use myselfformed the group which became ROBERT SIMPSON CO., of calculatorsenters the problem solving pro 1910, 10<: the Ontario Mathematics Coordinators cess.I taught a course in the Mathematics of Association. Finance at Humber College last year and found PUBLIC SCHOOL the calculator essential if we wanted to use ► Peter Hilton who brought sanityto the ARITHMETIC many new approaches to mathematics in different rates of interest and frequency of AUTHOR NOT INDICATED compounding. Students fromGrade 6 onward the 60's. A man distributed535 ½ lb. offlour among should start their mathematics class with a Editor: Norm co11ti11uesto have a beneficial calculator on the desk. a number of poor persons,giving 14 ½ lb. to effect011 Mathematics Education.I have the each. How many received relief? Had there privilege of worki11gwith him and marvel at Editor: Now that we have co11vi11ced been 2 persons fewer,how much more would his pedagogical i11Sight and hismathemati elementa,y school teachers that students each assisted person have received? should use a four-functio11 calculato,; how cal ability- he still has fundoi11g matlze willwe co11vi11ce seconda,yschool teachers matics. Did you hww that lze and Betty Froma heapofshot weighing7 ¾ lb.,3465 that students should use graphi11g calcula Hallamoreputto gethero11e oftlzefirst"semi shot are taken, and the heap is then found to tors and algebra calculators! tra11Spare11t minvrs" that eve11tuallyevolved weigh 4 ¾ lb. Find the weight of a single shot i11to tlze Mira? Did you hww thatNonn was and thenumber originally in the heap. For a while teachers became concerned 011 tlze executive oftlzeMehv T01v11to Hockey On the reopening of school after the mid about the computer nuts. In their own way Association wizen Abbie Hojfma11 played summer holidays John bought a ThirdReader these nuts were discovering for themselves mi110rlwckey incognito. for36¢, an arithmetic for 25¢, a grammarfor more ideas than we could possibly give them in 25¢,ageographyfor 68¢,aslatefor15¢,acopy class. Both the computer and calculator make book for13¢ and a bottle of ink, a pen, and a the students organize their thinking,and dis penholder for 8¢. How much did the whole covery takes on a new meaning. FROM TH IEARCH IVIES cost? The use of calculators has increased the CANADA PUBLISHING, need fora good background in decimal nota A SECOND-CLASS 1887,25<: tion and decreased theuse of fractions.When I CERTIFICATE AND say this I keep reminding myself of the tenden INTERMEDIATE A HIGH SCHOOL cy, in all curriculumchange, for the pendulum EXAMINATION ENTRANCE to swing too far. One ofthe most difficulttopics AUTHOR NOT INDICATED EXAMINATION to teach to the elementary student is the algo InBabylonia a capithe of meal was sold for AUTHOR NOT INDICATED rithm for the addition of fractions. However A cannon balltravels at therate of1,500 feet this skill is still important when we wish to 4sigli.Asigluswasworth7 ½ obols,the capithe in a second and a half; how far will it have gone simplify algebraic formulae or to change the held 3 qts. Find the price of meal per bushel, 1 formof a trigonometric expression. Theneed taking the obol at 3½ ¢. in ½5 of a minute? forthe abilityto use the rational expression is J.W. CONNOR, HIGH DECEMBER, 1874 still with us and one who can is ahead of one SCHOOL, BERLIN who can't. ONTARIO HIGH SCHOOL ONTARIO HIGH SCHOOL HIGH SCHOOL ALGEBRA ARITHMETIC ARITHMETIC J.T.CRAWFORD BAILARD,THOMPSON, CRAWFORD AUTHOR NOT INDICATED The long process forcube root is eliminat At 10.24 a.m. a steamerin longitude 25° 16' Preface... Chapter IV closes the subject of ed, as cube root is not now required in arith W.sends a wirelessmessageto another steamer. pure calculation ... The curious and those who metic .... It is received at 10.19 a.m., true time in each care to spend time on a subject of no practical Prove algebraically that if two rectangles case. What is the longitude of the second and of but little speculative importance may have equal areas and equal perimeters,they are steamer? consult theArithmetics of ... equal in all respects. A regiment lost 20% of its men in a battle; 1\vomen, A and B, hired a span of horses Take any two proper fractionswhose sum is 10% of the remainder deserted, there then and a carriage for$7 to go fromM to R, a dis unity.Add unity to thedifference between their remained 360 men. How many men were there tance of 42 miles. At N, 12 miles fromM, they squares. Show that the result is always twice originally in theregiment? took in C, agreeing to carry him to R and back the greaterfraction. to forhis proportionate share of the expenses. Editor: An interesting problem considering N A rancher sold 50 head of horses, part at AtP, 24 miles fromM,they took in D, agreeing the date thatit was p1vbablyw1itten. $125 a head and the balance at $150 a head. to takehim to R and back to P for his propor After spending $50 he was able to make the A farmer tested the skim milk from his tionate share of the expenses. What should first payment of ½ of the purchase price of separator and foundit to contain.13% of butter each person pay? (Give brieflythe arguments 1200acres of land at $18 per acre. How many fat.The separator was adjusted and a second forand those against each of the two commonly horses did he sell at $125 a head? test showed .05% of butter fat.If the separator presented solutions of this problem.) had been out of adjustment for 30 days what MACMILLAN, 1916 Editor: Now we lawwwhy Stephe11Leacock was the loss on a herd of 20 cows each averag wrote his essay011 algebra! AN ARITHMETIC FOR ing 25 lb. of milk per day, butter fat being HIGH SCHOOLS valued at 28¢ per lb? Assume thatthe weight of GLASHAN, ROSE the skimmilk is 90% of thewhole milk PUBLISHING, 1890 A.T.DELURY Preface... I have thoughtthat if less time Editor:If these problems seem difficult rn EXAMINATION PAPERS weregiven to the solving of strangeand artifi member that, even whenI was in Grade8, IN ARITHMETIC cial problemsand more on the theory of the you had to wlite Entral!CeExaminations to JA. MCLELLAN,THOMAS KIRKLAND subject and to the carefulworking out of nor makeit to Grade 9. Even ifyou passed (I was Preface... To be successfulat theseexam worriedthat I would fail theArt exam!)you mal problems, thesubject would have a higher inations,students must be trainedto a complete value educationallyand practically. still had to decide whether or ,wt to go to independence of the mechanical rules and rou High School. A teacher's salary of $800 is paid in four tine of theordinary textbooks.This indepen quarterly payments at the end of each quarter. HUNTER-ROSE, 1918, 40� dence, with the self-reliance resulting fromit, Find what sum paid at the beginningof the year is to be secured, not by solving questions set is equivalent of these payments, reckoning A Fl RST-CLASS under given rules and formulas,but by constant compound interest at 1½ per cent., a quarter. CERTIFICATE AND practice in properly prepared set of problems, By means of a drawing shew �t a cube UNIVERSITY HONORS in which neither rule nor answer is at hand to may be divided into three pyramids with square EXAMINATION furnishclews and crutches to the halt and the bases and equal in all respects. blind ... Inmaintaining the superiority of the JAMES BRUCE, ESQ. "Unitary Method," it is not intended to assert Editor:This, of course, leads to the fonnula Theratiooftwosidesofa triangle is 5:6, and that rules should be entirely ignored.On the for the volume of a pyramid. thesegments of the base made by a perpendic contrary, rules have their proper place; but the ular falling fromthe vertical angle on the base CANADA PUBLISHING, pupil should be the master of therule, not the 1904 are 10 and 14. Find the sides of the triangle. rule the master of thepupil. To secure intellec WATERDOWN HIGH SCHOOL tual training, independent methods must be HAMBLIN SMITH'S followed;but for thesake of practical facilityin ARITHMETIC reaching results, rules may be framedas logical THOMAS KIRKLAND,WIWAM inferences fromindependent investigation. SCOTT Editor:I wish that I had said that! On p. 33/40 we have a fascinating account of "Methods of Verifyingthe Operations and ADAM MILLER&C0., 1877 some PracticalMethods of Shortening Labor in the ·Fundamental Rules". W.J. GAGE, 1887, 60� COMMITTEES INVOLVED THE FOUNDING OF WITH THE MINISTRY OF OAME EDUCATION Since the time OAME was organized we MORLEYAND MONA MACGREGOR have seen a steady growth of the involvement On May 13, 1973 at 9:30 a.m. at Weaver of OAME/ AOEM and the Ontario Ministry of Auditorium, North Bay, the Ontario Associa Education. The first brief presented to the tion forMathematics Education was formed. Ministry ofEducation was on, TheQualifica Many months of preparation had gone into tions and Preparation of K-9 Teachers of preparing a constitution that - in the years to Mathematics. It was prepared by L. Ridge, J. come - would fulfiland expand the ideas that LeSage and P. Broughton and sent to the had been the backbone of the Ontario Mathe Ministry in June 1974. However, no direct matics Commission and the Ontario Associa action followedon this brief. tion of Teachers of Mathematics. Both parent SENIOR CYCLICAL REVIEW COMMITTEE organizationshad agreed that one organization AND INTERFACE COMMITTEE was the best solution to promote good mathe OAMEset up the Senior Cyclical Review matics education in Ontario. The firstpresident Committee in 1974. The original members was David Alexander and he was ably assisted were R. Leigh, T. Griffiths, R. Scoins, W. by Past Presidents of OATM and OMC, D. Higginson, D. Attridgeand N. Vtlre. In 1977 a Attridge and A. Vertesi. report was sent to the Ministry of Education. Morley and! will touch on several highlights Thisreport was beforeits time and some of its of this organization in its first 16 years of ideas are only now being acted upon. In the existence. Thesehighlights illustrate how this meantime the Senior Cyclical Review became organization functions to assist teachers and the Interface Committee of OAME.Its mem students in the province of Ontario. bershiphad changed to F.Maskell, P. Pogue, R. Acheson, F. Ebos, T. Griffiths, E. Silcox, A. REVISED NAME Of THE Norrie, G. Peters and D. Roberts. This com ASSOCIATION mittee was disbanded and the work of the At the Annual Conference at Brock Uni Interface Committee was taken up by the versity (1976) the FrenchTranslation of our COMA Chapter. Theybecame involvedwith a official nameand logo were approved. Ministry of Education project and did an out ► Ontario Association forMathematics standing report forthe Ministry.The report was Education / Association Ontarienne pour submitted in the summer of 1983. L'Enseignement des Mathematiques THE SENIOR GUIDELINES COMMITTEE ► "OAME/ AOEM" Thiscommittee was revised in 1982. The active members were D. Davidson, T. Griffiths, LOGO P.Pogue, J. Shifrinand N. Wilson. Thiscom R. Patterson of Sarnia designed the first mitteetookanactivepartintheSeniorDivisions logo which was accepted at the firstexecutive revisions, by recommending and reacting to meeting held at Bonnie and David Alexander's thedraft guidelines as they became available. home. In 1981 we chose the design of G. OAME/AOEM-TV ONTARIO Cumyn of Ottawa as the new logo. OAMEwas approached by the then Ontario Educational Communications' Authority to form an advisory committee to assist in the development of TV programs in Mathematics. This request was accepted and a committee consisting of Sharon McPhail, Paul Lessard, Paul Pogue and President Neil Williamson was formed.After a needs assessment survey sent to all OAME members it was decided that IntermediateGeometry would be developed ThreeOAME/AO EM members, GeorgeK nih, FROM THIEGALLERY: MOIUIEY MACGREGOR, SHIRLEY MCINTYRE, ANII>ALEX NORRIE AT THE NCTM ANNUAL MEETING, 1981
Peter Ullrichand Neil Williamson worked with OAME/AOMIE'S bers.A regional meeting of NCTM was held in TVOasmathematicswritersduringtheproject ASSOCIATION WITH Hamilton May 9-12, 1990. The general Co In 1983 theseries "Landscape of Geometry" NATIONAL COUNCIL Of Chairmen of this conference were G. Knill and became available. This is an excellent series TEACHERS Of R. Robinson. Theprogram Co-Chairman were and one program "It's Rude to Point" won an A. Norrie and R. Connelly. InternationalAw ard. MATHEMATICS By constitution OAME/ AOEM is an af ONTARIO INTERMEDIATE CURRICULUM filiate of NCTM. But our relationship with GUIDELINES: 1980 AND 1985 NCTM runs much deeper. When the organi MATHEMATICS T. Griffiths and J. LeSage were asked to zation was less than five months old it assisted COORDINATORS represent OAME/ AOEM on these Ministry at a Name-of-Site Meeting of NCTM at the ASSOCIATION Committees. They conveyed to the Ministry Royal York Hotel in Toronto. In 1975 OAME The OMCA has been a vital part of Math many ofthe concerns of OAME councillors contributed $1000to the NCTM building fund. ematics Education in Ontario. In the late 1980's and their fellow teachers. J. Routledge was the Canadian representative OAME/ AOEM and OMCA began having an OAIP to NCTM 1975-1978 followedby R. Robinson. observer at each other's meetings. The Ministry asked OAME / AOEM to J. Egsgard, our second president, was president providerepresentation on this committee.Three of NCTM. R. Robinson has been an NCTM of the members to represent OAME were S. Director. McPhail, P.Ullrich and R. Connelly. OAME/ OAME / AOEM succeeded in convincing AOEM continues to have representation (that NCTMto hold its Annual Meeting in 1982, for is well received by the Ministry) on various the first time outside of the United States, in OAIP committees. Toronto. This had been brought about by a BILL 82 strong selling campaign of OA.MECouncil. A In November 1983 a committee chaired by tribute should be given here to D. Alexander E. Harvey and composed of members B. who waschairman of local arrangements for Laframboise, D. Handley, I. Brown, L. Marshall this annual meeting and to his wife, Bonnie, andC. Poce completed a brief on Bill 82 to be who chaired committeesfor spouses and social sent to the Ministry. events. Many OAME / AOEM councillors worked OAME/AOEM members have been active on the various committeesassociated with the in the National Council of Supervisors of Ministry. Some of those who served in later Mathematics, a division of NCTM. years were E. Carli, D. Henderson,M.L. Jeffer The excellent reports on NCTM activities ies,G. McNabb, R. Morrow, M. Sandblom,J. given by R. Robinson will long, long be re FROM THE GALLERY: ll>AVE Shifrin, S. Stuart - to mention but a few. membered by OAME/ AOEM council mem- ALEXANDER AWARDS PRESENTED BY OAME FATHER FAUGHT AWARD Thisaward was given in memoryof Father Faught. He was a highschool mathematics teacher, a university mathematics professor, the frrst president of OMC, an honourary president of OA1M, and the manager of a Major Junior AHockey team - St. Michael's Majors!It was originally presented to the On tario school that received the highest mark in the Junior Mathematics Contest. Today it is given on the basis of the Fermat Contest. The award is a plaque forthe school and $50 cash prize to purchase books for the Mathematics department. YEAR FATHER FAUGHT AWARD WINNER 1976 ScarlettHeights School, ► Etobicoke 1977 ThornhillSecondary School, ► Thornhill 1978 Glebe Collegiate, Ottawa ► FROM THE GALLERY: JOAN ROUTLEDGE ► 1979 TorontoFrench School, Toronto McCARTNEY SCHOLARSHIP L1FE MEMBERSHIP Thisscholarship was presented by SRA in Lifemembership was closely allied to OEA 1980 University ofToronto Schools, ► Toronto recognition of the late John McCartney's con affiliation.When OAME was formed we ac tributionto education. cepted all the Life Members of OEA who ► 1981 LoyalistCollegiate, Kingston OAME/ AOEM was assisted by the Sci belonged to the Mathematics section of O.E.A. 1982 Etobicoke Collegiate, ence Research Associates in this scholarship. It These were F.C. Asbury, L.S. Beattie, E. ► Etobicoke was a $400 scholarship given to an Ontario Durrant, J. Egsgard, J.T. Jenkins, G.W. Keith, WoburnCollegiate, student who had successfully completed three W.J. Lougheed, W.B.Maclean, J.I. McKnight, Scarborough Grade XIIIMathematics courses and intended N. Miller and P.A.Petrie. futhe frrstyears of 1983 Woburn Collegiate, to study mathematics at University. We ad OAME.,OEA asked us to present names for ► Scarborough ministered the scholarship and we selected two consideration forLife Membership in OEA. 1984 University of TorontoSchools, educators to judge the applications. Thefollowing rec eived Life Memberships: R. ► Toronto YEAR McCARTNEY Leigh, J. LeSage, M. MacGregor, E. Magee SCHOLARSHIP WINNER and J. Routledge. Theseare recognized as Life 1985 WoburnCollegiate, ► Scarborough 1979 Puiwing Wong,Don Mills Members of OAME / AOEM. Since 1986 ► OAME/AO EM as anAssociationhas awarded 1980 Lai LaneLuey, Willowdale ► 1986 TorontoFrench School, Toronto ► its own Life Memberships. They have been 1987 WoburnCollegiate, 1981 GregoryPlaxton, London awarded to D. Alexander, D. Attridge,L. Auck ► ► land, D. Dottori,A. Norrie,N. Sharp and R. Scarborough 1982 John Omielan, Ingersoll ► Smith. 1988 WoburnCollegiate, ► Scarborough ► 1983 Neale Gi nsburg, Kingston CANADIAN AND INTERNATIONAL 1984 Alex Pak,Scarborough OLYMPIADS 1989 Dr.J.C. MacKenzieHigh ► OAME/ AOEM now contributesannually ► School,Deep River ► 1985 EricVeech, Samia a sum of money to the Canadian Olympiad to assist in the training of Ontario students who 1986 GuiseppeRusso, Sudb ury ► wish to compete at the futemational level. ► 1987 RockyLee, Scarborough OAME / AOEM also purchased blazer badges forthe Canadian futemationalTeams. ► 1988 Patrick Surrey,London ► 1989 Philip Jong,North York PROBLEM SOLVING AWARD LEADERSHIP SEMINAR Chapters with two exceptions, have been TheAssociation formeda Problem Solving The OMC for 2 years had conducted an the hostsof our Annual Conference. One ex Committee in 1982. Themost active personin Elementary Leadership Seminar for teachers ceptionwastheSarniaConference,1981, which this committee was C. Carlow. The Associa of Grades K-6. Thiswas under thedirection of was organized by the MacGregors and the tion is indebted to C. Carlow for a sum of J. Girhiny. The OATM had given a grant of McPhails and greatly assisted by our friends. money which the Association matched to give money to help pay forthe seminar. The1986 Annual was organized by B. Rachar an award. This award was to be given to Ele The1973 seminar was cancelled byOAME. and T. Griffiths and their friends and held at mentary Teachers who developed "neat" and In197 4 Morley and I were asked, along with B. UWO.In some cases the Chapters were formed effective ways and means of improving the Jay (formerlyof Stamford Collegiate,Niagara as a result of the area teachers organizing the teaching of problem solving in their class Falls), to arrange for the Third Leadership annual conference. Many areas of Ontario do rooms. To date three awards have been given Seminar.We were to look afterthe administra not have chapter organizations and yet math and one teacher received honourable mention. tion of the seminar and Bruce theprogram. The ematics thrivesin these areas. Perhaps it would POSTER CONTEST 1974 and 1975 Seminars were held at the Park thrive better with an area Chapter. This contest has always been under the Motor Hotel, Niagara Falls. The 1976-1979 direction of T. Griffiths. The purpose is to Seminars were held at the Ascot Inn, Rexdale. TRAVELLING LIBRARY encourage Mathematics students across On Beginningin 1980 they have been held at the Few of our present members will know tario to research mathematical problems. Priz Ramada Airport Inn. The program coordina what this is. The Ontario Mathematics Com es were given by OAME / AOEM forposters tors since 1978 have been thepast presidents of mission had sponsored a library of mathemat illustrating unsolved problems in Mathemat OAME I AOEM. As we view it, the whole ics books and materials for any teacher on ics. Prizes were awarded in 1988, 1989 and problem of the leadership seminar, is to obtain request. Therewere both an elementary and a 1990. the correctbalance on the program of offering secondary package. Most of the materialwas CERTIFICATES FOR EXCELLENCE IN classroom mathematicsand leadership skills. out of date and OAMEdonated theSecondary MATH The numbers of participants has varied from Library to Althouse College, London and the Since 1986, OAME / AOEM has been year to year. On the average, attendance has Elementary Library to NorthBay Mathematics providing thesecertificates to elementary and been about 70.We