THE NEWSLETTER OF THE MATHEMATICAL ASSOCIAnON OF AMERICA Martin Gardner Receives JPBM voIome 14, Number 4 Communications Award Martin Gardner has been named the 1994 the United States Navy recipient of the Joint Policy Board for Math• and served until the end ematics Communications Award. Author of of the Second World In this Issue numerous books and articles about mathemat• War. He began his Sci• ics' Gardner isbest known for thelong-running entific Americancolumn "Mathematical Games" column in Scientific in December 1956. 4 CD-ROM American. For nearly forty years, Gardner, The MAA is proud to count Gardneras one of its Textbooks and through his column and books, has exertedan authors. He has published four books with the enormous influence on mathematicians and Calculus Association, with three more in thepipeline. This students of mathematics. September, he begins "Gardner's Gatherings," 6 Open Secrets When asked about the appeal of mathemat• a new column in Math Horizons. ics, Gardner said, "It's just the patterns, and Previous JPBM Communications Awards have their order-and their beauty: the way it all gone to James Gleick, author of Chaos; Hugh 8 Section Awards fits together so it all comes out right in the Whitemore for the play Breaking the Code; Ivars end." for Distinguished Peterson, author of several books and associate Teaching Gardner graduated Phi Beta Kappa in phi• editor of Science News; and Joel Schneider, losophy from the University of Chicago in content director for the Children's Television 10 Personal Opinion 1936, and then pursued graduate work in the Workshop's Square One TV. philosophy of science. In 1941, he enlisted in

12 Stroik Centenary Recognition and Rewards in the Mathematical Sciences Lecture Allyn Jackson But today the debate is taking on added urgency as colleges and universities struggle to respond This article was also published in Noticesofthe 16 Networks in American Mathematical Society, May/June to increasing demands from government and 1994,andappearshereinslightlydifferentform. the general public. A number of reports, most FOCUS notably Scholarship Reconsidered: Priorities How can mathematical sciences departments of the Professoriate, by Ernest Boyer, have 20 MAA Gopher evaluate and reward the full range of faculty explored the question of what constitutes schol• activities? How can teaching be evaluated? arship and what the appropriate balance is What constitutes "scholarship"? How should between teaching and research. 22 1993 Annual service to one's institution or to the profession The mathematical sciences community has at• Report be rewarded? How should departments bal• ance research, teaching, service, and tempted to take the lead in examining these scholarship in making decisions about pro• issues. The Committee on Professional Recog• motions, tenure, and salary increases? nition and Rewards of the Joint Policy Board 39 Employment for Mathematics was established in 1991 to Opportunities Such questions have long been the subject of examine the rewards systems currently in place debate within the mathematical sciences com• munity and within academia more generally. Please see Rewards on page 3

The Matbematk:81 JUS Places First in 35th International Mathematical Olympiad AaodIItioa ofAmerIca 1529Eipteeoth Street, NW and Makes History with Six Perfect Scores. Washington, DC 20036 More details in the October FOCUS. FOCUS August 1994 FOCUS Editorial FOCUS is published by The Mathematical Association of America, 1529 Eighteenth The Report on the Recognition and Rewards in the Mathematical Sciences from the Street Northwest, Washington, DC 20036• Committee on Professional Recognition and Rewards of the Joint Policy Board for 1385,six times a year: February,April,June, Mathematics started landing on the desks ofmathematics department chairs in late May August, October, and December. and early June. [See the article on the front page.] It is sure to set off considerable Editor and Chair of the MAA Newsletter discussion in the mathematics community. I am certain that photocopies of various Editorial Committee: KeithJ. Devlin, Saint sections will find their way onto the desks ofdeans and college presidents as mathema• Mary's College of California ticians try to foster change in the way they do business. Associate Editor: DonaldJ.Albers,MAA One of most hotly debated items is likely to be the means used to evaluate college and Associate Executive Director, and Director of Publications and Programs university teaching. This is, of course, hardly a new issue, but the new report will undoubtedly rekindle the fire. Managing Editor: Harry Waldman, MAA I confess that the longer I have been in the business of academic administration (first at Production Specialist: Amy Stephenson, department chairlevel, now as a dean), the less happy I am about the way this is currently MAA done at most institutions. Proofreader: Meredith Zimmerman, MAA