Journal of the British Columbia Association of Mathematics Teachers
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ECT(DR Journal of the British Columbia Association of Mathematics Teachers 1 Volume 26 Number 1 Fall 1984 B.C. Association of Mathematics Teachers 1984-85 Executive Committee Past President Ian de Groot Denis M. Hamaguchi 3852 Calder Avenue 3807-22nd Avenue North Vancouver, BC V7N 3S3 Vernon, BC V1T 1H7 H: 980-6877 5: 985-5301 H: 542-8698 S: 545-0549 President, PSA Council Delegate, Membership Person and Newsletter Editor J. Brian Tetlow John Kiassen 81 High Street 4573 Woodgreen Court Victoria, BC V8Z 5C8 West Vancouver, BC V7S 2V8 H: 479-1947 S: 479-8271 H: 926-8005 S: 985-5301 Vice-President Primary Representative Garry W. Phillips Wendy Klassen 4024 West 35th Avenue 49-6880 Lucas Road Vancouver, BC V6N 21`3 Richmond, BC V7C 4T8 H: 261-4358 S: 526-3816 5: 274-9907 Secretary Intermediate Representative Nigel A. Cocking Doug Super 4-1333 Fort Street 313-2255 York Avenue Victoria, BC V8S 1Y9 Vancouver, BC V6K 105 H: 595-7716 S: 479-8271 H: 736-0960 Treasurer Post-Secondary Representative Jessie Rupp Ian de Groot - 1122 Duchess Avenue 3852 Calder Avenue West Vancouver, BC V7T 1H2 North Vancouver, BC V7N 3S3 H: 922-8315 S: 922-3931 H: 980-6877 5: 985-5301 Journal Editors Tom O'Shea NCTM Representative 249 North Sea Avenue Jim Sherrill Burnaby, BC V5B 1K6 2307 Kilmarnock Crescent H: 294-0986 North Vancouver, BC V7J 2Z3 0: 291-4453 or 291-3395 H: 985-0861 0: 228-5512 Notice to Advertisers Notice to Contributors Vector, the official journal of the British We invite contributions to Vector from all Columbia Association of Mathematics members of the mathematics education Teachers, is published three times a year: community in British Columbia. We will fall, winter, and spring. Circulation is give priority to suitable materials written approximately 550, mainly in B.C., but it by B.C. authors. In some instances, we includes mathematics educators across may publish articles written by persons Canada. outside the province if the material is of particular interest in British Columbia. Vector will accept advertising in a number of different formats. Pre-folded 21.5 x 28 Contributions may take the form of letters, cm promotional material may be included articles, book reviews, opinions, teaching as inserts at the time of mailing. Advertis- activities, and research reports. We prefer ing printed in Vector may be of various material to be typewritten and double- sizes, and all must be camera-ready. Usable spaced, with wide margins. Diagrams, if page size is 14 x 20 cm. Rates per issue are possible, should be camera-ready. We as follows: would appreciate a black-and-white Insert: $150 photograph of each author. If feasible, the Full page: $150 photo should show the author in a situa- Half page: $ 80 tion related to the content of the article. Quarter page: $ 40 Authors should also include a short state- ment indicating their educational position Deadlines for submitting advertising for the and the name and location of the institu- winter and spring issues are December 1, tion in which they are employed. 1984 and April 1, 1985. Inside This Issue 5 From the Editors ................................................ Tom O'Shea 6 Letters .................................................................... 9 The 1984 NCTM Annual Meeting................................. John Kiassen 11 Did You Know That ........................................... Ian de Groot Mathematics Teaching 12 A Word About Word Problems..................................... Bonar Cow 15 Brain Teasers for Intermediate Students ....................................... 16 The Answer As a Key: Does It Shut or Open the Door in Problem-Solving? ............................ Walter Szetela 23 Bulletin Boards: An Enrichment Tool ....................... Bernadette L. Harris 26 Diagnosing Pupil Performance in Decimal Multiplication.......... James H. Vance 33 The Terrible Demise of an Algebra Flunk-Out...................... Susan Quinn Mathematics Issues 37 Streaming in Mathematics at the Junior Secondary Level .......... Hugh S. Elwood 40 Mathematics Teacher Qualifications: A Principal Reacts ............... Ed Collins Miscellaneous 42 The 1984 Euclid Mathematics Contest ........................... George Bluman 47 The Third Annual SFU Mathematics Enrichment Conference ........ Larry Weldon 48 1984-85 BCAMT Executive Meeting Dates..................................... 49 The 1984 BCAMT Summer Conference ........................... Garry Phillips 50 1983-84 BCAMT Financial Statement ........................................... 51 New Books Across My Desk ........................................ Ian de Groot 90m Howitz Memorial Scholarship The mathematics education community was saddened by the news of the death of Dr. Tom Howitz on August 8, 1984. Tom's many con- tributions to mathematics education in B.C. and beyond were featured in the last issue of Vector. The Department of Mathematics and Science Education at UBC is creating a scholarship in the memory of Tom. If you would like to con- tribute to the fund to set up the scholarship, make a cheque out to Jim Sherrill and send it to the following address: Jim Sherrill Faculty of Education 2125 Main Mall The University of British Columbia Vancouver, BC V6T 1Z5 Tom O'Shea From the Editors Tom O'Shea and Ian de Groot We have had a number of favorable com- terrors of testing and the deficiencies of the ments on the quality of the previous issue present mathematics curriculum. of Vector, and we are pleased that the articles in that issue seemed to meet the needs Controversial issues in mathematics educa- and interests of mathematics teachers. tion are addressed by Hugh Elwood and Ed Vector has always enjoyed a good reputa- Collins. In response to the ministry's white tion, not only in this province, but across paper on curriculum, Elwood argues for the Canada. For that reason, we have decided introduction of streaming at the junior to upgrade the physical quality of the secondary level. Collins takes a hard look, journal. As a first step, we have moved to through the principal's eyes, at teacher a heavier cover, with perfect binding. We qualifications. We encourage readers to sub- hope that readers will approve of the mit opinions on these and other issues of changes. Your comments are most welcome. concern. In this issue, we have again put together a Finally, we present reports from various variety of articles. Bonar Cow provides a sources. John Klassen and Carry Phillips delightful example of how problem-solving look at the annual conferences of the NCTM can be introduced into the elementary class- and the BCAMT. George Bluman reports the room. Walter Szetela's extension of the results of the 1984 Euclid contest, and Larry checkerboard problem is an excellent exam- Weldon summarizes events at the 1984 SFU pie of the power of - Looking Back in high school enrichment conference. problem-solving. Bernadette Harris gives many fine suggestions for using bulletin If you like the contents and appearance of boards for enrichment at the junior secon- the journal, let us know. The new binding dary level. Jim Vance's article on decimal requires that the journal be at least three multiplication is a model of a research pro- centimetres thick, so we need lots of con- ject that yields important insights into tributions. Deadlines for the winter and students' thinking in mathematics. Susan spring issues are December 1, 1984 and April Quinn's fantasy is a timely reminder of the 1, 1985. 5 AW hi AWAIF Capilano College question and hopefully has a number of in- 2055 Purcell Way teresting applications at hand. North Vancouver, BC V7J 3H5 The minimal qualifications necessary for Dear Mr. de Groot, "Content Awareness" are the easiest to The Capilano College Mathematics Depart- address. Minimally we believe that all ment recently discussed the issue of teachers of mathematics in the public school qualifications of teachers who teach mathe- system should have Algebra 12. Further, matics in the public schools of British Algebra 11 and 12 teachers should have at Columbia. While we admit that we are not least a mathematics or physics major in their aware of all of the present requirements undergraduate degree. What formal post- necessary to teach mathematics at the secondary mathematics training a teacher of various grade levels, we were able to iden- K-10 should have is unclear, although it does tify the following three areas of critical not seem necessary (or practical) that they importance to the qualifications issue: be specialists in math. Content Awareness The necessary qualifications for "Attitude" To gain the mathematics content familiar- and "Application" are more difficult to iden- ity, a teacher must have successfully com- tify. One step in this direction would be the pleted a number of courses beyond the requirement that all teachers of mathematics content level of the course that he/she 'is must complete at least one full year course teaching. in mathematics education. Further, mathe- matics teachers should be encouraged to Attitude pursue studies in mathematics-related fields One of the greatest areas of concern to our such as computing or technology. department (that many of us have observed first hand with our children in the public Hopefully these comments will be of assist- school system) is that mathematics is all too ance to your committee in the preparation often taught by a teacher who, while tech- of its report on the qualifications of teachers nically qualified to teach the subject, has of mathematics. very little enthusiasm for it. Often negative feelings toward the discipline are unwittingly Yours truly, passed on to the student. A.E.T. Bentley Application Co-ordinator of Mathematics How often have we as mathematics teachers been asked "What applications does this have?" or more bluntly "What good is this?" A good mathematics teacher anticipates this 6 University of Victoria abacus does not "fit" into this part of the in- Faculty of Education structional sequence. These are points well P.O. Box 1700 made. However, one danger should perhaps Victoria, BC V8W 2Y2 be pointed out.