have enlarged thescope of Resource Centre. secondaryschool principals fordistribution to the Leadership seminar encouraging second students who display excellenceinmathematics. ary mathematicsteachers to attend.We believe ELECTIONS these seminars are one of the highlights of Our constitution called forvoting by ballot I LOVE MATH BUTTONS Thiswas the dream child of the Membership/ OAME /AOEM. at Annual Meetings. At the very firstAnnual Publicity Committee andM.Sandblom made it Meeting a motion was put forth for proxy very successful. I Love Math Buttons promote CHAPTERS OF OAME voting. Council rejected the idea.Then began a theappreciationofmathematicsamongstudents Our first president was very adamant that longstruggleforvotingbymail.The constitution and teachers. OAMEwould only succeed if Chapters were was amended in 1981 at the Sarnia Annual developed. Theidea of Chapters was not new Meeting to declare the method of voting to be AWARD FOR OUTSTANDING SERVICE to members ofOATM.At themeetinginNorth voting by mail. TO MATHEMATICS EDUCATION IN Bay the followingfour were accepted as Charter ONTARIO: THE MONA MACGREGOR Chapters of OAME. AWARD EUREKA (CRUX This award was established in 1989 and the ► NorthernOntario Mathematics Associa MATHEMATl(ORUM) tion firstrecipient was Mona MacGregor. No highlight would be complete without mention of thispublication which one of our THE MORLEY MACGREGOR ► Ottawa Carleton Association members, Fred Maskell of COMA Chapter, MEMORIAL AWARD ► Prescott,Russell, Stormont, Dundas & Thisannual award, to commence in 1991, is Glengarry Association toiled long and hard to edit, publish and distributeworldwide. administeredby OAME/ AOEM but theset Renfrew County Association ► It was startedin 1975 as a COMA project by ting of criteria,naming of the award winner etc. Duringthe executive and council meetings L.Sauve and F.Maskell of Algonquin College. are to be theresponsibility ofWOMA. of the first year, guidelines were set up for The award pays the registration and ban It was read world-wide and had an impressive creation of more Chapters. From thevery be list of readers and contributors. quet feefor a "Junior to 8 teacher in Laµibton ginning the organization encouraged mathe County". matics teachers in variousareas of theprovince to form chapters and gave them financial as sistance in formof a set-up grant and a refund of part of themembership fee. GVMA PUBLICATIONS CONSTITUTION PUBLISHERS & SUPPLIERS The Grand Valley Mathematics Associa BYLAWS/GUIDELINES Morley and I feel no highlight would be tion which works very closely with Waterloo Inthe winter of 1983 I undertook to rewrite complete without a tribute being paid to all University has published and continues to the Constitution Bylaws and Guidelines so that publishers and suppliersof Mathematics Books publish a number of extremelyvaluable pub they more trulyreflected how the Association and materials.They have unselfishly support lications.These have always been available to handled its problems than did the motions that ed, QA.ME/ AQEM at Annual Conferences, allQAME/AQEMmembers atanominalcost. had been passed at various council meetings. Leadership Seminars and Mini-Conferences. For the next 3 years at each executive meet CONTINUOUS SERVICE ing the members attempted to edit thematerial. PROVINCIAL AND One interesting note we foundwas that R. At the end of that time Mona retyped it and LOCAL ASSISTANCE Robinsonattended the firstcouncil meeting of handed it on so that the futureexecutives could I would like to say thanksto the personnel QA.MEand has served continuously till the end build on it. I on 1988, D. Davidson and W. of the Ministry of Education, Mathematics of our term of 1989. Sebben were asked to prepare a finaldraft of Coordinators and the Boards of Education, the constitution to be presented at the 1990 Editor: Bob, Tom Griffiths and Dave Dav their Directors, Supervisors, Consultants and Annual Meeting. idson "retired" on '91-05. Theyhad a total Staffwho have assisted QA.ME/ AQEM not of 55 years of service! only at Annual Conferences and mini- confer ences but also in the general operation of the QA.ME/AQEM. Their assistance has been both of a professional and a financialnature.
IN MEMORIAM
FROM THE GALLERY: JIM FENCOTT FROM THE GALLERY: FRED MASKELi!.,ED BARBEAU, AND FRIENDS
Morley and I would like to pay special ► R.Acheson ► D.Fox ► R.Hood ► F.Maskell tribute to the following members, now de ► F.Asbury ► K. Fryer ► B.Jay ► N.Miller ceased. ► C. Cardenas ► C. Gravelle ► E.Magee ► P.Ullrich We also sincerely remember all other mem bers of QA.ME/AQEM who are now deceased, ► J. Fencott with whom we worked. FROM THE GALLERY: El>ANDERSON, RON SCOINS, KEN FRYER, ll>OROTHY DUNKLEY, RON DUNKLEY, ANII> FRIENll>S-WATERLOO, 1972 CONCLUSION "Morley and I thank every member of the It has been a pleasant task for Morley and I Association fortheir tremendous support and to put these Highlights on paper. We trust you for sixteen years of very happy fellowship." will bear with us for any errors. Perhaps you "We wish OAME/ AOEM every success in would have chosen a different format. We reaching higher and higher heights as the years know we will have missed items you would go by". have included. We included some names and if Editor: When we we,� planning this issue, your name was not included it is not that your we knew that it would not be complete with contribution was any more or less than some out something from "M & M". When we one whose name was mentioned. The benefits talked to them about it at the Hamilton of the work done by the council and executive NCTMthey asked us to use their"Highlights" is work that will eventually affectthe students produced in 1990 as a basis for an article of mathematics. We see great benefitof OAME written01ztheirbehalf.Sincewehavereduced / AOEM coming from the association of six the number of pages, we have introduced executive members meeting seven times a year some discontinuities and we apologize to and thirty-fourcouncillors meeting three times Monafor this. In case someonefrom another a year. Each one cannot help taking back to his/ planet reads this, theymay not be awa,� of her students some gem of knowledgethe next the impact that Morleyand Mona have had Monday morning. 011 the Mathematics Education community We close these Highlights with two simple in Ontario. One can get a sense of it here and sentences. elsewhere in this histo,y. Mona: We know that you miss Morley,and so do we. We hope that you will continue your association •,vith us . Fr. Faught said, "We have all day so we do WHAT HAD BEEN GOING HOWTHE NEW not need to feel in a rush. Let us spend the ON BEFORE? MATHEMATICS morninganswering the question: Is there any For decades prior to 1960, Copp Clark change I would like to see in the current high Publishing Company had a monopoly in CAME TO ONTARIO: school mathematics programme?" One super mathematicstext-books. This had occurredin visor formathematics felt that everything was a perfectly honest, understandable way. In the PREJUDICES AND absolutely perfect and that it would be foolish "good old days" - 1910 say - therewas no to contemplate any change. Everyone else had money to be made from mathematics text UNRESEARCHED their pet proposal which would, in their view, books so that part of the prescribed duty of the revolutionize forthe good the current terrible professor of mathematics education at OCE REMINISCENCES programme! was to write a book. Naturally this became the AJ.COLEMAN At the end of the morning the motion one and only text he used with his students so "Change is necessaryand desirable" was passed One day in the Fall of 1958, Dan DeLury the texts written by the OCE professors were with only one objector. The afternoon was thenew Head of Mathematics at the University authorizedby the Department ofEducation for devoted to inventinga strategyfor implementing of Toronto - said to me "Coleman, the De universaluse in the schools. By 1960 the eco this motion. The OTF quickly created a partment has been asked to nominate a member nomic advantage of publishing text-bookshad Mathematics Commission which organized a for some committee which the Ontario improved but the OCE professors still enjoyed meeting at LakefieldSchool near Peterborough, Teacher's Federation(OTF) wants to create to a monopoly. The mathematical content of the at which a new curriculum was adumbrated. look at the teaching of mathematics in the programme had remained essentially un schools. Would you like to go? I knowthat it Editor: Thereader should not take umbrage changed forabout fiftyyears. Theone excep will be a nuisance. You cannot hope to get at the c01rect use of this word! tion to this of which I am aware was that Solid teachers to change so probably, nothing will Geometry was, unfortunately, dropped form Fr. Faught insisted on stepping down and I come of it. You will likely be involved in only the syllabus around 1930 just beforeI entered was elected chairperson of the Mathematics one meeting." High School. Commission of the OTF.Within a year this was If a young staffmember knowson which On the other hand, during the 1950's in reorganized as the Ontario Mathematics side his bread is buttered, when the boss sug Europe and the USA there had developed a Commission sponsored by the OTF,the uni gests something he replies immediately, "Of strongmovement to de-emphasize rote learn versities of Ontario, the Provincial Department course, I would be pleased and honoured to ing of mathematic factsand to attempt to teach of Education and the Mathematics and .Physics represent the Department!" understanding of the structureof mathematics. Section of the O.E.A. So it was that a fewdays later I foundmyself There was a major attack on Euclid. When I To test the new ideas it was necessary to in a small room, in a house owned by the OTF was in Grade Ten, for example, theprogramme produce text-book material. In the school year on Pr.Arthur just north of Bloor St. near St. consisted of the memorization of about sixty 1959-60 some very ad-hoc materials were tried George St., packed togetherwith several high theorems of Euclid. This had been going on out in a few places and on the basis of these school mathematics teachers named by the since Newton, except that he probably had to experiments a provisional text forgrade nine Federation and a bunch of representatives from memorize two hundred! (Certainly it is clear was written by John DelGrande of St.Andrew's Ontariouniversities. from the Principia that he had a phenomenal College, Howard Mulligan ofBathurstHeights Unhappily, there was no one from the grasp of Euclidean geometry.) Prospective C.I. & V.S.,Ernie Totton (Editor: Ernie later University of Waterloo, because the OTFwas mathematicians like myself loved geometry wrote the firsthist01y of our Association.) and unaware of its existence! Perhaps it was forthis and it was an excellent training. But for the myself during four months in the spring and reason that theHead of Mathematics at Waterloo majority of students it was dull and meaning summer of 1960. By thistime I had become the challenged the New Mathematics. less. Head of Mathematics at Queen's. Themeeting was chaired by Don Faught, Professor Jean Dieudonnee, one of the The resulting text was calledMathematics theHead of Mathematics at Assumption Uni founders of Bourbaki (the name under which a 9. It was illustrated by my older brother who versity- now, the University of Wmdsor - group of very able young French mathemati was a draughtsman, sold for$2, had a softgreen who had previously taught at St. Michael's cians wrote an ambitious treatise in a dry and cover and was produced in 3000copies. These College High School. Don Faught andHoward axiomatic style covering the "whole of mathe were used in 40 classrooms each of which was Mulligan, both now deceased, are the principal matics" declaimed "Euclid must go!") This visited twice by the two provincial mathemat heroes of my story. Fr. Faught was a member of unleashed the production in Europe of a flood ics inspectors. They were convinced that the the Basilian Order. As the reader is doubtless of absurd school texts mimickingBourbaki's new approach was a defmite improvement aware, to survive successfully in a religious dry exact style of writing formathematicians. over what had been going on before. order one needs to be a master of diplomacy In the USA there came another flood of books and psychology. based on the premise that if the word "set" occurred three times or more on every page, true understanding of the beauty and infinite matics. It is not enough that they can add, worth of mathematics would be inevitably subtract and multiply. I admit that the old FROM TH IEARCH IVIES enhanced! method was better at achieving this latter goal. Of course, Canadians were not to be swept This year, teaching Freshman Calculus, I PRESIDENT'S REMARKS offtheir feetby such nonsense.The Department note that many students are at a disadvantage GEORGEKN/U of Education insisted that any experimental because they make frequenterrors in manipu (URRENT EDUCATIONAL ISSUES AND text for Grade 9 must cover the approved lating polynomials and rational functions.They DIRECTIONS curriculum. It bowed to the winds of change to have little insight in recognizing structure. To ► How will computersenhance mathemat theextent of adding a sentence to the official gain this latter facility I know of no better ics education? syllabus which gave permission to teachers to method than proving trigonometrical identities. Are there appropriate mathematics use the words "set", "commutative", "asso If you get a chance to pick up Hobson 's Plane ► programs forthe learningdisabled and ciative" and "distributive"!The rest is history. Trigonometry, seize it. Make your students the gifted? Soon publishers circled like vultures around prove 150 trigonometric identities. Once they the authors of Mathematics 9. We settled on get into it they will love it and emerge with the ► Do the senior guidelines meet the needs W.J. Gage because, at that time it was the only abilityto perceive mathematical structure. of the students? Canadian-owned publisher which approached For successful teaching there are no pana ► How can education promote mathematics us. For several years, universities offeredshort ceas. Everything useful that can be said is in to the general public? courses in the evenings or summers to help A.N. Whitehead's, "The Aims of Education ► OAMEmust investigatemeans in which older teachers adjust. Fr. Faught reported that and other Essays". Read this every second it can continually become a more as he emerged fromone such session he over year! Encourage your ableststudents to become proactive voice in Ontario education. heard an old man say "Thank heavens, I am independent, to read on their own and to enter For this year your council has formulated over the edge". a mathematical career. As long as Canada at ► the followingas its goals: Compared with many other jurisdictions tempts to be a technologically advanced country the change in Ontario was sensible and rela there will be need formore and more mathe 1. To determine and establish OAME tively painless. In large measure this was due to matics. positions on current issues such as ... Howard Mulligan. Howard was, I feel sure, If you have a copy of the 1960 Edition of Computersin Mathematics one of the most effective and best loved Mathematics 9 put it in your safety deposit box. VOLUME 21, NUMBER 1, mathematics teachers in the Province. He was It will soon be a priceless cultural artifact! SEPTEMBER 1982 a member of the Executive of the Ontario Editor: I had the privilege of hm•illg Jolm as Secondary School Teachers' Federation and, a teacher at Ulliversity of Torollto. he is a about 1957, had the idea that the Federation FROM THE ARCH IVIES scho/a,; a teacher and a gent/email just like should be concerned about something other his predecessor Sam Beatty who also pro than salary.Possibly, even, the relevance of the foz1ndlyajfectedMat/1ematicsEducation.His COMPUTING MACHINES curriculum forthe students he was teaching! It altruism (he set up afimdto aid Mathematics AND THE BRAIN was his initiative which led to the meeting on Educatioll from his share of the royalties HANSHEINING PrinceArthur to which Dan DeLury sent me. In fromthe Gage te.,ts that he co-authored) is all ... It is certainthat thinkingmachines can be addition, the two provincial inspectors, (Editor: inspiration to us all. Personally and through built - and have been built which ap AlfBishop and FrankKinlin) having seen in the Gage series of te.,1s he co-autlwred, he proximate certainparticular functions of a brain. 40 classrooms that in the hands of able and has touched and influenced mally of us. It may in fact be faultless.However to build enthusiastic teachers, the difference between machines which simulate the brain in all its theold and the new approach was the difference modes with all its versatility and adaptability between night and day, foughtresolutely against seems impossible... the upper bureaucrats in the Department of VOLUME 9, NUMBER 3, Education who were frightened by the mere MARCH 1971 idea of change. At one point Mr. Kinlin told them that if they did not approve the change he would resign. Was the change good? To this question there is no objectively valid answer but I certainly think it was. The role of mathematics in our society has become much more important and visible since I was young. It is thereforeessen tial that average citizens understand mathe- speaker,Heather-JaneRobert HERSTORV:THE son, author of The Idea Book, published by the Canadian WOMENAND TeachersFederation, spoke on the topic, "PromotingGender MATHEMATICS Sensitivityin the Classroom." COMMITTEEOF Well over a hundred people attended. The second annual OAME breakfastwas held on May 11, 1990, at theNC1M/OAME/ ELAINE HARVEY AOEM Conference in Hamil "Moved that OAME establish a stand ton. Sylvia Gold, facultymem ing committee, the focus of which will be ber for the Canadian Centre in the area of math anxiety and issues forManagement Development involving women and mathematics, the and formerchairperson of the name and goals of the committee to be CanadianAdvisoryCouncil on decided by the committee." the Status of Women, spoke on With this motion which I proposed at the the timely topic, "From Al FROM THE GALLERY: ELAINE HARVEY AND DAVE OAME/ AOEM Council meeting of October chemy to Chaos". The Com- ALEXANDER 15, 1983, the Women and Mathematics Com mittee wasfortunate in obtain- Technology. Thisorganization held a very suc mittee was created. � cessfulconference at Glendon College in May An informal brainstorming session on Ever conscious of inequities, the Commit- 1989. women and mathematics was held at the 1984 tee requested in 1986 that the plannersof the On October 15, 1988, the Committee, con annual OAME/ AOEM conference held in Leadership Seminar obtain some men speakers cernedthat its membership was small and that Kingston. The level of interest in this session at the elementary level and women at the its memberscould not participate in the other and the ideas brought forthprovided a sound secondary level and that equityissues be ad standing committees because they met in the foundation for the work of the Committee dressed. At the October 1987 Council Meeting same time slot, began holding breakfastmeet whenitwasfinallyestablishedattheJune 1984 the Committeeraised the concernthat no women ings prior to the Council meetings. Atten Council meeting. Lorna Wiggan and Irving had been appointed to any of the Committees dance at these meetings has been excellent. Pupko were named as co-chairs and Elaine announced during that particular business Now all councillors and executive members Harvey as executive liaison. meeting and determinedto send a letter to that are invited and receive agendas in advance. Since its inception, the Committee has effectto the executive. In October, 1988, the Between 25% and 40% of the councillorsattend worked in conjunction with the planners of the Committee noted that Council had no repre these early morningmeetmgs, and this does not annual conferences to obtain speakers on top sentation at that time from private schools or preclude their participation in another"eom ics related to women and mathematics. There community colleges. mittee. was a two-foldpurpose to this goal: to increase In 1986-87, the Committee also began to An attempt has been made to see that at least the number of women speakersat conferences seek out competent women who would be one article for each issue of the Ontario because traditionallythe podia were dominat willing to accept nominations as councillors Mathematics Gazette deals with a topic related ed by men; and to heighten the awareness of and executive members since only a quarter of to the interests of the Committee. During the issues regarding women and mathematics. the councillors at that time were women. It has editorshipof the late CliffordGravelle, a Women Because such topics had seldom been presented also assisted interested women in building their and Mathematics Department was established in past conferences,an identifiable Womenand profiles in preparation for their future contri first appearingwith the December 1986 edition Mathematics Strand of presentations was of bution to the organization. and continuing forthe followingtwo editions. fered at the 1985, 1986, 1987 and 1988 con Recently the Committee has identified as a It was a completely separate entity from the ferences.At the Ottawa conference in 1989, the goal the establishment of a speakers' list for Committee and was not meant to reflect in any Committee discontinued the systematic plan distributionto local chapters. Olive Fullerton is way the goals of the Committee or receive its ning of a strandin which a women and math coordinating the compilation of a list of women endorsement. Elaine Harvey was editor of that ematics workshop was offered in every time who can address issues related to women and department. slot. Instead the Committee began offering a mathematics, and women who can provide With Clifford's untimely death in Decem scheduled breakfast. appropriate leadership in mathematics. ber of 1987 the Women and Mathematics De May 13, 1989, marked the firstannual con In 1987 Loma Wiggan became the Com partment along with other departments ference breakfast meeting arranged by the mittee's representative on CEMSAT, the Coa established by Clifford ceased to exist. How Women and Mathematics Committee. The lition for Equity in Mathematics, Science and ever, an editorial and two articles which had been submitted forthe Women and Mathemat 3. It is recommended that the Ministry ics Departmentappeared instead in the March FROM THE ARCH IVES consider theestablishment of a 1988 edition. mathematics course forthose students Since that time and at the invitation of the RECOMMENDATIONS TO who plan to study Social Sciences editor, at least six members of the Women and THE MINISTRY aftersecondary school. Thiscourse Mathematics Committee have joined the edito MORLEY AND MONA MACGREGOR shall be composed of topics selected rial board of the Gazette. .. . This report has been prepared for the fromthe present guidelines. In the seven years that the Women and Ministryof Education by the Ontario Associ The focus of thiscourse would be applica Mathematics Committee has been in existence ation for Mathematics Education for consid tions of mathematics within the social scienc the number of women participants in Council eration during their review of the Senior es. meetings has increased form 28% to 40%. Division Mathematics Curriculum ... 