Maybe I should start by backing up a bit. The early part ofmy careerwas spent in Britain, where there were no institutionalized student evaluations of teaching. As a fairly fre• Copy Editor: Nancy Wilson, Saint Mary's quent visitor to the USA, often for periods of one or two semesters at a time, where I College of California would teach one or two courses at a time, I went through the familiar end-of-semester Letters to the editor should be addressed to: student evaluation process, and found it extremely useful. Keith Devlin, Saint Mary's College of California, P.O. Box 3517, Moraga, CA As a visitor, my career in no way depended on the results, but the process was neverthe• 94575, e-mail: [email protected] less stressful. It is virtually impossible to please all of the people all ofthe time, and so The FOCUS subscription price to individual I would brace myselffor the almost inevitable complaints, and just pray that they were members of the Association is $6.00, few in number. included in the annual dues. (Annual dues But for all that the process was stressful, I found it very useful, and I am sure that the for regular members, exclusive of annual subscription prices for MAA journals, are feedback I received contributed greatly to better teaching on my part-and I should say $68.00. Student and unemployed members that in the traditional teaching versus research debate, I have always come down firmly receive a 66 percent discount; emeritus in the middle, regarding both activities as important and enjoyable (and, for that matter, members receive a 50 percent discount; new mutually supportive, though in different ways for the two directions). Student evalua• members receive a 40 percent discount for tions ofteaching are, I am sure, a valuable tool for the instructor. When I returned to the the first two membership years.) UK after my first spell at a US university, I imported the student evaluation procedure Copyright © 1994 by The Mathematical for my own use to gain feedback on my teaching. Association of America (Incorporated). Educational institutions may reproduce The question is, how valuable are student evaluations in terms of judging teaching articles for their own use, but not for sale, performance as part of the faculty evaluation process? In my view, this question does provided that the following citation is used: not have a simple answer. "Reprinted with permission of FOCUS, the newsletter ofThe Mathematical Association Having had experience reading evaluations as a chair, a dean, and a member ofa tenure of America (Incorporated)." committee, I have no doubt that, when read in an appropriate manner, the forms can provide valuable information. (All the evaluation forms I have had to deal with have Second-class postage paid at Washington, provided both statistical information and individual student comments, and it was the DC and additional mailing offices. Postmaster: Send address changes to the combination of the two kinds of information that seemed useful. Statistical data on its Membership and Subscriptions De• own would strike me as being extremely uninformative.) partment, The Mathematical Association of However, if student evaluations were the only source of information, I would be very America, 1529Eighteenth Street Northwest, Washington, DC 20036-1385. uncertain as to how much weight to attach to them. They present a very one-sided view. Moreover, they are written by individuals who, by definition, are not in a position to ISSN: 0731-2040 evaluate many important aspects of teaching, such as does the course cover the really Printed in the United States of America. important topics, is it correct, is it up-to-date, is the standard comparable to that at Printed on recycled paper. similar institutions? It is in conjunction with a number of other evaluative mechanisms that the student evaluations help form a reasonably all-round picture. Equally important are peer evalu• ations (which, to ensure fairness, should be carried out not by a single individual but by groups of two or three faculty, one or more of whom should be chosen by the person being reviewed). Experienced colleagues can see important components of good (or @------poor) teaching that a student could not. August 1994 FOCUS well its faculty, its institution, and its con• eral consensus about the importance of Rewardsfrom page 1 stituents. The guidelines could also be used research, most faculty would like to see a in mathematical sciences departments and in negotiations between departments and broader and more flexible rewards struc• to formulate guidelines to assist depart• administrations about changes in the re• ture that values not just research, but also ments in making decisions about their wards system. teaching, scholarship, and service. In par• rewards systems. With funding from the ticular, there is a wide array of activities National Science Foundation and the The Report's Findings which many faculty believe should count Exxon Education Foundation, the com• The first section ofthe report presents ten for more in the rewards system; these ac• mittee carried out site visits to twenty-six findings which describe what the commit• tivities include classroom teaching, service institutions, as well as a survey of nearly tee observed on its site visits and in its to the institution or to the profession, in• 2,000 mathematical sciences faculty and survey. The findings provide a look at re• terdisciplinary research, research on over 600 chairs in departments of various wards systems as they operate in educational issues, expository writing, and types (including Ph.D.-granting and mathematical sciences departments to• student mentoring and advising. Some• bachelor's-granting institutions and two• day-how faculty feel about them, what times the rewards system can actually year colleges). In presentations at influences rewards systems, how they are discourage work in these areas, even when numerous meetings and conferences, the changing. As might be expected, research the work is extremely important to the committee aimed to inform the math• plays a central role in the rewards systems department and the institution. The report ematical sciences community about its at most institutions, and faculty believe particularly notes a "great dissatisfaction work. The culmination of these efforts is that this is as it should be. The survey asked about inadequate rewards for faculty's the report Recognition and Rewards in about the importance to rewards systems educational responsibilities." the MathematicalSciences, which was re• of three kinds of research: research in the leased in early May. Despite these tensions, there have been discipline, interdisciplinary research in• changes in the last five to ten years. In The report does not contain a "blueprint" volving new mathematics, and particular, the report points out a gradual for a rewards system. Indeed, the com• applications of existing mathematics to evolution inmathematical sciences depart• mittee was very much aware that no single otherfields. The survey found widespread ments along two parallel tracks: rewards system could be workable in all agreement that research in the discipline departments which traditionally empha• mathematical sciences departments in all is very important. Interdisciplinary and sized teaching are placing heavier kinds of institutions. Rather than making applied research were also viewed as im• emphasis on research, while departments prescriptive recommendations, the report portant, though not as important as which traditionally emphasized research provides guidelines that any department research in the discipline. are placing greater emphasis on teaching. can use as a basis for discussions about The report indicates that.despite the gen- how to craft a rewards system that serves Please see Rewards on page 14

Letters from paststudents can also be use• now theplotthickens. Evaluationofteach• including stylized student evaluations as ful. Indeed, I recall a number of occasions ing is not the same as observation of a part of a comprehensive evaluation of where past students wrote in to say that, distant planetthrough a telescope; the very teaching. But I don't think this is the case. although they had been highly critical of process of evaluating teaching has a di• My own opinion is that we would be bet• Professor X at the time, with hindsight it rect, and, in my experience, very ter off looking for alternative ways to had become clear that Professor Xhad been significant effect on teaching. It would be secure student input. (I am not for a mo• a very good teacher. (Obviously, such let• a rare individual who, faced with the hurdle ment suggesting we do not listen to what ters are only valuable if solicited by the of tenure or promotion, could resist the our students have to tell us.)As things stand evaluationcommitteeon a random or blan• temptation to "teach to the evaluation". right now, I think that we have a system ket basis.) And, with the best will in the world, I can• that, by inhibiting good teaching, may do not see the pursuit of glowing student Another important part of the review pro• more harm than good to our students' evaluations as necessarily leading to bet• cess, in my opinion, is a discussion education. ter teaching. Good teaching, that is to say, between the instructor and the evaluation teaching that is of long-lasting benefit to Needless to say, this is just one person's committee or its chair. What might seem the student, involves a significant degree opinion, not a carefully drafted report of a to be negative aspects of a profile could of discomfort-thediscomfortthat comes detailed study. My words are designed to look very different when placed in the with pushing beyond what is known and prompt thought and debate, not to be used context of what the instructor