4. It is recommended that the Ministry There has been a similar increase in women ... The OAMEconsiders the present senior provided detailed support documents speakers at both the annual conference and the division guidelines to be basically sound cur forthe following: Leadership Seminar. In 1990, the keynote riculum statements. We also believe that the (a) "A Mathematics Style Guide" speaker at theLeadership Seminar was a women present format should ·be maintained in future outliningcurrent notations, correct - the outstanding University of Toronto revisions ... use of symbols, and concise, physicist, Dr. Ursula Franklin. .. .We offerthe followingrecommendations logical proofs. in order to improve the senior division curric (b) "Problem Solving" requiring the GOALS AND OBJECTIVES ulum and facilitateits eventual implementation use of many conceptsto stress OF THE WOMEN AND mathematical interrelationships. MATHEMATICS . . . It is recommended that the Ministry contact the OntarioAssociationforMathematics (c) "The History of Mathematics" COMMITTEE relating both the history and people The goal of the Women and Mathematics Education to assist with the implementation of of mathematics to specific topics. Committee is to encourage greater participation revisions within the Senior Division .... of girls and women in mathematics. 1. It is recommended that the core topics (d) "Mathematicsand theSocial EXECUTIVE and skills fora particular course be Sciences". YEAR CHAIR LIAISON clearly identified so that greater (e) "A Mathematics Bibliography". understanding and mastery can be ► 1984-1985 LomaWiggan/ Elaine 5. It is recommended thatthe Ministry IrvingPupko Harvey achieved. This recommendation does identifythe prerequisite skills required not conflict with the spiral approach in foreach SeniorDivision Mathematics ► 1985-1986 JerriLunney Elaine the present curriculum but allows for course. Harvey the establishment of priorities within The identification of the required knowledge ► 1986-1987 Elaine Harvey Marylou that approach. Kestell and skills will enable the student to make more 2. It is recommended in principle that rational course selections. This will also enable ► 1987-1988 Elaine Harvey Ralph externallyprepared provincial teachers to identify topics which need review Connelly common examinations be available and consolidation within a-eourse of study. for students proceedingto post ► 1988-1989 lomaWtggan Jay 6. It is recommended that the Ministry Symington secondary educational institutions. authorize the provision of opportuni Consideration should be given to the ties forhigh ability students to realize ► 1989-1990 lomaWtggan Marylou establishment of examining boards Kestell and exercise their fullpotential in involving participation by universities, mathematics. ► 1990-1991 LomaWiggan/ Mickey colleges, professional organizations, Olive Fullerton Sandblom the Ministry of Education, the This involves the encouragement of special Ministryof Colleges and Universities courses for special individuals, and the en and local school boards. couragement of school boards to provide classes for fewer than 15 students, when appropriate. Editor: Elaine, in her own quiet way, has These examinations would complement the had a significantirifluence on Mathematics 7. It is recommended that the Ministry evaluation within the school and aid in estab contact the Ontario Association for Education in this province as well as being lishing provincial standards. an important member of the Women and Mathematics Education to assist with Mathematics Committee since its inception. the implementation of revisions within It's alwaysnice to meet her and discuss old the Senior Division. and new-times. VOLUME 15, NUMBER 3, MARCH1977 FROM THE GALLERY OF THE OAME with mathematics teachers to discuss topics of development that Norm Sharp mentioned, one money. I found that incredibleand said, "But interest. As an outcome of the Coleman evening day, that the use of coloured plastic mirrors books are the toolsof my trade!"I have always it was decided to invite teachers to a small helped children with reflections or flips. We feltthat the best teachersare those who are also gatheringto discuss topics of mutual interest. adapted the idea to geoboards and the related learners. I have triedthroughout my career to John Coleman was to head up the group and I geopapers. This work preceded the develop be open to new ideas and techniques. I read was to act as Secretary. We organized a meeting ment of the Mira by George Scroggie and current math journals and attend conferences for Forest Hill Collegiate expecting at most 40 Norm Gillespie. We were to applaud and sup as a way of maintaining professionalcontacts teachers to attend. Notices were sent out to port the work of these two men in bringing the and keeping up to date with current philosophy Toronto schools and to our surprise more than Mira to market. Our work in geometry led to and practices. Forexample,I'veattendedICME 150 teachers attended. Out of these meetings the writing of my book on Geoboards and (International Conference on Mathematics came the leaders of the New Math movement Motion Geometry for Elementary Teachers, Education) 2 , 3, 4, 5, and 6, an international in Ontario. published by Scott Foresman and Company, in conference held every fouryears. Lorna: Just how did the new math get Chicago. Lorna: Inrecognition of your accomplish started inOntario? Lorna: As I recall you were involvedwith ments you have received some notable awards John: In the scrabble that followed the setting the Ontario Mathematics Achievement during your career. One of the most prestigious launching of the Russian Sputnik there was Test at OISE. Wasn't there an interesting out is the NCSM Glenn GilbertAw ard formaking great interest inthe suitability of the mathemat come from this? a significantcontribution to mathematics edu ics beingtaught in schools. Begle from Stan John: Yes, even though the correlation be cation. You received the first one given, in fordwas leadinga group to develop the SMSG tween this test and success in mathematics 1982, and are still the only Canadian so program and Vaughan and Beberman were courses was high, the Ministry could not per honoured. Are there any other awards you developinga new program at the University of suade the universities to take it over. But there would care to mention? Illinois. Prior to this time Howard Mulligan was one notable outcome from our meetings. John: I have received two awards worthy had been working on new approaches to the Ken Fryer was a member of the OMAT group. of mention. In 1965 the Professional Engineers teaching of mathematics with the support of We met once a month. On one of the meeting of Ontario gave me an award in recognition of OTF and I was trying the new math in a grade days Ken and I were having a little refreshment contributionmade to engineersby a secondary 12 class. John Coleman,Howard Mulligan and before lunch (minewas rum and coke) and Ken school teacher. ThenI received the Descartes Father Faught encouraged the OTF to under was bemoaning the fact that the Waterloo Medal fromthe Universityof Waterloo. write the cost of holding a meeting of leading mathematics students would never become Lorna: I was goingto close this interview educators to set directions in mathematics for teachers because industry employed them dur by asking how long you intended to continue Ontario. Thefirst meeting was held at Lake ing their work terms and would lure them into being actively involved in mathematics edu fieldPreparatory School and was attended by those firmsupon graduation. Ken asked,"Why cation, but I think the question is unnecessary. university professors, high school teachers and can't you hire these students during their work Hopefully, Dr. John Del Grande, Phd., scholar one representative of the public school teach terms?"I took the question back to North York extraordinaire,will continue to be around fora ers. Theoutcome was the birthof the Ontario and with little effortconvinced senior adminis long time. Mathematics Commission. John Coleman was tration that here was our chance to influence the Editor: LomaMonvw worked withlolm in president and I was vice-president. We decided training of mathematics teachers. Ken was North York and co-aut/wred a number oftext to write text materials forhigh schools incorpo invited to North York to make a presentation. books with him. Sheis an active memberof rating many of the new ideas of the time. John He brought with him Art Beaument, Steve NCSM. In NCI'M she is a member of the Coleman, Howard Mulligan, ErnieTotten and Robinson and a vice-president of the university. Arithmetic Teacher editorial panel. She is a I undertook to write the grade 9 materials and They came with the idea of convincingNorth past president ofOAME and collfinues to act the grade 10 was to be investigated by John York to accept one student to pilot the program. as a council/01: Loma /wsjust completed co Egsgard. Those were very busy years as we Kendidn'tknowthatwehadalreadydecidedto autlwring a series of teA1s K-8 for D. C. were being asked to speak across the province take 5 students. Heath in Boston. John is one of the giants of to teacher groups almost every week. Lorna: After all these years in education Mathematics Education. He has p1vfoundly Lorna: I've used many of the materials you have you any secrets to share? What makes a affectedthe development of the mathematics developed. What were some of the firstideas good teacher? cwriculum in Canadaand the USA. For a you pursued? John: Let me beginby giving you an exam retiree, he is busyindeed, working at OISE, John: We investigated the geoboard and its ple of a poor teacher. During my firstyear of writing texts, active in NCI'M,and more.) applications to mathematics. We soon found teaching, the math head scoffed at me for that by lookin'g at slides, flips and turns of buying a book on mathematical recreations figures we could mathematize many of the called "Mathematics: Its Magic and Mastery", activities on geoboards. It was during this by Aaron Bakst. He said it was a waste of of OMCA meet regularly to discuss current AIMS OF TH IE OMCA AHISTORYOFTHE trends, the direction that mathematics educa ► To promote quality mathematics educa ONTARIO tion should take, and to exchange ideas and tion in the provinceof Ontario. materials to achieve specified goals. Each year ► To encourage and stimulate professional - MATHEMATICS theOM CA holds a two day retreat,organizes a growth and development on the part of its special seminar to which an outside speaker is members and the members of the COORDINATORS usually invited, and sponsors a Basic Level mathematics community in the province Conference forteachers. of Ontario. ASSOCIATION Presentlythere are 40 members in OMCA. Included are representatives fromthe Ministry ► To encourage communication with regard JOHN DEL GRANDE & PAUL ZOUS of Education and others with special assign to all aspects of mathematics education The roots of the Ontario Mathematics Coor ments in mathematics. amongst its members. dinators Association (OMCA) were planted Many of the coordinators/consultants are about 40 years ago when Mathematics was also members of OAME/ AOEM,NCSM (Na MEMBERSHIP IN OMCA being scrutinized by educators and politicians. tional Council of Supervisors of Mathematics) ► Membership shall be open to all individu In October 1957 the Russians startled the world and other mathematical organizations. Alex als, on the basis of one representative per by launching the firstsatellite, Sputnik,beating Norrie' Coordinator of Mathematics for the board who: are working in an educational the USA by several months in achieving this Peel Board of Education, is also a director of jurisdiction in the province of Ontario, scientificbreakthrough. The politicians and the NCSM and was program chair forthe Hamil and have system responsibility for the public believed that mathematics and science ton Conference for the Joint NCTM/OAME/ curriculum review, development and/or education had to be improvedto overcome the AOEM Conference in May 1990. John Del implementation of mathematics program Russian lead. Leadership in the proposed chang Grande, former Coordinator of Mathematics within a School Board (as definedby the es was given by theUniversity of Illinois, the forthe North York Board ofEducation is still an Education Act, 1974). School Mathematics Study Group and the active member of OMCA and was the first ► With approval of the membership, the College EntranceExamination Board. In On winner of the prestigious Gilbert Medal from executive steering committee may second tario the OTF and the Ministry of Education NCSM. additional members forspecial purposes fund�a large group of teachers to study the Bob Robinson, a formerconsultant with the on an annual basis. implications of the proposed changes for the Hamilton Board of Education and presently ► Thecurrent President of the OAME / Ontario curriculum. with the Ministry Education, has also been AOEM and representative(s) fromthe In the period of dynamic change, experi active with NCTM/OAME/ AOEM forover a mental courses and course materials forgrades Ministry of Education shall be invited to decade. Bob was also Chairman of the Program be members each year. 7 to 13 were developed for Ontario schools. forthe NCTM Utah Conference, and is always Many of the teachers involved in the writing active in organizing many of the OAME / went on to become coordinatorsof mathemat AOEM conferences. FROM TH IE ARCHIVES ics and curriculum leaders in some of the larger Brendan Kelly, former Coordinator from school boards. The first coordinatorswere Wyn the Halton Board of Education, and presently ONTARIO ASSOCIATION Bates (Toronto), John Del Grande (North York), an instructor at FEUT, (Faculty of Education, Joe Perrell (Hamilton), Norm Sharp (Etobi University of Toronto) has been very active OF TEACHERS OF coke ), and Jack McKnight (Scarborough). with NCTM and OAME / AOEM and is pres MATHEMATICS AND These coordinators met informally at first to ently on the computer committee forNCTM. PHYSICS/ ONTARIO talk-shop over lunch. After a few lunches, it Many of our other members have been EDUCATION became apparent that fullday meetings would actively involved with OAME and NCTM, and ASSOCIATION be very useful. The meetings were informal have made numerous presentations and con WILFRED CUNNINGTON andwere called whenever one of the members tacts with mathematics educators across North suggested that a meeting was warranted.John The Easter Convention will again be held in America and other countries. the Ontario College of Education buildings at Del Grande acted as secretary (pro tern) for OMCA is certainly a very active organiza about 6 years. Any person with a K-13 respon the comer of Bloor Street and Spadina Avenue. tion inthe teaching and learningof mathemat Lectures will be in room 374; book displays sibility for mathematicswas invited to join the ics, and is presently publishing (with OAME/ group. and seminars will be in nearby rooms. AOEM) the "Ontario Mathematics Standards" VOLUME 1, NUMBER 1, As the group became larger it was formally for Mathematics Education from JK to OAC. FEBRUARY196.2 named the Ontario Mathematics Coordinators This document will be distributed to all math Association (OMCA). A constitution was writ ematics educators in Ontario. The 1990/91 ten and the group expanded to include consult President is Ron Sauer of Waterloo County. ants frommany smaller boards. Themembers room teachers.It has remainedtrue to this ideal TheGVMA has continued to hold to the AHISTORYOFTHE throughoutits existence. From its inceptionto same principlesas when it was founded.It has thepresent, every presidentor chair has been a shown leadership in addressing the issues of GRANDVAL LEY classroom teacher. mathematics education through seminars and MATHEMATICS By the Fall of 1972 a two-day seminar conferences. Thebibliography of publications program had been established, semi-annual forclassroom supportbrings greatsatisfaction ASSOCIATION general meetings were occurringand fourwrit to the writers in knowing that students have ing projects had been established. It is of inter been the beneficiaries. The success of this RONSCO/NS est to note that by the Spring of 1973, the organization is a tributeto the many teachers Three ingredients came together in theearly following publications had been produced: a who so willingly have given of their time and 1970's that led to the establishment of one of GeometryHandbook, a Grade Nine Prepared talents for thecause of excellence in mathemat the most vital andinfluential chaptersofOAME. ness Test, a MathematicsContest forGrades 7 ics education. The need fora forum to addresscurriculum and and 8 and a grade 13 sample examination One of the greatsatisfactions of my profes pedagogical issues, a group of dedicated and package. sional careeris to have had the opportunity to willing mathematics educatorsalong with the The contest for grades 7 and 8 had an helpnurturean�guidethisassociationthrough leadership and generosity of the Faculty of enrolment of 756 WentworthCounty students out itsexistence. Mathematics at University of Waterloo com in its firstyear. bined to spawn the Grand Valley Mathematics THE KENNETH D. FRYER Association. Editor:bzfact, this contest was, in itsfirst few AWARD TheNASSMT (Nameless Association of years, the brainchild and product of Jim Inmemoryof the lateDr. K.D. Fryer,OAME Secondary