is trying to what is familiar. In my experience, enough as a recipe. Doubtless, readers of FOCUS achieve. students react negatively to that discom• will have their own opinions. The pages The sum total of my observations so far is fort to cause many (most?) young, of FOCUS might be an excellent medium that, as part of a more comprehensive untenured faculty to ease off, if only sub• to air those views. evaluation procedure, studentevaluations consciously. -Keith Devlin (which should include studentcomments) For all its obvious faults as a system of The above are the opinions ofthe FOeUS can be useful for those charged with the government, democracy is the least ter• editor, and do not necessarily represent task of evaluating faculty teaching. But rible. It may be that the same is true for the official view ofthe MAA. ------@ FOCUS August 1994 CD-ROM Textbooks and Calculus Roland E. Larson This is the second part of an article that In either setting, animations appeal to the of three dimensions. began in the June 1994 issue of FOCUS. visualleamer in all of us. • The motion of objects such as rockets The first part discussed two advantages of For acalculus instructorwho has struggled and automobiles can be animated. a CD-ROM calculus textbook: storage with chalk drawings or preparation of capacity and interactivity. "Part II" looks Figure 2 is the first screen of an animated overhead transparencies, it iseasy to imag• at two additional benefits: use ofmultime• dive. Asequence of eighteen frames shows ine dozens of other animations that can dia and nonlinear organization. the diver leaving the platform, rising, and assist with the instruction of calculus. Here then falling to the water. As with the ani• Use of Multimedia: A printed calculus are a few examples. mation shown in Figure I, the dive can be textbook makes use of a single medium, • Transformations of graphs in the plane played or viewed step-by-step. The explo• print, to convey information. A multime• can be animated so that students can ration that accompanies the animation asks dia textbook uses print, motion, and sound. "see" vertical shifts, horizontal shifts, the user to analyze the dive visually, nu• You don't have to think much about the and reflections. merically, and analytically. potential uses of motion in a calculus text• book before you come up with an exciting • The generation of a solid of revolution As appealing as they are, animations are list of possibilities: animations, simula• can be animated to allow students to see only part of the brave new world of mul• tions, video clips, and portrayal of how a two-dimensional region traces out timedia calculus. Simulations carry the three-dimensional objects. a three-dimensional solid. concept of an animation one step further. The difference between the two is that an Animated motion can bring life to calcu• • The process of finding the limit of a Ri• animation depicts the same motion each lus instruction. For instance, Figure I emann sum can be animated to allow time it is played. With a simulation, the shows an animation of a secant line ap• students to see how the approximation motion is dependent on user input. proaching a tangent line. The animation tends to improve as the maximum sub• can be "played" or viewed step-by-step. interval width approaches zero. For instance, the simulated motion of a baseball could depend on the initial speed As part of a CD-ROM calculus textbook, •A three-dimensional surface can be ani• and direction of the baseball and the speed animations are ideally suited forclassroom mated to rotate in space. This type of and direction of the wind. Some simula• demonstration and individual student use. animation greatly enhances the illusion tions go one step further and introduce chaos into the simulation so the result is not entirely predictable. The function s thatgivesthe position(relative to the origin) Much has been written about the three• of anobjectas a function oftimet iscalled aposition pronged approach to problem fanction. If, overaperiod ornme dr,the objectchanges it3 positionby the amount.o.s = set +M) - s(t), then,by the solving-graphical, numerical, and ana• familiar formula lytical. Simulations add a dynamic fourth Distance approach to problemsolving-theexperi• Rate = --:=--• Time mental approach. Consider the classic the aYerqe velocity is problem of finding the angle to project an Change in distance .ds """"::::---:--:-- = -. Average velocity object from the top of a cliff to travel a Change intime M maximum horizontal distance. The ana• Supposeyou wanted to find thevelocity of anobject lytic solution of this problem is at a particulartime~ ay when t = 1. Just as you can approximate theslope ofthe tangentline by calculating the surprisingly tedious, but a simulated solu• slope ofthesecant tine, youcan approximate thevelocity IIII tion is actually fun. at t = 1 bycalculating the average velocityoverasmal1 