School Mathematics Teachers)start Mattice, and his mathematicsDepa1tme11t at / AOEM in conjunction with theGVMAestab ed meeting as an unstructured body of mathe ParksideHigh Sc/wol in Dundas. lished the KennethD. FryerAw ard for Excel matics teachers in 1970. Meetings were held at ItwassubsequentlynamedtheGaussMath lence,to be presentedannuallyto a Mathematics the University of Waterloo to discuss issues ematics Contest and is now part of the Canadi Departmentdemonstrating excellence in Math impacting the mathematics classroom. A pop an Mathematics Competition. In1990, 75,000 ematics Education as well as contributing to ular beverage of the time, "TheTea - known studentsfrom across Canada participated. the overall development of students beyond byitsgoodtastealone",inspiredthename.This Over the next two years theGVMA gained classroom activities. was to be a Mathematics Association to be support forits activities froma steadily grow SCHOOLS HAVING RECEIVED THIS AWARD come knownby its good works and thus other ing membership. It remained as an indepen 1985 O'Neill Collegiateand wise would remain nameless. dent association running seminars, general ► A significant step in the passage from a Vocational Institute,Oshawa meetings and fosteringwriting teams thatpro (Durham) loose organization to a formalassociation was duced support materialsfor mathematics teach LaSalleSecondary School, ameetingheldonMarch4, 1971,atwhich 150 ers. Sudbury teachersmet in groupsto discuss the Ministry In 1973, the Ontario Association forMath 1986 Overlea SecondarySchool / of Education's proposal forGrade 13 mathe ematics Education was formed with a new ► MarcGarneau Collegiate matics. It became clear that inorder to become organizational structurethat included chapters Institute(East York) a positive influence in mathematics education, to better serve all regions of the province.The 1987 Merivale HighSchool, Nepean a new mathematics association should be GVMA was not consulted nor included in the ► (Carleton) formed. planning of this new organization. Under the On January 4, 1972 representatives from 1988 LomePark Secondary School, founding by-laws of OAME, chapters were ► :Mississauga (Peel) counties surrounding the University of Water definedin a top-down model and as such the loo decided to form the Grand Valley Mathe GVMA Council decided that it would have 1989 Northern Collegiate Institute matics Association. The GVMA was founded ► and VocationSchool, Sarnia been unfair to its membersto become a chapter (Lambton) on the principle of improving the mathematics at that time. The executive of OAME was programs of the schools in this geographical disappointed by this decision. The president of ► 1990 AlbertCamp bell C.I. area, and of providinga forumfor the exchange OAME initiated discussions with GVMA, and (Scarborough) of teaching ideas and professional growth. as a result ofnegotiated changes in the by-laws, From the outset, the GVMA was to be an the membership of GVMA voted in favour of association of classroom teachers for class- becoming a chapter. The application forchap ter status was accepted at the annual meeting in May, 1974. RECRUITED tists".I showed interestand later he sent me an MAGICPENCILS In the Spring of 1932 Professor Lougheed autographed copy which I used as a reference JEAN LEPPARD of the OntarioCollege of Education addressed foryears. September, 1928. My trunkwas packed! I the final meeting of the M & PSociety with the Times were rough in the Spring of 1933. had been vaccinated forsmallpox! At age six aim of recruiting student teachers of mathe There were 7 43 student teachers at the Ontario teen I, who had never been more than twenty matics. I liked his enthusiasm and decided to College of Education and to say that they were fivemiles away fromthe red brick farmhouse become a disciple. In September, 1932, I en well qualified would be an understatement where I was born,was setting out forToronto to roled in the College and in the Spring of 1933 indeed. Inthe science section there were law register at Victoria College and to enrol in the I became a member of the Ontario Association yers, dentists, doctors, Ph.D.'s of all kinds, Mathematics and Physics course. The money of Teachers of Mathematics and Physics. It is engineers and business men looking fora job, in my purse - four hundred dollars - would good to knowthat, aftera succession of name any job. Of the 743 I believe only 57 had coverall expenses of my first year. To date I had changes over the intervening years, this organi positions by September. spent ten years in school -firstat the"little red zation - now the Ontario Association for schoolhouse" in DeCewsville where all grades Mathematics Education is, on the eve of its AJOB were gathered into one classroom, andthen at hundredth anniversary, still vigorous and pro I applied fora position in Fergus. On the day Cayuga High School. ductive. of my interview it rained heavily and, like the other candidates, I had to walk about town in VICTORIA COLLEGE PRACTICE TEACHING the rain to keep appointments with the Princi After registering I went for an interview My first practice teaching was done at Bloor pal and the 13 members of the School Board. I withthe Dean of Women, who literally begged Street Collegiate Institute under the eye of had little hope of being chosen: first, I was a me to stay clear of the honours course in Major Lamb, a friendlyman andobviously a woman; and second, I knew that many of the Mathematics andPhysics and advised me to great favourite with his students. (Wilbur applicants had qualificationssuperior to mine. talk to one of the professors beforemaking up Howard was one of them: he later gained fame Some time after I was established in Fergus I my mind. I left her officewith threethoughts: as a Moderator of theUnited Church of Cana asked my Principal what had tilted the scales in I was going to study mathematics and physics; da.). Major Lamb said, "If you don't enjoy my favour.He told me that after 200interviews I was going to work hard; and I was not going teaching, don 'tteach! "Icertainlyenjoyed teach he still could not pick a teacher: there were just to fail! ingfor him. too many good ones. At this point his ever The course was certainly demanding. I can For practice teachingin physics I was placed helpful wife had said, "Surely there was one recall having two three-hour laboratory ses with Dr. Charles G. Fraser, Jr., at Harbord who was different... " ,"Well," he had replied, sions every week and lectures from professors StreetCollegiate Institute. Dr. Fraser had earned "there was a young girl who didn't complain Beatty, Pounder, DeLury (A.T.), Robinson a reputation of beingimpossible to please and about the rain." His wifehad said, "Take her." (D.A.F.), Sheppard, Satterly and Kenrick. In when he asked me to prepare two lessons on So the farmer's daughter who didn't know later years professors Chapelon, Mackenzie, Centreof Gravity for a Grade 13 class I decided enough to come in out of therain got the job. Webber, Synge, McLennan, Burton, Gilchrist, to put forthevery effortto impress him favour What a turningpoint in my life! What a twist! Mc Taggart, Chant, Young, Barnes,Ireton, Ain ably. So, I was lucky. I had a job at Fergus High slie and Allinare some I remember. I returnedto my old haunts in the University School. For $1700 a year I agreed to teach There werelightermoments too: the Recep of Toronto. Physics Building, seeking advice mathematics to Grades 9, 11 and 12 and also tion tendered byProfessor and Mrs. McLennan from Dr. Satterly. He was most helpful: he had algebra, geometry, trigonometry and physics to in the library of the Physics Building; the Percy, his famouslab assistant, assemble some Grade 13, as well as Senior Girls' Physical monthly meetings of the M & P Society in demonstration items which I might borrow. Training. If any student should aspire to a Room 43 and social evenings in the homes of Among these was what Dr. Satterly called "a scholarship in mathematics I was to be the Dr. Burtonor Dr. Chant. disobedient egg". One prepared it by making a coach forthe Problems examination. In my first year one of my assigned lab tiny hole at each end of a hen'segg, blowing out A year later my colleagues and I were asked exercises was the making of a thermometer. I the contents, inserting some lead shot in the to accept a ten percent salary cut which lasted was desperately failing to produce a present small end and securing it in place with melted until 1939. But, if salaries were low, so were able bulb at the end of the tube when a passing wax. With suitable restoration of the damaged expenses. For example, my room and board third year student noticed my plightand offered shell the egg would look natural but would cost me $9 a week, $7 if I was away for the assistance. In no time he had blown a beautiful stand only on the small end. I used this prop in weekend. bulb I continued with the project and he kept my first lesson and Dr. Fraser was fascinated. I loved Fergus. The pupils were away above coming back to check progress. He became my One of his students was given the job of creat average and so I was always under-estimating friend, my tutor andeventually, my husband.A ing a duplicate. At the time, Dr. Fraser was them. One year I submitted to the Department turningpoint! A new direction! writinga book eventually to be published un a trigonometrymark of 25 as my estimate of a der the title "Half Hours withthe Great Scien- certain student. On the morningof the exami- nation she came down with chicken-pox and before I met them, but they did behave. I had year I had a particularly good Upper School couldn't write the paper. However the Depart come to Vaughan with the idea of staying till class; good, that is, with the exception of poor mental marks, when they came in, showed her Easter. It turnedout that I stayed 17 years - struggling Louie. I bought five dozen lead with a pass in that subject. The rationale was and enjoyed them. pencils at a varietystore and had them sharp that her class had, on average, made 26 more GEORGE TUCK ened by the proprietor. Next day I brought them marks per paper than I had allowed them in my George Tuck was head of mathematics at to school in a brown paper bag and as my estimates, so, with 25 + 26 = 51 marks she had Vaughan. He was a seasoned pro and his de students were gathering for the Algebra paper her pass. What I had was a fmn reprimand from partment was second to none in the province. I I stopped each one, took a pencil fromthe bag, the Department fornot being a realist. longed to teach grade 13 but as a newcomer rubbed it between my hands, kissed it and said, In the Spring of 1940 my fiance was on a among such a talented groupof teachers I had "This is a magic pencil; I have put a spell on it. training course at the University of Toronto to keep quiet. Imagine my delight when in June Just take it into the room with you. It will guide preparatory to induction in the R.C.N.'s Spe 1956 he told me that, startingin September, I you." Then I solemnly passed the pencil to the cial Branch (hush-hush work later revealed to could have two Upper School classes -Alge student as one hands over the baton in a relay involve radar service with the Royal Navy). bra and Trigonometry. Later, when sets were race.Afterthe examination I met Louie coming Unexpectedly I was also confronted with an being introduced in the lower grades, I attended down the hall: he was clutching the pencil in opportunity to serve when Professor Burton ameetingoftheNCTMinChicagoandbrought both hands. With a shaking voice he said, "My recommended me fora staffjob with the Brit back a few work-books on sets. He accepted God, Mrs. Leppard, it is magic." Louis made ish Scientific Mission in Washington under them and filed them in our mathematics library 53, far more than I expected of him. Therest of Professor Lindemann ("the Prof'). Since our under L with the title "Leppard's Folly". I the class did extremely well, as I knew they departures were imminent we decided to get respected George Tuck and learneda lot from would. married without delay. There was no chance him. Next year the students lodged early enqui that I might continue teaching; married women I encountered many bright young minds at ries as to whether I was intending to provide were not eligible forclassroom work. So my Vaughan. Theone that achieved the most bril magic pencils forthe Departmentals.Horror of husband departed overseas but my plans liant success in the world of science was Leslie horrors, they really trusted my magic! One changed when it became clear that our first Saunders whose work at Princeton had brought student bought a 14k gold clip and carried the child was on the way. There ensued a decade him world-wide recognition. He died of pencil in his breast pocket for yeats. Next and a half during which I had little or no contact Hodgkin's Disease at age 29, shortly afterhis Spring there was no refusing: I repeated the with the classroom. returning to take up a professorship at the ritual and again it worked! Fortunately the UniversityofToronto. What a privilege to have Departmental were abolished the following VAUGHAN ROAD been a factor in the early training of such year and I was offthe hook. I am still wondering COLLEGIATE INSTITUTE people! And it was fun- teaching them was a whether I really am a witch! In theSpring of 1956 our dinner was inter breeze! Editor: Jean significantlyaffected the pro rupted one evening by a phone call fromMr. THE NUMBER CRUNCHING GAME - fessionallivesofbotlzofusandweadmireher George Evans, Principal of Vaughan Road WITH SPICE and thank her for this. (She spotted Joan Collegiate Institute. One of the mathematics In those pre-computer days we had to look Routledge at the 1965 Conference and per teachers had suffereda massive stroke and each for useful short-cuts in practical calculations sonally·welcomed her to the g,vup-and we of the five substitutes he had called in to help done the hard way. I suggested, forexample, hzow the impact Joan has had 011 the scene.) had resignedafter a fewdays. Would I come? that it would be nice to memorize the logarithm Her upbeat view of the world shines through I had been away from the classroom for 16 forpi to five places. Now it was easy to call up these pages. years, it seemed that piere was a student disci the first three places (0.497) because 49 is the pline problem, and the classes in question were square of lucky 7. How to remember the 15 either Grade 9 or 10 whereas I much preferred which followed? Someone said, "That's the Upper School Work. Thinking to stall things age of Fred's girl friend". So log pi became completely I said that I wouldn't consider 0.497 "plus" the age of Fred's girl. Everyone in coming forless than $500 a month nor without my classes had log pi on the tip of his tongue a guarantee that the students would co-operate and Fred's girl (whom he eventually married) and settle in to learn.I walked away fromthe was dubbed "0.49715". This and many other telephone telling my family, "Don't worry dodges we worked out added spice to the they'll never pay me $500 a month!" Five number-crunching game. minutes later Mr. Evans was back on the line The Departmental Examinations were al saying he was ready to meet my terms and ways approached with a certain apprehension would like me to begin work the next Monday. by the students, and !always did my best to ease I don't know what he said to those classes the tension. Eventually I tried sorcery. That MEMBERS OIF THE FIRST EXECUTIVE, 1973 ► Mr.J. Ryan, Chairman ► Mr.F. Maskell, Secretary ► Dr. M. Closs ► Mr. J. Quesnel ► Mr. E. Sparling ► Mr. B. Topping The next several years found increasing co operation between COMA and the local uni versities. Numerous seminars and meetings were hosted by the post-secondary institutions. By 1978-79 COMA could boast of 120 mem bers. In May, 1970, theOAME asked for Ottawa FROM THE C:.ALILERV: ll>UFF BUTTERILIL, BRUCE TOPPING-OTTAWA, '11970 to be the location of its province-wide confer ence (Editor: This was the firstannual confer Joe Ryan as chairman and Fred Maskell as ence outside Toronto and COMA played the AHISTORVOFTHE secretary shepherded COMA through itsincu host with flying colours.) For all his work bation and the Association grew. By April, among mathematics teachers, the Conference CARLETON·Ol14'WA 1974, membership convenor, Bruce Topping, was dedicated to Don Fox. Bruce Topping and MATHEMATICS could report 68 active members. For the next DuffButterill were co-chairs. Dozens of other several years, liaison with the parent body, Ottawa teachers participated. ASSOCIATION OAMEproceeded. Members joining OAME/ In March, 1975, the first edition of a math AOEMareconsideredtobemembersofCOMA ematical magazine EUREKA was published. DUFF BUTTER/LL and a portion of their membership fees is rebat The name was subsequently changed to CRUX Duringthe 1960's, in the relatively compact ed. to COMA. MATIIEMATICORUM.This magazine grad geographical area of the Ottawa-Carleton re ually took a life of its own, separate from gion, the teachers of mathematics were the MEMBERS OIFTHE COMA, and became known, quite literally, employeesofnumerous boards of education - FOUNDING COUNCIL, world wide. The editor for11 years, until 1986, TheOttawa Public, The Carleton Public, and 1973 was Leo Sauve of Algonquin College; the several separate school boards. There were ► Mr. J. Ryan, Carleton R.C.S.S. Board managing editor, Fred Maskell literally dedi also two universities with active mathematics cated his life to the magazine until his death in ► Mr. P. Brady, OttawaR.C.S.S. Board departmentsandAlgonquin College. TheEast January, 1985. ernOntario regional office of the Ministry of ► Miss B. Wright, Ottawa Board OAME / AOEM again had its province Education was located in Ottawa. Therewas a ► Dr. F.Morrison, Ottawa Board wide conference in 1989 here in Ottawa. The clear need for an organization which would ► Mr. B. Topping, Carleton Board chairman and workers experienced a greatdeal bring together representatives of the mathe of satisfactionfor a "job well done!" maticsteachers fromeach of these administra ► Miss J. Starrs,Ottawa Board tiveentities. The Carleton-Ottawa Mathematics ► Mr.W. McLeod, OttawaBoard Association (COMA) was founded on Tues ► Dr. R. Semple, Carleton University IFROMTHEARC:HIVIES day, June 5th,1973, at 3:30 PM in the Ministry If a triangleis subdivided into any number ► Mr. M. Carmelon, Carleton Board of Education Officeson Woodward Avenue. of smaller triangleswith the sole restrictionthat From among the Founding Council, an ex ► Dr. V. Diab, Carleton University no side of a subdivision may contain a vertex ecutive was chosen, a constitution was devel ► Dr. M. Closs, University of Ottawa (except at itsend points), then the number of oped, and a program begun. An early decision ► Miss R. Seguin,Teachers' College such triangular subdivisions must be odd. by the executive was that every meeting (wheth ► Mr. I. Pressman, Carleton University Duff:I wonderif Mac Camelon remembers er executive, council or general) should begin the neat p1vof he gave for this problem? with some mathematical item. ► Mr.L. Sauve, Algonquin College ► Mr.D. Fox, Ministryof Education ITEM FROM A COMA EXECUTIVE MEETING, ► Mr. D. Butterill, Ottawa Board APRIL 1974 tario with chapters throughout the province was born that day and NOMA, especially through Art Dayman, had a stronginfluence on the present constitution of OAME. As it does now, NOMA dealt with contem poraryissues in mathematics education. Some topics, such as the metricsystem and teaching efficientuse of the slide rule seem rather archa ic now. Programmes in the early 1970's fea tured debates which would still be apropos today. Among the resolutions were: "The se mester system is an abomination,""The calcu lator is the most promising invention for the improvement of mathematics education since thechalk-board," "Mathematics education in Ontario is better now than it has ever been." FROM THE GALLERY: SHARON MCPHAIL ANP BOB ROBINSON There is no record of the outcome of these debates; it is certain that they continue in some form in staff-rooms across the province even SWOAMEHISTORY NOMA,THE EARLY today. One ofNOMA's strengths as an organiza THEEDJTOR YEARS tion has been its abilityto attractparticipation SWOAME,designed to serve all of South from elementary as well as secondary panel westernOntario, wasformed in 1974 very soon DOUG HENDERSON teachers. Much of the credit goes to speakers afterthe foundingconvention of OAME. The Aftera May, 1969 conference of