Animation interval [1,1 +M], as ind~ated inthe figure. Bytakingthe The average velocity In addition to animations and simulations, limit as.o.t approaches zero,you obtainthe velocity when between tl and fl is theslope a multimedia calculus textbook can also t = 1. Thevelocityattimet is atsocaTIed theinriantaneoul' ofthesecanttine,andthe include video clips that transport the user velocity at timet. instantaneous velocityattl is into real-life settings such as rocket liftoffs, theslope ofthetangentline. interviews with engineers and mathema• ticians, on-the-job construction sites, and tours of scientific laboratories or research centers. Figure I This animation contains a sequence of twelve frames that show a secant line's approach to a Nonlinear Organization: A printed cal• tangent line. The creation of the animation involved several different software programs, beginning with culus textbook has a linear organization. a program that generated the graphs. After the graphs were completed. other programs were used to an• notate, digitize, and crop the frames. Finally, animation software was used to assemble the screens. Page 2 follows page I, page 3follows page <@------August 1994 FOCUS

ton provides a discovery mode for getting into the section'sconcepts. And, of course, Using the Derivative to Find Velocity for those users who want to jump right into the examples or exercises, those op• Attlme t = 0,a diverjump.!from a diving boardthatIs32 feet above the water. Thepo.smon ofthe diverisgivenby tions are also possible. set) = -16~ + 16t +32 Allin all,the seventeen buttons of the open• where sis meuured in feet andtis measured inseconds. ing screen lead to 171 different screens, L Whendoesthe diverhit the water? some of which contain "live" mathemat• b. Whatisthe diver's velocityat Imp~t? ics that can be edited to provide an SOLUTION unlimited number of examples. L Tofind whenthe diverhitsthe water,lets = 0 and The advantage of this type of hypertext solvefort to obtaint = 2. organization is that it easily adapts to a variety of uses. It provides quick tours for b. Thevelocityattimet isgivenbys'(t) = - 32t + 16. those who want a "lean" presentation, but Thevelocityattimet = 2 Is it also provides options for those who want 8'(2) = -32(2) +16 = -48 ftI.sec. additional helps, historical insights, real• IIII life applications, explorations, and so on. Animation Thus, CD-ROM technology with hypertext programming is able to answer - the decade-old call for a "lean and lively" calculus.

Figure 2 This animated dive contains a sequence of eighteen frames that show a diver leaving the plat• A nonlinear organization not only in• form, rising, and then falling to the water. As the diver moves through the air, the times are projected creases the versatility of a CD-ROM onto the animation screen. By viewing the animation step-by-step, the viewer can compare the times (I = 0,1= 0.5, 1= I, and so on) with the diver's heights. The exploration button asks the user to analyze the calculus textbook, it also helps solve an dive numerically, graphically, and analytically. age-old dilemma with printed textbooks: the amount of explanationthat is presented 2, and so on. In practice, however, most ton" and "career interview button" pro• on a page. Every time an author adds more students don't use textbooks linearly. vide real-life motivation for the concepts Thus, the organization of a printed text in the section. The "Explore it First" but- Please see CD-ROM on page 13 doesn't conform to its use. Of course, a CD-ROM calculus textbook could be organized linearly so that a user would be forced to move from one screen to the next. But the point is that the CD• In Section2.1youusedthelimit definition to find ROM format doesn't require an author to derivatives. Inthissectionyou winbe introduced toseveral use a linear organization. "differentiation rules"that anowyouto find derivatives without thedirBctuse ofthelimit definition. Thenyou will By using a nonlinear (or hypertext) orga• .see howthe derivative is usedto detenninerates ofchange, nization, an author can provide additional such asthe rateofchangeinthe heightof a free-faning object details, helps, examples, explorations, and with respectto time. excursions without cluttering the basic concepts of a section. Explore it fbost As an example, consider the opening sec• EXAMPlES I tion screen shown in Figure 3. A user who CONCEPT EXPLORAT10N wants only a quick overview of the sec• Basic Differentiation Rules -- tion can select the three "conceptbuttons." The main path through the three concepts of this particular section consists of only Denvatin of 8ine and Cosine nine screens. While on this main path, stu• Rates of CJumae dents can take optional paths that provide proofs, additional remarks, or historical insights. Instead of browsing through the quick Figure 3 A nonlinear (or hypertext) organization is evident from this opening screen for a section. The overview, a user can approach the section 171 screens in the section cannot be traversed with a single linear path. Instead, users navigate through the screens as if they were moving along the branches of a tree. Users who want more help or details can along other paths. The "connections but- move further out on the branches, while those who want quick tours or a general overview can stay close to the tree's trunk. ------~ FOCUS August 1994