mathemat like Joan Routledge, Bob Tuck, Don Fraser, charterpresident was Dave Skoyles and he was ics teachers, organized and publicized by the Norm Sharp and Frank Ebos who graciously followed by Arn Harris and later by Gary OTF Toronto office but held at Laurentian agreed to take part in NOMA meetings. At Peters. University, attracted only a dozen delegates; Laurentian University in 1973, W.W. Sawyer In 1977 a constitution wasformally adopted Doug Henderson and John Milliken agreed gave a demonstrationlesson to a class of grade and the chapter continued tis sponsorship of that such a meeting could only be successfulif fivepupils, showing how he would introduce regional conferences. The Chapter Council, it were sponsored and promotedby Northern conceptsin algebra to young children. which represented the 25 educationaljurisdic ers themselves. Beginningwithout anyformal support from tions in the region spent a significantamount of To overcome the problem of communicat a parent organization, NOMA managed to re its time on educational issues. For example, ing with teachers spread over an area of hun main financiallysolvent by charging $2.00 for they spent at least two meetings discussing the dreds ofthousands of square miles (it was 1970 membership and $3.00 as a conference fee. Pogue Report (Recommendationsfor Interme and the metric system was used only in the Buffetlunches cost $2.75 and a double roomat diate Division Mathematics in Ontario, Uni science lab!), they took advantage of John's the Pinewood Inn in North Bay was $14.18, all versity of Ottawa, 1976). This included a position as Ministry of Education Programme with taxes and tip included! meeting with Paul Pogue and the writingof a Consultantfor Sudb ury, Sault Ste. Marie, Wawa Like the rest of the province, Northern briefto OAMEand the Ministry. and points in between and Doug's role as Ontariohas always had an abundance of able By 1980 the Chapter was essentially de MasterTeacherofMathematics in the Sudbury and dedicated teachers, eager to assist their functand so the SarniaMeeting was organized area. Enlisting the help ofArt Dayman (Minis students' growth by improvingtheir own knowl by Morley MacGregor and Sharon and Dave try Programme Consultant) they spread the edge of mathematics and mathematics learning McPhail. word from North Bay to Timmins, Kirkland through organizations like NOMA. Teachers In 1987 Todd and his colleagues resurrected Lake and furtheralong Highway 11. and students today owe an immense debt of SWOAMEto serve Essex and Kent Counties. An organizational meeting in May 1970, gratitude to people such as John Milliken, Art It is once again thriving and hosts semi-annual attended by 100 teachers representing all levels Dayman and Doug Henderson who began meetings (a dinner meeting in May and a of education from kindergarten to university NOMA and assisted it through its early years; Friday-Saturday meeting in November.) wasfollowed bythefirstofficialNOMAmeet to Bob Tuck, Andy Czempinski, Robin Hill, ing at Laurentian Universityin October 1970. Jeanette Bedard, Peter Weygang, Jim Hill and Editor: This was written based upon 1wtes Two hundred and twenty-five enthusiastic that ToddRomiens gathered for me. I apolo John Savage who served as executive members teachers fromas far away as Wawa, Hearst and and organizers in the early years and to the gize for any omissions caused bya lack of IroquoisFalls were present. Theconcept of an intimate hwwledge of the Chapte1: many teachers who give the organization life organization formathematics teachers in On- by their participation and enthusiasm. 38 � OAME ¼ AOEM AHISTORYOFTHE PINE RIDGE MATHEMATICS ASSOCIATION RON ENNIS This story startedin Oshawa sometime dur ing the years 1974-1976 when Bill Jeffersheld officeas the Mathematics Consultant for the DurhamBoard. During his visits to schools and FROM THE C:.ALII.ERV: NEIL WILLIAMSON, l>AVIII> MCPHAIL, ANI>FRIENDS AT THE discussion with teachers throughout the Board, OAME ANNUAL CONFERENCE - PETERBOROUGH, 1970 Bill sensed a need to improve the interaction The PRMA has come into its own since that the Ontario Education Association it has given between elementary and secondary teachers of time and is instrumentalin organizing several mathematics teachers some participation in the mathematics. During this time several meet activities for teachers and sa.:Jents each year. wider Ontario educational scene. It has been in ings were held where elementary and second The Spring Mini-Conference was established a position, through its representation on the ary teachers discussed problems related to in the early eighties and attracts 100 to 150 OEA senate, to influence recommendations to curriculum, teaching methods and manipula elementary and secondary teachers to a dinner the Minister in the interest of mathematics tive materials. The groundwork had been laid and two presentations in April of each year. The education. for the establishment of an OAME chapter in PRMA also assists in the arrangements forthe OATM leadership over the years has grap the Durham area. Durham Board-Wide PA day held in Novem pled with two problems: (1) the building of a In 1977, a request was made to host the ber. larger base of support and involvement through OAME/ AOEM Conference in 1979. Armed In 1984 a Mathematics Awards Ceremony increasing membership (2) development of with thesupportofseveral dedicated colleagues, was instituted and is held every year in June. At service to the support from the_ elementary Bill agreed on our behalf to host the 1979 thisfunction, students who have been success school teacher withspecial interest in mathe conference. fulin the elementary and secondary mathemat matics. In the 1960's progress was made in Since provincial conferences are usually ics contests are honoured by the Durham Board. both of these areas, but much more is desired. hosted by a local chapter, it was now incumbent PRMA members assist with the organization Now, without detailing its history, let us try on the organizers to establish a chapter. The of this function each year. to summarize the role of the Ontario Mathe decision was made to include institutions in the Even though in recent years our geograph matics Commission (OMC). In the late 1950's, JuniorMathematics Contest, Zone 68 Region: ical region has shrunk, our membership has great concernwas feltfor the school mathemat Trent University, Durham College and schools expanded, and the current executive is looking ics curriculumin Ontario. This concernfound in Simcoe County, Victoria County, Northum at ways to improve this next year. Another expression among mathematics teachers at a berland, Newcastle and the Durham Board conference perhaps? conference at Lakefield, Ontario, and the re were included. In the school year 1977-78, the sulting organization (OMC) was supported by PRMA (named after the pine-covered ridge of the Ontario Teachers Federation and the On hills which runs through these areas) was born. FROM TIH E ARCHIVES tario Department (now Ministry) of Education. Bill was installed as the first president and went This support was both financial and in the form on to organize a very successful conference at AN ORGANIZATION FOR of personnel appointed to the Commission. Trent University in May 1979. Conference MATHEMATICS The Commission was composed of approxi delegates were treated to top-notch meals, en A REPORT FROM THE OATM-OMC mately fifty persons appointed fromthe com tertainment, accommodationand speakers. The COORDINATINGCOMMITTEE plete spectrum of mathematics education in conference focus was on elementary mathe The cause of mathematics education in Ontario - elementary, secondary, private matics and many elementary teachers were Ontariohas been served in various ways past schools, college, university, teacher, OATM, attracted by some special incentives. The con and present by a number of groups and organi and Department of Education. In my opinion, ference was planned for450 but 700 attended. zations. this wide representative nature of OMC was its Needless to say the conference produced a In its long history to date the Ontario Asso greatest strength. The Commission plunged profit for OAME / AOEM and the PRMA, ciation of Teachers of Mathematics (OATM) into its task of reviewing, designing, testing, which used the proceeds to provide scholar has provided a two-foldservice forteachers. It writing, proposing changes in mathematics ships forelementary teachers taking upgrading has been a meeting-ground for its members for curriculum. courses in Mathematics (M. Ricciuto, S. Allan, VOLUME 11, NUMBER 3, professional updating, forstimulation, refresh MARCH1973 C. Hunt, J. Lubitz, G. Gadanidis, S. Bernard ment and information through provincial and and others). regional conferences. And in its affiliationwith 1973-1990 From the beginning, editorshave taken pen AHISTORYOFTHE TheOntario Mathematics Gazette has been in hand to voice their concerns.Each has been ONTARIO the officialpublication of theOAME since its challenged to comment on the issues of the day. beginning in 1973. Most often this had to do with a curriculum MATHEMATICS The mathematics community has main issue. tained a strong voiceof concernin education GAZETrE over the last 100years. What have been these EDITORS' REMARKS concerns? BOB SMITH OVER THE YEARS From its very beginning,The Association 1904 was concerned with ways in which it might "resolves that the mathematics and phys FOREWORD extend its influence. In 1895, PresidentAT. To writea history(a systematic, continuous ics section of OEA heartily approvesof DeLury suggested: the work on geometry outlined for the record of events) of the Ontario Mathematics " ...a Committee of theAssociationmight Gazette and its predecessors, requires deeper lower school in the draftprepared by the report on all, or the more important Education Department." insight, and a bettersense of the times than I textbooks appearing during the year" have beforeme. Thus,the followingpages will and that "the teachers in any district 1964 R.G. Stanton pointed out where he thought briefly outline the views of the editors as the might organize themselves to prosecute the Math curriculum process could be im Journal changed through the years. The real some special studies ... (which) the As proved: record of Ontario Mathematics Gazette is in sociation could bring togetherand ( then) ► Approving of textbooks: At the present the many articles printed and the few bits make accessible the results of the re time, there is a distressing "sameness" reprinted here can only wet the appetite. search." about school textbooks ... Let the With the firstpublication of Ontario Math Curriculum Branch give up "approval" 1892-1962 ematics Gazette in 1962, it was decided to ... Let us have an independent board. Although there was not a particular Journal continue the communication function of the knownas Ontario Mathematics Gazette, a sec newsletter formerly published by OATMP. ► Curriculum Committees like Canadian tion of (OEA) met to share their thoughts (Editor: The first reference to the OATMP cabinets seem to "represent" varied concerning mathematics and some of their Newsletter wecanfindisinl953.)Itwashoped interests. Surely the best qualifiedpeople meetings were reported in the OEA "Journal" there would be continuing liaison between to discuss content should be adequately and later in the OATMPnewsletter. The name secondaryschool teachers and universitypro represented on such committees. (OATMP)was formallyadopted in 1951. Prior fessors. Insubsequent publications of the Ga Editor:In 1964, the Gazettewon the presti to this, the group was knownas the Mathemat zette, liaison with teachers of mathematics gious Greer award from the OEA. ical and Physical Association of Ontario. Pa both in the elementaryschools and the commu pers on mathematics and minutes of their nity colleges was included. To accomplish this, meetings are available in the OEA centennial 1976 special elementary school editionsof Ontario A.Harris reviewed the Canadian Chambers publication InThe Cause of Education. Ma thematics Gazette were printedin 1966 and of Commerce Report on Basic Education 1967. In 1973, a newsletter called ABACUS Skills. He then went on to comment: 1962-1973 was instituted. In1986, the ABACUS became "Since 1946, a percentage of the 15-19 The first issue of Ontario Mathematics an insert in the Ontario Mathematics Gazette. year age groupin the schools has risen Gazette was published in 1962 under the joint Until this year the Ontario Mathematics dramatically (35% to 80% in Ontario). sponsorship of the OATMP, a section of the Gazette had been available to non-members on Society has decreed that elimination is OEA, and the OMC, with Editor Ralph Stanton a subscription basis. From 1986 on, it was no longer a satisfactorysolution to the of the University of Waterloo. During this available only to members. Editors over the problem of non-performingstudents ... period, it was also supported at various times years have been looking for articles on new The Ontario Education Curriculum by theSamuel Beatty Fund, and the mathemat teaching techniques, innovative pedagogical Development report on Canadian edu ics departmentsof various universities. Print material and have accepted mathemati�al ex cation states that we neglect our under ing and distribution were organized fromthe positions as well as materialon the historical privileged, handicapped and native OAE and the OMC officesin Toronto. For one and psychological aspects of mathematics. people. Are these not basics we should critical year, when it appeared that therewere Recently, more effort has been made to have be looking at?" insufficientfunds, Professor John Coleman of Ontario Mathematics Gazette act as a forum 1981 Queen's University agreed to personally un fordiscussion as well as publishing "teaching R. SmithcommentedonthedocumentMath- derwrite the shortfall. Luckily there was no tips" and "research clips" to help teachers in the 1980 Curriculum Guidelines for the Interme shortfall. classrooms. diate Division and made the following suggestions: ► It is to be hoped that at some future date Your editorscontinually try to improve the the Ministry'sproposed document The journalto meet the needs of its readers as well JntennediateYears will be completed. It as the needs of OAME/AOEM. Surveys in should provide a reasoned, logical variably receive a very limited response. How framework as well as practical help at the ever, the fewwho do respond make excellent various grade levels for the sample suggestions and appear to enjoy the articles that objectives. are offered.InApril, 1990, your present editors ► To help in implementation, begin a sent the latest editions of Ontario Mathematics cyclicalreview so that implementation is Gazette to several well-known mathematics monitored. educators. Thecovering letteroutlined Ontario Mathematics Gazette circumstances and re Grade 7 and 8 teachers are generalists. , ► quested a critique. Before me are letters from Either we need more specialist teachers D. Robitaille, T. Romberg, H. Tunis and J. in the intermediate division or we need KilpatrickAllow me to quote fromone of the more in-service courses to help the above: "I found it an interesting and high generalists. qualityJournal, one of which any mathematics 1983 organization might be justifiably proud. I like S. Pravica wrote an open letter to the Min the mix of articles ... the layout is clean and ister of Education voicing his concerns,regard attractive... I read the issue with interest and ing The Intermediate/Senior Mathematics plan to use at least one of the articles in a course Curriculum Committee. D. Alexander, the I am teaching this summer. The quality of the Chainnan for the Committee, replied in the articles I read is every bit as high as that ofM.T. next issue. It was a useful exchange of views. and A.T. (Editor: Mathematics Teacher and TheOntario results forthe Second Internation Arithmetic Teacher) ... Best wishes to you in al MathematicsStudy were published the same your largely unsung but very important work" year and the editor asked, "Do the proposed Any journalis only as good as the articles new Senior Guidelines seem to be addressing submitted by authors.Their topics are varied, themselvesto the learningshortcomings iden well presented and represent classroomexperi tifiedin thisstudy?" ences, results of studies, as well as ideas on Thefonnat has changed fromtime to time. curriculum. Readers have enjoyed book re Ontario Mathematics Gazette began as a 6" x views, solving math problems and their favou 9" booklet of 46 pages with a softcover title rite authors. May the work of Ontario page. The text was typed by secretaries of the Mathematics Gazette continue into the next editor. Expenses were absorbed but additional century. fundswere sought through voluntary contribu tions of one dollar. In 1970, a 7" x 10" fonnat (Editor: Bob has been Editor of the Gazette was adopted anda colourfulcover added. By for two tem1s and has written numerous 1975, printing was moved to Pole Printing in articles during the tenure of other editors.) Forest,where it is still done. Since 1988, galley proofs are being returned to the authors for proofreading, French articles are included, a FROM THIEARCH IVES split page text has been adopted, and typeset ting using WORDPERFECT 5.1 with laser ... "WHERE ARE WE printing has become standard. Ontario Mathe GOING? WHY ARE WE matics Gazette is presently 44 pages and the GOING THERE? AND ABACUS insert is 16 pages. It is printed three HAVE WE GOT TO THE times a year and is sent to all OAME/ AOEM RIGHT PLACE EVEN IF members. This centennial issue of the Gazette was set WE GET THERE ... ?" in Lithos and Times, composed in PageMaker, G.G.STEEL and output fromLaserMaster high resolution TITLE OF AN ARTICLE FROM VOLUME 5, laser printersby MARK illText Management, NUMBER 2, MARCH 1967 a Division of School Services of Canada. ondary school and the number of schools had readers. The formationof chapters seems to be THE OATMP AND increased exponentially. Theteachers recruit providing the forumfor local initiatives in in ed had come from a variety of sources. No service work and curriculum development to THEOAME: longer was physics an assumed second teach take place, if somewhat sporadically. Unfortu SOMETHINGLOST? ing option.The grade 13 courses had changed nately, the organization has not founda way of fromthree to two (Mathematics A and Mathe recreating the atmosphere of excitement and DAVID ALEXANDER matics B) with little content in common with influence that was part of the discussions of The 100thannivers ary of mathematicsas the formercourses and the departmentalexam curriculum in the smaller OATMP and the sociations in Ontario is a time to reflect upon inations were being phased out. The "Robarts OMC. the changes thathave occurred in those organi Plan" had fundamentally altered the focus of As we move toward the 21st century I zationsover the yearsand how these changes the secondary schools with much concernon believe that the Ontario mathematics educa have effected their influence on curriculum the part of mathematics teachers as to what tion community must finda way once again to change. were appropriate content and teaching strate involve all the players in the discussion of My first experience withwhat was then the gies forthe non-university bound student. curriculum change. Some of the matters for Ontario Association of Teachers of Mathemat The organization had responded to these concernare listed below. ics and Physics was the annual meeting of changes in a variety of ways. It was now the ► How are the interests of mathematics 1959. I believe the total attendance was less OntarioAssociation of Teachers of Mathemat education to be best served in the debate than 100, but included were many of the de ics. The annual meeting was held in a hotel to around teaching generic thinkingskills partment heads across the province, depart accommodate the 500 or more in attendance rather thansubject discipline skills? ment chairs fromthree or fourof thehalf dozen and Don Fox had introducedthe radical pro ► How should the mathematics curriculum Ontario Universities of the day, ProfessorPet posal of holding an annual meeting outside of be structured to best respond to the needs rie of the Ontario College of Education (the Toronto in Ottawa! Programs included topics of all learners? only secondary school teacher education insti aimed at attractingelementary teachers as well ► How should the mathematics curriculum tution), and the two Departmentof Education as second . While the organization was pro ary respond to the availabilityof graphic and inspectors of mathematics. This combination viding an excellent forumfor in-service devel symbolic manipulator calculators? of small numbers and attendance of persons opment it had lost its role as a medium for froma variety of institutions resulted in discus various constituents to discuss curriculum de While the current council and committees sions of provincial curriculum policy that do velopment. Now the Ontario Mathematics of OAME/ AOEM provide an excellent repre not occur in our much larger meetings of today. Commission (OMC) rather than the OATM sentation fromdifferent regions of the province Theteachers who belonged to theorganiza provided fordiscussion of curriculumby ele they do not provide the mix of representation fromelementary, second ary, and post-second tion were a very homogeneous group. Most mentaryteachers, secondaryteachers, and rep were graduatesof a Mathematics and Physics resentative of the CAATs, faculties of ary institutions that I believe is necessary for program of Queens, Western, Toronto, or educations, universitymathematics department, these difficultquestions to be adequately dis McMaster, and had been taught at OCE by and the Ministry of Education. cussed. TheMinistry of Education appears to Professor Petrie,or one of his predecessors - In the early seventies it became clear that be moving away fromthe model that preserved Lougheed or Workman. the two organizationscould no longer go their a voice for a subject specialist in ongoing The courses they taught were almost exclu separate ways. The increasing monopoly of curriculum policydevelopment. If the OAME sively those leading to theGrade 13 coursesof OISE inresearch and development had drasti / AOEM does not speak formathematics edu Analytic Geometry,Trigonometry and Statics, cally reduced the fundsavailable to the OMC. cation who will? and Senior Algebra. The"success" of a teacher and the OMC was increasingly looking toward Editor: Dave holds a unique position in (and a school) was to a large part measured by sponsoring in-service activities such as the Mathematics Education since he is involved how well the students did on the grade 13 Leadership Seminars rather than development with the Facultyof Education (U ofT), and departmentalexaminations. Theshared back activitieswhich were now being undertaken by the Ministry. In each of these places he grounds and shared concerns led to. veryfo theMinistry. The result was the formationof continues to amaze and impress people with cused discussions on curriculum policy. While the Ontario Association forMathematics Edu his grasp of the issues, his capacityto juggle differentpoints of view were expressed every cation, formedin the hope that it could main his heavy and important responsibilities, his one understood the positions being taken, some tain the strengths of both the founding approachabilityand his se11Seof humow: He thingthat I think is difficult to achieve in our organizations. It has succeeded in many ways. was the cha,terpresident of OAME. much more complicated educationalsystem of The annual meetings continue to provide in today. service opportunities among the best of their By the late sixties the direction of the sys type in North America. The Gazette and the tem and of the organization had fundamentally Abacus are excellent publications which seem changed. Thebaby boomers had entered sec- to be better satisfyingthe varied needs of their matics and Physics as councillor, it was with As an Assistant Superintendent of Curricu RECOLLECTIONSOF considerable anxiety that I set out fromBarrie lum I was given the job of organizing what AJOVFUl RETIREE formy initial meeting. It was to be held in that came to be known as the 'Biggs' Workshops' sombre shrine of the S.S. (secondary schools) throughout Ontario. This was the first large J. R. MACLEAN knownas OCE. Fortunately anotherneophyte scale in-service program jointly underwritten My experience as an educator spans partsof councillor from Barrie acted as mentor and by the Department,school boards, and colleges five decades, 1948 to 1983. Thiswas a period guide, which served to reduce my apprehen and universities. It was also unique in that each of dramatic change in every aspect of the sion considerably. His name was Jack LeSage. board was represented by elementary and sec school system but particularly in mathematics. The year was 1964. The firstmeeting was not ondary school teachers, a department head, a My 'reformation' began with a meeting in without trauma.The Council wanted to expand principal, and a superintendent. Inan attempt to Penetanguishene with Mr. Frank Kinlin outlin themembership of OATMPinto the elementa provide leadership at the local level afterthe ing changes in the courses of study knownas I ry schools and the program for the Easter workshop ended panels of 'tutors' were trained 12A and I 12B and ended with the struggleto Meeting in 1965 was to have elements that to help in the workshop and to carry on the produce the Ontario Assessment Instrument would entice teachers of younger children to work. One of the 'stars' to emerge and give Pool formathematics. The request of the edi attend. Jack and I were appointed as co-chair yeoman service to mathematics education in tors of this special edition of theGazette to men of the seminar committee. Afteran enor the province was the late Morley MacGregor. prepare "a personal view of my time" is not mous amount of work;getting advice on topics, Another firstin Ontario was the active partic easily met considering the dimness of my mem choosing presenters and recorders, arranging ipation of school book publishers in the pro ory but their invitation was flattering enough to forequipment and supplies, even securing ad gram. This involvement of Department spark this effort. vance registrationto keep the groups small and personnel, teacher educators, supervisory offi Serious study of mathematics curricula be ensure that each teacher's preferredtopic would cials, principals, teachers from all divisions gan in the 1950's. Generously fundedprojects be available, we learned an important lesson. and publishers was intended to provide a broad in theUnited States, notablythe School Math Teachers of mathematics behave in a way that range of support for individuals to undertake ematics Study Group, the Madison Project, the they wouldn't tolerate fortheir students. They rather dramatic changes in classroom organi Greater Cleveland MathematicsProgram, and forgottheir chosen topics, ignoredinstructions zation, teaching techniques, and choiceofleam others, resulted in a rash of new textbooks that and chose to join friendsin whatever session ing materials. Few can deny the impact this foundtheir way into Ontario and influenced the was immediately appealing. So much for pre initiative has had on mathematics education. reforms taking place here. These 'new' pro cise planning and preparation! The annual busi And to think that it's origins could be tracedto grams consisted of arithmeticgeneralized and ness meeting saw the acceptance of a new the decision of OATMto move to the Innon the formalized by the introduction of sets and constitution which included dropping the "and Park fromOCE. emphasis on laws and properties. Precision of Physics" fromour title and the election of Mrs. In 1965 a sub committee of the Ontario language, early introduction of inequalities, Jean Leppard as the firstpresident of the new Mathematics Commission began a study of numeration systems with bases other than ten OATM various experimental programs for teaching were characteristics common to most of the The association's rather fragile ties to the mathematics to young children. Recognizing text series. Where geometrywas studied it was Ontario EducationalAssociation were stretched the futilityof a spare time ad hoc approach the relegated to a minor role associated with mea even further with the decision to move the committeerecommendedtheformationofsum surement and in the few cases where it received annual meeting of OATM to the Inn on the Park mer study group to investigate mathematics more attention the emphasis was still on the for 1966. Despite dire prophecies of financial teaching from kindergartento grade six. With traditionalpreparation forEuclidean plane ge ruin fromsome councillors, the move was an fundingfrom the OntarioCurriculum Institute ometry.The authors of the new texts in Ontario unqualified success. Who could have foreseen (the forerunner of OISE) the Math Commis adopted a similar philosophy although the top that it would lead to regional conferences and sion appointed ten teachers to work during the ics generally appeared later and the approach to the rotation of the annual meeting around the summer at the Royal MilitaryCollege inKing many of them was much more traditional. It province? More people became involved and ston. With Joe Ryan as chairman and Dr. Andy was the Ontario Mathematics Commission and the Association's activities influenced more Elliott as host and mentor we waded through theOntario Association of Teachers of Mathe and more teachers. A larger membership meant literally hundreds of texts, workbooks, and matics that drew attention to the reforms in a greater budget and better programs. Who can other materials. There was a great deal of Europe, particularly in England, which were in forget the dramatic presentation of Miss Edith uniformity in the materials originating in the marked contrastto those of theUSA. Being a Biggs at the 1987 Conference? Her perfor United States. In contrast, the materials from member of both these organizations at the time mance resulted in the Departmentof Education Europe, especially the NuffieldProject and the I will outline the eventswhich led to the uniquely arranging her secondment from England to Schools Council in England, developed num Ontario mathematics program. As the first ele Ontario fora period of fourmonths beginning ber concepts and operations through the use of mentary school teacher to be invited to serve in September 1967. concrete materials and visual patterns.Geom the Ontario Association of Teachers of Mathe- etryoccupied a major place in the program and emphasized topological and non- metriccon elements of the committee 'srecommendations. Editor: In my viewJim was one of the leading cepts as well as symmetries and transfonna Those three years of work were both exhilarat cwriculum thinkers of the mid-sixties and tions. Acknowledging the great influence ing and frustrating. They also provided the seventies. I figuratively sat at his feet for American publications have on Canada yet richest learningexperience of my life. marryyears and am the better for it. He was believing that the British approach offered . My transferfrom the CurriculumBranch to tlzefirst President from tlze elenzentary pa,zel more forOntario students the committee pro the newly expanded Research Branch in 1975 (1968). People such as Jim Maclean and duced a report which attempted a balance be offerednew challenges. Accountabilitywas in Joan Routledge convinced elenzenta,yedu tween the two viewpoints. Coinciding as it did vogue and the public was demanding evidence cators that we had sonzething to offerthem with the publication of the Interim Revision that "standards" were being maintained. Vari and convinced tlze Association that elenzen Mathematics PlJl by the Department of Edu ous schemes were put forward to collect data ta,y people hadmuch to offerit. cation it marked thebeginning of substantial that would assure the Minister that teachers changes in elementary school mathematics pro were doing a good job. It grams. More detailed and specific materials was our good fortuneto be were subsequentlydeveloped by teams of teach able to participate in two in ers working out of OISE with Dr. Chester ternational assessment ac Carlow as project director and Eldon Pipher as tivities designed by the field supervisor. IntemationalAssociationfor As educators in Ontario became more aware the Evaluation of Education of the developments in England, especially in al Achievement [IEA].The the Primary Schools, there was a dramatic Association had acquired the increase in the number of Canadians studying services of absolutely the top overseas and in the number of British experts brains in educational evalu- invited here. The working visits of people like ation in the entire world. FROM THE GALLERY: WALTERSO KO LUK AND FRI ENDS Dr. Edith Biggs, Mrs. Dora Whittaker, Miss Knowledge gained fromthose experiences led Doris Nash, Miss Eleanor Duckworth and oth theResearch Branch to embark on the project FROM THE ARCHIVES ers would lead one to believe that all British knownas the Ontario Assessment Instrument experts were female.Education in Ontariodid Pool and to do provincial evaluations by testing PRESIDENT'S REPORT benefitfrom the work of expatriateBrits like a sample of students using instruments from WALTERSOKOLUK Dr. Andy Elliott, W. W. Sawyer, Dr. Griff the Pool. Removing the threat of a return to . . . Lest the foregoing quotation be mis Morgan, Dr. Doug Crawford, Alf Hanwell and 'Departmentals' and making evaluation an in leading, I hasten to add that Mr. H.E. Totton others. tegral part of the teaching-learningprocess and compiled an excellent manuscript from the In January 1971 thePlJl CurriculumRevi providing quality test instruments forthe pur records of the Association. Infact, after reading sion Committee was fonnedby the Ministryof pose was the most positive policy to come from it I was so proud of the past accomplishments Education to review existing guidelines, to the Ministryin a long time. The involvement of of our organization that I was moved to fonnu examine thedata collected throughoutthe prov classroom teachers, supervisors, and expertsin Iate the slogan which I shall recommeng later to ince as a result of Cyclic Review activities, to evaluation in the creation of banks of test the incoming Executive Council. During this study current research on child development instrumentshelped ensure that the items were past year in officeas Presidentof the OATM,I forthe purposeof recommending revisions to relevant to the curriculum and actually mea have examined activities of the past as well as the CurriculumGuidelines forthe Primary and sured the skills forwhich they were designed. tried to forecast thefuture in an attempt to Junior Divisions. It was the largest and most As with any initiative of thismagnitude mis determine the best means of fulfillingour role representative curriculumcommittee ever es takes were made and will continue to plague forthe currentand futureyears. In thisregard, tablished by the Ministry.My job as chairman ongoing development. However as teachers I invite you to add your appreciation to my was to focusthe enonnous and diverse talents and others gain experience in the process the personal thanksto all members of the Execu of over 60 educators and parents on the task of product will get better and better. tive Council for their support and sincere ef preparinga report that would reflect a consen It is immensely satisfying to read the latest fortsduring the past year. Our organizationthis sus. To say thatthe outcome was controversial NCTM publication Curriculum and Evalua year has required that they not only attend would be an understatement. The Ministry tion Standards forSchool Mathematics. This meetings in Toronto but assume a leadership undertook a validation procedure never before report, endorsed by an impressive list of pro role intheir geographical region as well as to be applied to a committee report. The outcome fessional organizations, embodies much of the active members of committees, in liaison with was the publication of two documents: The work initiated by the OMC and OATM in other organization or special projects ... FonnativeYears [ outliningpolicy] and Educa 1964-65.Perhaps now that the same ideas can VOLUME 10, NUMBER 1, tion in the Primaryand Junior Divisions [giv be imported they will gain wider acceptance. SEPTEMBER 1971 ing good advice]. Only the latter contained What goes around - comes around, although it may take twenty-fiveyears. Theeighth was that: places in teacher education programmes. These THE FATE OF THE "The annual fee shall be 50 cents". are characteristics which jurisdictions in most Therest, as the saying goes, is ( our) history. other parts of the world can only envy. Admin ART:CENTENNIAL And so, toward the invited indulgence - istratorsin the United States and Great Britain, REMARKSON THE personal, and consciously subjective perspec forinstance, have a much harder time finding tive on the current state of the community art. qualified mathematics teachers than do their MATHEMATICS (These remarksare, forthe most part, limited to Ontario counterparts. Our best students and our the elementaryand secondarylevels of educa strongest institutions have shown clear evi EDUCATION tion. The tertiary level has many of the same dence that they can hold their own on national problems of these areas plus a fewquite knotty and internationalstages. ENTERPRISEIN ones of its own.) But first, a note on process. Commenting publicly on one's colleagues, self A CLOSER LOOK ONTARIO or family is never a particularly comfortable Once we leave this broad-brush, distanced, WIWAMHIGGINSON task. Evaluation from without is invariably relativistic perspectivefor a closer look at what cleaner and almost always easier, but can very Anniversaries are invitations to reflection. is going on, however, the situation becomes oftenmiss the essence. The grand chimera of Located, as we always are, between the imme fuzzier,and in many ways less positive. From diacy of the recent past and the fog of the objectivity has been largely put to rest in recent any significant examination of the enterprisein decades by all but the most recalcitrant of neo sometime future,anniversaries are arbitrarily, question, three fundamental features of the positivists, but going against the powerfulfolk and usually mathematically, designated times Ontario mathematics education world would to celebrate, to acknowledge, and to wonder. wisdom ofmaternal ("if you can 'tsay something seem likely to emerge. These are: extreme nice ... ") and bureaucratic ("Cover your vul Temporal markers on thelandscapes of lives variability in quality, sharp bimodality with and communities we can conceptualize them nerabilities") advice is something that requires respect to practice and problems between ele a certain screwing of one's courage to the as peaks( or perhaps as plains or valleys) where mentary and secondary levels, and the inade sticking point. The most important issues in we can conveniently pause to remember from quacy of teacher education programmes. We whence we have come and to speculate when educational evaluation are often not consid begin with an elaboration of the third feature ered explicitly. Indeed, in many cases one we might be bound. And hence, thisgathering since it is a centralcontributor to the othertwo might suspect that examiners are not even of anniversarialarticles. Thecommunity is that areas. Stated bluntly, Ontario teacher educa conscious ofthem. They ha�e to do with aware of "Ontario Mathematics Educators", a collec tion practices in mathematics are at best satis ness of the context and purposeof evaluation, tion of boundary contingencies - political/ factory and at worst scandalously weak. The the sets of assumptions about what is worth geographical, academic and social - which gap between the strengths of the Ontario sys examiningand the ways in which one might get sufficesto identifya moderately well-defined tem - in particular, the range and quality of worthwhile insights about important educa resources to which it has access, the general set. The anniversary is that august double digital, the centen . tional goals. Assessment is a functionof crite quality of its teachers, and the priority, at least ary ria and criteria are oftenrather more arbitrary Some 36,500days ago one Fred F. Manley, in theory,which it accords mathematics and the than we might care to admit. wrote (OATMPHistory, 1962) fromthe Colle major structural weaknesses inherent in its giate Institute on Jarvis Street in Toronto to a feeblesupport for classroom teachers is ex number of our predecessors: A BROAD PERSPECTIVE tremely large. The best of a mediocre lot is Dear Sil; Several meetings of gentlemen Withthe reader suitably warned,we begin probably the pre-service secondarylevel. Here in Toronto, who are interested in the with a broad, geographical perspective. Com the chance of finding a well-qualified and formation of a Mathematical and Phys pared to other political entities, be they prov motivated candidate engaged in a course of ical Association for the Province, have inces, states, or countries, what are the intellectual and practical substance is fairly been held, and I am directed to forward outstanding aspects of Ontario mathematics high. you a Draft Constitution, and also to education? It seems likely that thisis one of the The same cannot be said of his or her peers request you to become a member." most positive perspectives fromwhich to con enrolled at the elementary level. Here the norm TheConstitution in Question had nine sec- sider our activities, forthere are many features is more closely approximated by anxiety,brev tions of which thefirst was that: of our professional lives of which we can, ity, fragmentationand incoherence and if one "The Association shall be known as the justifiably, be proud. We would appear to have looks on the dark side, cynicism and raw in Mathematical and Physical Association maintained a highlevel of public support and competence. (While we have notedthe frenzy of Ontario", confidence. Our enrolments have stayed rela for admittance to Primary-Junior B Ed pro grammes, it needs to be recognized that there Thesecond was that: tively high. We are very well paid and teaching "The objects of the Association shall be as a career seems to be appealing to increasing is, on the part of an unfortunatelylarge percent the promotion of the study and teaching numbers of young (and not so young) gradu age of applicants, no corresponding enthusi of Mathematics and Physics" ates as evidenced by the fierce competition for asm for teaching mathematics.) That it is FROM THE GALLERY: A MATHEMATICS-TEACHING FAMILY-PAUL SHERK, JOHN STOUFFER (MATH HEAD), BETTYSHERK (GRADE TWO TEACHER),JOHN SHERK (MATH TEACHER),AND BOB SHERK(MATH & PHYSICS TEACHER)-OAME ANNUAL CONFERENCE, 1980 possible in the last decade of the twentieth ofthe whole gamut from' outstanding',through competitive businesses, too many secondary century to become qualifiedto teach elementa 'good','satisfactory', and 'marginal' to 'unac mathematicsteachers seem to have lost touch ry mathematics forup to fortyyears by surviv ceptable'. What most classical theoretical mod with their clientele. The processes of yester ing a twenty-hour course of dubious quality is els might not suggest would be the very high year slog on unabated in small, isolated and not defensibleby any set of criteriaworthy of percentage of teachers who would fall into the ineffectualworlds dominated by texts and quiz the name, be they pedagogical, economic, so satisfactoryand marginal categories. (As sup zes and frequentreferences to needing this for cial,or philosophical.At the graduate level the port of a type for this claim note our perfor "future-purpose-x". As a community we ac situation is equally dismal. Ontario must be the mance on recent large-scale evaluation projects knowledgethe factthat many students fail to largest educational jurisdiction in the eastern both 'internal'(asfor instance,McLean(l982) cope in any effectivemanner with secondary world where there is no opportunity forthe vast and the ongoing Provincial Reviews at several school math (focusing, perhaps, on the rela majorityof teachers to pursue directly a grad levels) and 'external'(McLean et al (1986); tively positive fact that this happens to fewer uate programme in mathematics education. Lapointe et al(1989) (Editor: Second Interna students and later than it does in most other Thecontrasts with most American states, and tional Mathematics Study) where the "gen partsof the world). What we tend to shy away provinces such as Alberta and Quebec are tleperson's C" is about the strongest overall fromis the reality thatfor many of our "suc particularly pronounced in this area. The in grade we could assign ourselves.) cessful" students mathematics is a meaning service domain has, until recently, been quite Therewould seem to be two differentsorts less and not particularly pleasant set of bleak as well. We can hope that the era of'One of reasons for this. At the elementary level the techniques and rituals. Day-Wonder' Workshops and 'Primary' and contributing factory is academic. The majority And to the extent that this analysis is valid, 'Junior' additional qualification courses with of primary and juniorlevel teachersdo not feel what might the futurebring to our community? minimal mathematical content are over,but it is comfortable with mathematics and in most Can we look forward withany degree of real probably too early to come to that conclusion. cases operate with a constrained and increas ism to improvements in this situation? If so, One could expect with some justification, ingly inappropriate conception of the nature of what actions would assist this process? First we given the size of the population in question, the discipline. At the secondary level technical must acknowledgesome quite powerfulforces considerable diversity fromclassroom to class competence is not so much of a problem as is a which will become increasingly strongin the room in the quality of mathematics instruction certainstaleness andnarrowness in methodol near future. The most significantof these will in the province. It is not hard to findexamples ogy. Like jaded spouses or proprietors of un- be major changes in social and economic pat- terns as the world grapples with the implica instance with the Universityof Waterloo's very ► Franklin,Ursula, The Real World of tions of the"world problematique" -environ adrnirableDescartesMedalsandOAME'sown Technology. Montreal: CBC Enterprises, mental degradation, population pressures, Father Faught award and theK.D. Fryer award) 1990 climatic change and thelike. To the extent that we have not made it at all easy for other ► Jones,Philip S. (ED),A Histo1y of mathematics will be seen to be centralto under teachers to learn from those examples. And Mathematics Education in the United standing and attempting to remedy these prob when we begin to look for excellencein our States and Canada: Thirty-Second lems (and perhaps questioned for the role it midst it is surprising to find how often if Yearbook of the National Council of played in getting us in to them in thefirst place) appears. Take forexample the cases of two of Teachers of Mathematics. Washington: we are going to see even more public pressure the best contemporary popularizers of mathe National Council of Teachers of Mathe forincreased and improved mathematics edu matical ideas. Ivars Petersonof Science News matics, 1970 cation. (See, forinstance, documents such as and the author of Islands of Truth: A Math ► Lapointe,Archie E,Nancy A. Mead and Corporate-Higher Education Forum (1991), ematical Mystery Cruise (1990) is a Univer Gary W.Phillips, A World of Differences: Premier's Council (1990) and Mathematical sity of Toronto graduate and a formerOntario An InternationalAssessment of Mathe Sciences Education Board (1990) which states secondary school teacher of mathematics and matics and Science. Princeton: Educa on page 1, "What is required is a complete science.AK. Dewdney (1990),of theUniver tional Testing Service,1989 redesign of the content of school mathematics sity of Western Ontario has been a regular and the way it is taught".) Second,and closely columnist writing about computing and math ► Mathematical Sciences Education Board, related to the previous factor, we will see a ematics in Scientific Americanfor more than Reshaping School Mathematics:A demand fromat least part of our constituency to fiveyears. philosophy and a Framework for reshape schooling in general and perhaps math It is oftenthe case that periods of economic Curriculum Washington: National ematics in particular to reflect the values,expe difficulty are ones where human values and Academy Press,1990 riences and research findings of some two creativity become particularly highly valued. ► McLean,Leslie D., Willing But Not decades of research by feministscholars (see, We might hope that this will be the case in the Enthusiastic: Ontario Students' Views on among others, Allen (1991), Bateson (1990) next fewyears forthere seems little doubt at the Mathematics. Calculators and Computers and Franklin (1990)).Third, as the tools of new timeof writing (late 1990) that we are set fora in Grades 7 to JO. Toronto: Ministryof information technology become even more period of economic hardship of indeterminate Education, 1982 powerful there will be increasing pressure to duration. We have many strongdimensions to ► McLean,Les, Richard Wolfe and Merlin teach more formeaning (why and when) and our community and numerous initiatives which Wahlstrom,Learning about Teaching less fortechnique (which these machines will seem to be on theright track(as, forinstance, from Comparative Studies: Ontario be more than capable of carrying out). the belated but none-the-less welcome series of Mathematics in International Perspective additional qualification mathematics courses Toronto: Ministry of Education,1986 THE NEXT DECADE at the primary-junior level and the very prom ► Ontario Association of Teachers of ising experiments with group learning in a We will,therefore, not want forchallenges Mathematics and Physics, Historical in the next decade, let alone the next century. number of schools). The prospect of learning Highlights of The Ontario Association of Organizations likeOAME / AOEM and those from and with each other in an attempt to Teachers of Mathematics and Physics: grapple with the very significant problems individuals who contributeto its existence have 1891 - 1960, Toronto: Copp Clark,1962 which faceus as a species is one which should a centralleadership role to play. One task where (29 pp,Sponsored by the OATMP to excite and hopefully will invite all of us. we must show dramatic improvement is in mark the100th Anniversary of the learningfrom our best practitioners. We are not REFERENCES Founding of the Ontario Educational very good at celebrating excellence in our Association. Compiled fromthe records midst. While we may have many reservations ► Allen, H.A.J.,"Mathematics and Gender" of the OEA by H. E. Totton,edited by about the practices of our southerncousins we Kingston: Mathematics,Science and F.C. Asbury) must acknowledge their willingness to high Technology Education Group,Queen's Islands of Truth: A light excellence as they see it (the accuracy of University,1991 (to appear) ► Peterson,Ivars, Mathematical Myste1y Cruise. New York: their "excellence sensors" would seem to be Composing a ► Bateson, Mary Catherine, Freeman,1990 questionable at times. Thecase of Jaime Es Life,New York: Plume,1990 ► Premier's Council,People and Skills in calante,the Los Angeles secondary mathemat To ► Corporate-Higher education Forum, the New Global Economy. Toronto: ics teacher who became, within a period of Be Our Best: Learning for the Future:A Provinceof Ontario,1990 about three years, the subject of a Hollywood ForumAdviso,y on Public Education movie (Stand and Deliver), a book (Escalante: Montreal: Corporate-Higher Education Editor: Bill is one of the thinkers in The Best Teacher in America) and a video N011h Forum,1991 American Mathematics Education today. series ("Futures"), is only the most obvious When Bill speaks, we listen! example. Even in those few cases where we ► Dewdney, A. E., The Armchair Universe: have recognized exemplary practice (as for An Exploration of Computer Worlds. New York: Freeman,1988 ing. The speaker at the banquet was John the curriculum recommended by OMC. Pub REFLECTIONSON Robarts,the Minister of Education. The suc lishers were anxious to produce the experimen cessof thismeeting led to my involvement in tal material as commercial texts. The THE HUNDREDTH the NCTMwith an appointmentto their Meet experimental material author group led by John ANNIVERSARY OF ings Committee. This appointment was fol Coleman wanted that group to act anonymous lowed by my membership on other NCTM ly like an Ontario Bourbaki group with all THE FIRST ONTARIO committees, then by my election to the Board royalties going back into mathematics educa of Directors in 1965 and eventually by my tion. But this idea did not find favourwith the MATHEMATICS election as NCTM president for the period OMC becausesomemembers feared that teach 1974 to 1976. ers would buy the "Bourbaki" books because ASSOCIATION Besides the 21st summer meeting of the of this arrangement even if other texts were NCTM,OAME / AOEM has sponsored three superior texts. JOHN C. EGSGARD other NCTMmeetings. The firstmeeting was In the year 1962 I was elected president of It was in th�fall of 1949 that I firstheard an area meeting in the fall of 1973 in Toronto. the OATMP.I can still recall the council meet about theOATMP - the Ontario Association The second was the 60th annual meeting in ings where our major work involved making of Teachers of Mathematics and Physics. The April 1982, also in Toronto. decisions about the next annual meeting. By Association was 58 years old. I was at the Both these meetings were under the chair this time OATMPmeetings had switched from Ontario College of Education, now called the manship of Dave Alexander. Thethird meet room 8 of UC to a large roomat OCE. I have Facultyof Education of the U ofT.All mathe ing, chaired by Bob Robinson and George fond memories of Edward Kasner telling us matics specialists were given freemembership Knill, took place in May, 1990 in Hamilton. how his nine year old nephew invented the in OATMPduring their OCE year. Meetings of TheOntario mathematics teachers organi name googol fora specificvery large number; the OATMPtook place during the Eastervaca zations have always had a close relationship of Max Beberman explaining the difference tion week in room 8 at UniversityCollege of with the NCTM.Three of our members, Don between a number and a numeral forthe new theUniversity of Toronto. Infact, all subject Hazell, Joan Routledge, and Bob Robinson, math; of Morris Kline warning us of thedan area groups met during that week under the have been chosen as the Canadian liaison with gers inherent in the new math because of its auspices of the Ontario Educational Associa NCTM throughmembership on the Commit abstract nature; of W.W. Sawyer explaining tion. (Teachersat that time did not have enough tee on AffiliatedGroups and its successor. Bob how to help children understand the meaning money to take vacations during the Easter Robinsonhasalso beenamemberoftheNCTM of the term "variable" by solving equations break.)This room was well knownto me as I Board of Directors. Among others who have using a bag containing an unknownnumber of took several mathematics classes in it as an served on NCTM committees are Dave Alex marbles. undergraduate.It was ten years later in the year ander and Ralph Connelly. Several members In 1964, the OATMPdropped its reference 1959, while I was teaching at St. Michael's have written for NCTM publications while to physics and became the OntarioAssociation College School, thatProfessor Petrie of OCE othershavespokenatNCTMmeetings through of Teachers of Mathematics. invited me to become a member of the council out Canada and the United States. For a few A major move forthe OATM took place in of OATMP.At my first meeting of the council years George Knill produced a section in the 1966 under the presidency of Jean Leppard a volunteer was needed to chair the local ar Mathematics Teacher on applications in math when the annual meeting moved fromOCE to rangements committee for the 21st summer ematics. a hotel - the Inn on the Park. Jean had a great meetingof theNCTM which was to be held at In 1959, Howard Mulligan persuaded the style in runningthe council meetings. Instead the U of T in August of 1961. The other OTF to finance a meeting of mathematics of askingfor volunteers to do tasks she decided members of the council "volunteered" me. educators to see what changes might be made ahead of time who would be best for a certain This was a big undertakingfor the OATMPas in the Ontariomathematics curriculum. About job. Then she asked that person to volunteer. theNCTM had never before met outside the 30 of us met at Lakefield School in August No one refused. USA. (Incidentally,the registrationfee was $1. 1959. Thatmeeting was the beginning of the It was during Jean's presidency that we The cost for a dorm room was $4, and for a reform in the mathematics curriculum. The celebrated the 75th anniversary of the frrst room at the Park Plaza $10.) We had an excel formation of the Ontario Mathematics Com meeting of an Ontario mathematics teachers lent meeting due largely to the expertise of the mission was a result of this meeting. Afterthat association. The NCTMBoard, of which I was chairs of the variouscommittees. These chairs meeting many teachers wrote experimental a member, was meeting at the same time in were heads of the mathematics departmentsof material and/or taught this material. I can re New York City. TheNCTM was so impressed the collegiates in Torontoor of private schools. memberthe frequentall day Saturday meetings by the age of our Association that the Board Among these teachers were Bill Darbyshire, during which we discussed ways of improving sent me fromNew York to Toronto to give JackMcKnight,JeanLeppard,JohnDel Grande, the material. The dedication of the teachers congratulations to our Association at the Dia and NormSharp. Jim Gates, the present Exec involved towards mathematicseducation was mondAnniversarybanquet. Incidentally, it was utive Directors of the NCTM,worked forthe exceptional. Eventually the Ministryadopted at this meeting that I heard Mary Dolciani NCTM for his first time at this Toronto meet- FROM THIEGALLERY: PAUL SIHERK,JOHN B>ELGRANDE, LORNA MORROW, DOHM IEGSGARI!>, LYMM IEGSGARI!>, DAVIE ALEXANDER speak forthe first time. She was a wonderfully I had been inactive in the OATM for a few organizations has stretched throughout 100 inspiring speaker who entertained us both math years when in 1972 the OATM and the OMC years. It is the magnificent achievement of ematically and humorously with her mixture of decided to merge into one organization to be these organizations that we are celebrating in Irishbrogue and Italian style. called the Ontario Association forMathemat this year 1991. I have been a part of this In the late 1960's the OATM, along with the ics Education (OAME).I had left St. Michael's organization for 42 years. I am grateful for all other provincial mathematics teachers organi College School in Toronto and taken a position of the wonderful things our organization has zations, formed a national organization of with Bob Mitchell at Twin Lakes Secondary given to me. May it flourish for another centu mathematics teachers called the Canadian School in Orillia. Don Attridge asked several ry! Association of Mathematics Teachers(CAMI). past presidents of OATM and OMC to run for Editor: As you can tell from John's reflec I was thefirst president. In its firstyear CAMT, office in the new organization. At the first tions, he wasn't bornyesterday! Howei-e r he under the leadership of Frank Ebos, held a meeting of OAME in the spring of 1973 in continues to bring the same sense of talent, national meeting in Toronto on the use of TV in North Bay, Dave Alexander was elected pres commitment and enthusiasm that you see the mathematics classroom. Unfortunately ident while I was chosen as president-elect. reflectedhere to his present classes. He is an CAMT lasted only a fewyears because provin During the formationyears we all relied heavi inspiration to all who know him. cial organizations were unwilling to commit ly on Mand M, Mona and Morley MacGregor. the fundsnecessary to hold cross Canada meet Until Morley's death in the spring of 1990, he ings. Organizations foundit less expensive and and Mona were the backbones of the OAME. easier to send representatives to NCTM meet In its 18 years of existence the OAME / ings inthe USA. AOEM, like its several predecessors, has been a major force in mathematics education in Ontario. The total influence of all of these SCARBOROUGH ASSOCIATIONFOR MATHEMATICS EDUCATION: A SHORTHISTORY STEVE MARTIN On April 29, 1981, Jim Fencott, the coordi nator of Mathematics, convened a meeting of interested Scarborough mathematics teachers ( elementaryand secondary)to explore the idea of forminga mathematics association in Scar borough. The new chapter would replace the Scarborough- East York Mathematics Asso ciation (SEYMA) which disbanded in January, 1981. At the meeting of the steering committee, the decision was made to proceed with an application for chapter status at the OAME/ AOEM Annual Meeting in Sarnia on May 8, 1981. The steering committee also prepared a survey which was sent to Scarborough teachers to determine thelevel of interest and the topics that teachers would be interested in exploring. FROM THE GALLERY: PAUi. ZOUS A memo from Jim Fencott dated July 8, 1981 outlined the first slate of officersfor the The highlight of our association was the new chapter. Thedecision was made during the SAME HAS PROSPERED successful1987 Annual OAME/AOEM Con firstyear to hold a mini-conference in the fall UNDER THE ferenceheld at Centennial College in Scarbor and to organizeP.A. Day programs in February LEADERSHIP OF THE ough. Our intriguingtheme "Of Mice & Math" in co-operation with the Scarborough Board of FOLLOWING captured the imagination of all who attended. Education. This is a traditionwhich has contin Unfortunately, our founder, Jim Fencott PRESIDENTS ued to the present. passed away in January1987 and was unable to YEAR PRESIDENT Our first Mini-Conference was held on witness the fruition of his effortsin founding 1981-82 Jeanette Jones December 1, 1981 from 4:00 to 7:30 PM at ► our chapter. The conference was dedicated to Tabor Park Vocational School in Scarborough. 1982-84 IrisBrown his memory. His memoryalso lives on in the ► Along with a series of workshops forteachers "Jim Fencott Award" which is presented annu 1984-86 Steve Martin fromprimary to senior, dinner was provided ► ally to a graduating student in Scarborough followed by an after-dinner address by Alex 1986-88 Arnie Carefoote who has made a significant improvement in ► Norrie. mathematics achievement. 1988-90 Shirley Fairfield The organization has continued to grow ► through the years fromthe 16-member steering ► 1990-91 Bill Haehnel committee in the beginning to the 175-250 As we enter our second decade, we look members who attend the mini-conferences. forwardwith continued optimism to our efforts to stimulate interest in mathematics and to promote the practice of good mathematics teach ing techniques. AHISTORYOFTHE GOLDEN SECTION DON ROBERTS Prior to OAME's birth in North Bay, the Mathematics Heads in the Hamilton, Niagara, Norfolk, Haldimand area along with staffat the local Ministry of Education Office, had an affiliation that planned and ran seminars for teachers in our differentregions. We shared the expertise we had in our local boards. When Chapterswere initiated as part of the OAME organization structure, the pre-existing group gave itself a new name. Geographically we were part of theGolden Horseshoe, so it was obvious (geometrically) that our new name would be the Golden Section! At least once a year (sometimes more of FROM THE GALLERY: GEORGE KNOLL ten), mathematics seminars are held in the region forour teachers. Thereis usually some representatives to the OAME/ AOEM Council MCMASTER thingplanned forboth elementary and second have contributedtheir time and effortsto OAME SCHOLARSHIP ary people. Theseminars in the firstpart of the / AOEM projects. fu addition, many Golden Following the Hamilton Annual Confer late afternoonare followed by a catered dinner Section members have been on council and ence (1978) an arrangement was made by thatis informal and allows fora sharing of ideas served in executive positions. OAME/ AOEM to set aside $3000 to be given among individuals. fu the past, except when the Our organizationalstructure is not as formal inscholarship to McMaster University. McMas annual OAME / AOEM conference is hosted, as some other Chapters but there has always ter set up the requirements needed to be an the Golden Section has not asked for money been a core of people fromeach division that applicant forthis scholarship. have made themselves available and provided from OAME / AOEM's general fund. Each THE WINNERS individual programme is financed by the fee leadership. If we can continue as in thepast to YEAR WINNER charged forthat particular event. The speakers keep open the lines of communication between for our sessions have come from across the our own differentdivisions, theOAME/AOEM ► 1980 George Tolomiczenki, Council, and other chapters, the staff at the Etobicoke Collegiate Institute. province. The increased networkingprovided Awarded by revernionto Hing by our affiliation as a chapter of OAME / Ministry of Education and our Federations, narnSeto, Harbord. Collegiate AOEM has paid offwell over the years and we then we will be able to serve each other well in Institute,Toronto. the future. thank thosepeople that have come out of their 1981 Stephen Worotynec,Univernity way to be with us. ► of Toronto Schools We have served the provincewell by host 1982 Todd Cardno, Cardinal ing the Annual OAME/ AOEM Conference in ► Newman High School, St. Catharines, Niagara Falls and Hamilton. Hamilton.Aw ardedby Elementary, secondary, post secondary per revernion toJimmy Lam, sonnel have worked together along with their Columbia Secondary School, various school boards to help us achieve our Hamilton. local and provincial objectives. Our Chapter 1983 Antony Davies,Nelson High ► School, Burlington. Awardedby revernionto Tracy Gardiner Waterford DistrictHigh School, Waterford. 1984 Peter Cheongand Kam ► Cheong.(School and Town not Mentioned!) CREDIT HUMBER ASSOCIATION FOR A'.ATHEMATICS PROMOTION US HENRY During 1984, Bob Jones discussed with Alex Norrie and Claire Zeller the fact thatthere was no local chapter of OAMEin such a large area. Therewas no forumfor K-13 math teach ers to share their ideas and expertise. Thusthe concept of the Peel Association forMathemat ics Education had been initiated! In June, 1985, thefirst meeting was held at Gordon Graydon Memorial SecondarySchool to investigate theformation of a local chapter. Ten people, including secondary personnel and elementary resource people, attended. Follow ing the meeting Bob Jones wrote to Morley MacGregortorequesttherecognitionof PAME, the Peel Association forMathematics Educa FROM THE GALLERY: MARY LOU ICESTELL tion. However he responded that it was neces Helen Baker, Janet Mitchell and JeffIrvine. dinner and a publishers display. Mathfest has sary to waituntil OAME'86. PAMEbecame officiallyrecognized at OAME since become an annual event enjoyed by many, Informalmeetings were held in 1985 with '86. Our firstofficial event was held on May 21 alongwith our spring events, math contests for Bob Jones, secondary, and Helen Baker, ele at Sheridan College. Following a wine and grades 8-11 and the elementary problem solv mentary, as the executive. A mini-conference cheese social, Brendan Kelly spoke on "Pro ing package. By November 1986 the member was planned and held at Brampton Centennial moting Excellence in Mathematics K-13". ship was up to 123. Secondary School fora February Professional PAME kept growing and, as of June, 1986, During the fall of 1988, PAMEwas joined Development Day. At that conference 42 peo there were 97 members. by Chris Dearling of Halton, JeffMartin of ple became members of PAME. In.March1985 PAME's first mini-conference, entitled Etobicoke and Walter Curranof Dufferin-Peel. John Hawkins designed a logo and a new "Mathfest", was held October 20, 1986. 190 It then became necessaryto change the name of executive was formedconsisting of Bob Jones, people attended, participating in workshops, the chapter as PAMEwas no longer applicable. After a contest in the springof 1989 the Peel Association for Mathematics Education be came the Credit Humber Association forMath ematics Promotion (CHAMP). A decision was made then to request spon sorship of OAME/ AOEM '91 and a presenta tion was made to council by Donna Del Re and Marg Warren. TheCHAMP proposal was ac cepted with Bob Jones and JeffMartin becom ing the co-chairs. During the fall of 1990 an impressive new logo was designed by Halton forCHAMP, a growingsuccessful chapter for math teachers K-13.
FROM THE GALLERY: ALEX NORRIE THE FOUR YORKS MATHEMATICS ASSOCIATION MIRIAM PEARLMAN The roots of the Four Yorks Mathematics Association (Y4MA) were planted by OAME / AOEM members in North York and York Region who feltthe need to have a local chap ter. North York, York Region and York Region Roman Catholic Separate became likely part ners, partly because of networks that were already established, and partly because of their geographic proximity. York Universityseemed like a partner that could make a unique contri bution and already had active OAME / AOEM FROM THE GALLERY: NEIL WILLIAMSON, J. SYMINGTON, ANI> FRIENDS memberson staffwho were interested in show ing leadership in the teaching and learningof By the fall of 1989, a full council was keynote speaker Veronica Lacey, the Director mathematics. formallyin place. The executive consisted of of the North York Board of Education. fuvitations were sent out to the coordinators BillNimigon (President, North York),Jan Scully Theannual conference was a success from of the three Boards and a professor at the (President-elect, York Region), J. Symington the very first.Each year the evening has been university to meet with two elementary and (Past President, York Region), Mary Lynn Jef wait-listed with maximum capacity of 250 two secondary teachers. Thisinaugural meet fries(Treasurer, York Separate), Bob McRoberts registrantsattending the dinner and workshops. ing was held on June 4, 1987 at Peckham (Secretary, York Region). Each of the four An annual spring event and social has been Centrein North York. Theinaugural group was jurisdictions have two councillors. North York held with guest speakersincluding Mary Lou led by J. Symington and Don Attridge(Math was representedby Miriam Pearlman andJackie Kestell, President of OAME / AOEM and Ron ematics Consultants, York Region) and Bill Marrocco, York Region by John Havercroft Lancaster, award winning teacher. Special Nimigon (ProgramLeader), and Hugh Beattie and Margaret Roberts, York Separate by Paul events are being planned forthe coming winter, (Mathematics Coordinator, later replaced by Nichol and York University by Pat Rogers and including an evening dedicated to York Uni John Havercroft) of North York. The energy Olive Fullerton. fu 1990, the currentexecutive versityFaculty of Education student teachers. present in this meeting was the driving force consists ofJan Scully (President),MiramPearl The membership has grown to include ap behind the agreement to pursue the vision of man (President-elect), Bill Nirnigon(Past Pres proximately 200 registered members. Mem forminga new chapter that would represent the ident), Mary Lynn Jeffries(Treasurer), Jackie bership in the parent organization is encouraged fournewpartnersand show leadership in math Marrocco (Secretary). The councillorsat present by having teachers join the parent OAME/ ematics education. fu September, 1987, the are Olive Fullerton (York University), Dave AOEM and then identifying Y 4MA as the group reconvened with some additional staff Simpson and Phil Feldman (North York),John chapter with which they wish to be affiliated. who expressed full commitment to go ahead Havercroft and Margaret Roberts (York Re The membership fees are paid forjoining the and plan an inaugural reception. gion) and Paul Nichol (York Separate). fu parent organization. Y 4MA is committed to The inaugural reception of Y 4MA was a addition, by the fallof 1989, committees had supporting OAME/ AOEM in every way pos wine and cheese held at York University in been formedto carryout specifiedtasks: write sible including sharing its aims and objectives. November 19, 1987 with guest speaker Bren a constitution, plan a membership drive, create The chapter looks forwardto growing ever dan Kelly. Each of the representatives fromthe a newsletter, and plan a conference. larger and being able to reach more and more four jurisdictions were encouraged to invite The newly formed chapter was energetic teachers of mathematics. It also looks forward people who would be interested in not on1y the and enthusiastic. An annual Fall Mini-Confer to supporting OAME / AOEM activities in evening's events but also in joining a new local ence was initiated on October 4, 1988 with the cluding exploring the possibility of hosting an chapter of OAME/ AOEM. Since that success theme Problem Solving. The following years Annual OAME / AOEM Conference in the ful first event, the chapter has continued to had a Mini-Conference with workshops and a future.There is wonderful expertise and lead grow and succeed. The simple reason for its featured keynote speaker: on November 14, ership in these four jurisdictions among the success is twofold:strong and talentedleader 1989, with theme Mathematical Investigations people that give so generously of their time and ship and a hunger for professional develop and keynote speaker Dr. Pat Rogers, York energy. The driving forceis their mutual vision ment opportunities in each of the four University and on November 13, 1990, with of excellence in Mathematics Education. jurisdictions. theme New Directions in Mathematics and A BRIEF HISTORY OF NWOAME MARILYN HURRELL Mathematics and Science teachersin North westernOntario (the area of Ontario bounded on the East by Sault Ste. Marie and on the West by the Manitoba border) have had association with their counterparts in the rest of the prov ince formany years. As well as I can traceback, persons such as Bill and Martha Gartrell,Len Clendenning, Gerry Vervoort, Brooks Rapley, among others, belonged to the OATMP, and travelledto meetings in the 50's and 60's. In theearly 1970's Gerry Vervoort, Brooks Rapley and themathematics staffof the Lake head College of education organized a well attended Mathematics Conference. In 1987 a local group of teachers organized "MathNorth west", the first conference for Math teachers from across NWO. It was held at the Valhalla Inn in ThunderBay and such a success that a FROM THE GALLERY: MORLEY MACGREGOR need was evident foran association forMath ematics teachers, centred in this part of the Sampson, Dryden, Dale Cooper and Holly Province. Joe Hall, on behalf of the Steering Stortini, east to Marathon, and Bill McKay, FROM THE ARCH IVES committee forNWOAME, in February, 1988, Geraldton. invited all educational institutions and Boards NWOAME'89 and '90 have been held in EDITORIAL across NWO to support such an Association. September at Confederation College for the RALPH STANTON Othermembers of the steering committee in past two years. The Executiveremains largely . . . And now to change the subject for a cluded Russ Garrett, GerryVervoor tand Brooks unchanged, but for a new Treasurer, Doug while. You have probably noticed that there is Rapley. Martin, and Councillors WilfDurham and Lin now a change on our frontcover. TheSamuel Response was favourableand onDecember da Horton. These Conferences have been ex Beatty Fund has been added to the list of 3, 1988, the First Annual NWOAMEConfer tended to Friday afternoon,dinner and Saturday sponsorsof the Ontario Mathematics Gazette .. . ence was held at Lakehead University. Fifty morning sessions. About 100 teachers, both VOLUME 2, NUMBER 3, one Mathematics teachers attended Saturday elementaryand secondary fromeast and west DEc::EMBER1963 sessions. Morley and Mona MacGregor trav as well as in-town, have attended. This past elled to ThunderBay for this occasion to repre year, several of our speakers were fromOAME. sent OAME. Morley was very supportive of NWOAME submitted materials for the our effort,both morally and financially. We in Gazette/Abacus forDecember 1990. NWOAMEremember him fondly. Although we are a relatively youngAssoci The first Executive consisted ofChairper ation, I feelthat the past three years have done son, Marilyn Hurrell, Vice-Chair, Bill Otto, a great deal to introduce teachers in NWO to and Secretary-Treasurer, Greg Giddings. Wayne OAME, and perhaps more importantly, to let Fletcher, Carolyn Carlson, Lakehead Board of OAME and Southern Ontario to know that Education, GerryVervoort, Lakehead Univer there is a very active Mathematics community sity and Doug Cole, Confederation College, inNWO! rounded out .the Executive. Communication is obviously very important since we deal with such a large area, so we elected some council lors to help us "spread the word" across NWO. These included Paul Sveinson, Fort Frances, Chris Frank and David Ross, Kenora, Barry WESTERN ONTARIO MATHEMATICS ASSOCIATION:A BRIEF HISTORY OF ITSBRIEF HISTORY TOM GRIFFITHS The geographic regions surrounding the cities of London and Sarniawas served by the original South Western Ontario Mathematics Association in the 1970's, but with the demise of that organization there was no chapter of OAME/ AOEM in the region. Many of the educators involved in mathematics became members of GVMA, and later the new SWOAMEwhen it was formedin 1987-88. In 1989, the organizing group responsible FROM THE GALLERY: BOB SMITH, KEN CARSON, BROCK RACHAR- LONDON 19751 forthe fallmathematics conference at Althouse From the first meeting in April, monthly College decided that it was time the area was FROM THE ARCHIVES served by a chapter of OAME/ AOEM and on meetings have been held to effectthe organiza March 2, 1990, a group of interested people tion of the dinner and conference. gathered at Ron Reesor's house to get the Ele Gibling and Janine Pitman took the EDITORIAL organization under-way. A pro ternexecutive responsibility fororganizing the inaugural din RALPHSTANTON was elected comprising Tom Griffiths, presi ner, which was held on Tuesday, November 13 ... This first issue of the Ontario Mathemat dent; Wally Webster, vice-president; Kay Ap at the London Art Gallery. The guest speaker ics Gazette is made possible through the fman pelby, treasurer;Ron Reesor, secretary; Rudy was Dr. Robert Thirsk, one of the Canadian cial assistance of the Ontario Mathematics Neufeld, communications and computers.Oth astronauts. The occasion was a very successful Commission (through itsAdvisory Committee erspresent at this meeting were George Allan, gathering, with nearly 100attending and shar on Research and Publications) and the Ontario John Clarke, Mike Dawes, Doug Edge, Mike ing a delightfulevening. Association of Teachers of Mathematics and Elsie, Ele Gibling, Duncan Isaksson, Barb At the time of writing this history, the orga Physics. fudeed, theGazette includes among Kaiser, Murray Kucherawy, Ken Mason, Mike nization of the spring conference is underway its functions those previously performed by the Mitchell, Bob Newman, Barry Onslow, Allan and planned forApril 4th. The fall conference OAMP Newsletter; it can be considered as a Pitman,Janine Pitman, Walker Schofield and in 1991 will be held at Althouse College and successor, inamplified form,of the Newsletter. Peter Weygang. This group represented most will be organized in co-operation with the Among the aims of the Gazette will be that areas of mathematics education in the region, Althouse mathematics department, all of for of increasing the liaison between secondary both geographically and by educational inter whom are involved in WOMA. Also at time of school teachers and students on the one hand writing our membership has just surpassed 100 and university professors on the other hand. It est ( elementary, secondary, university, college of education, community college, administra (the key number forthis centennial issue in this is hoped that portions of the Gazette will attract tion and ministry). centennial year of mathematics associations in student readers;perhaps this aim could best be It was decided that the main role of the Ontario). achieved if mathematics teachers would influ organization was communication. The major ence their boards to buy bulk lots of future methods used to serve this objective are a THE MORLEY Gazettes, since most boards probably have newsletter, mail network, computer network, MACGREGOR funds set aside for purchase of educational conferences and other meetings. It was decided MEMORIAL AWARD literature and materials ... that a fall conference would be the annual Thisannual award, to commence in 1991, is VOLUME 1, NUMBER 1, FEBRUARY 1962 gathering of the organization. For the initial administered by OAME/ AOEM but the set year however, since the Althouse College group ting of criteria, naming award winner, etc., are were already organizing a conference in Octo to be responsibility ofWOMA.The award pays ber, it was decided to hold an inaugural dinner the registrationand banquet feefor a "Junior to in November and a spring conference inApril. 8 teacher in Lambton county." HOW IT All STARTED
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