cret ofteaching, I would say "enthusiasm." with functional Open Secrets Enthusiasm makes mathematics lively and notation, I tell exciting. It conveys love for the subject them, "Takefix) = 2 Justin J. Price and its beauty. So I will exclaim, "Wow! x • Whatever ap• Euclid proved there are infinitely many pears in the Remarks on receiving the MAA's 1993 primes, starting from practically nothing. window, you National Award/orDistinguished Teach• Isn't that incredible? I get goose bumps square it. I don't ing, Cincinnati. Ohio, January 1994. every time I think about it," or, "Isn't it care if it's your Here is what one student wrote on his marvelous that you can evaluate certain grandmother, you evaluation of my teaching: "Since I hard definite integrals just by computing square her." I call this my Grandmother stopped comingto your lectures, my grade a residue?" Students need to see someone Principle, and the students like it-except has gone up from an F to a c." So before who is excited by mathematics. Unfortu• one who wrote on an evaluation, "Please the MAA changes its mind, let me express nately, many of our freshmen have never leave my grandmother out of it." my thanks for its recognition. had that experience. Let me mention a few other teaching prin• Pythagoras on the Porch Positive Terms ciples. The Charades Principle. I'm a good cha• lowe my lifelong interest in teaching to Excitement produces a healthy attitude rades player, although I'm a lousy actor. I my father who was an inspiring teacher. I towards doing mathematics. Recently, I just take some time to get my team tuned remember, at age eight or nine, how my observed a TA showing a college algebra in on approximately the right wavelength. friends would come to the front porch of class how to solve the system If asked to act out, say, Titus Andronicus, our house in Philadelphiaon summereve• 2 y2 y b I would make some gestures indicating nings because my father would teach us x + =9; =x + that it is a play, and a weighty play. Soon interesting things. I remember especially He was concerned because they had not someone would suggest Shakespeare, and how he told us that certain configurations yet dealt with a parameter. But by saying, we would be nearly home. I use the same in the porch railing were called right tri• "I know this is very hard for you ..." and strategy in teaching. Before plunging in, I angles, that the slanted sides had a funny "I know the b makes the problem confus• try to set the scene by explaining what we name-"hypotenuse"-and that a won• ing ... ," he createda negati ve effect. Later, will be doing, why,and what methods we'll derful thing happens: the square of the I suggested a more positive approach, use. In fact, this approach applies to pre• hypotenuse always equals the sum of the something like, "We are looking for the sentations at all levels. I remember a squares of the legs. intersections, if any, of a circle and a line. colloquium talk that started with the state• That depends on the value of b, and we From an early age, I looked forward to ment, "Consider the category of all can't tell in advance what happens. But being a teacher myself. I wanted to expe• co-groups." I slept through the rest. here is where math is so great! If we go rience that special thrill of seeing the light ahead and solve, the math will tell us the The ll}>att Earp Principle. Wyatt Earp ofunderstanding flash in students' eyes. I answer!"As Mark Kac said, the best thing survived many a gunfight in the Old West. still do. For example, I enjoy teaching we can teach our students is to sit down He didn't do anything fancy; he carried Fourier series to graduate engineers. I point and figure it out. only one gun. But he took an extra split out that expanding a function in a Fourier second to aim and got his man on the first series is like expressing a very long vector A corollary of enthusiasm is freshness. If shot. When students face a showdown at in a large i.j, k coordinate system, and that I am bored teaching the same old stuff, the an exam, I urge them to take a minute and the ans and bns they have been computing class quickly senses it. So I look for ways read the questions carefully. Otherwise• mechanically are just the components to keep the presentation fresh. One way is you know what happens-you pass out along the various orthogonal axes. Their not to use my old notes. Even though I the test papers from the front, and by the reaction is usually, "Wow! That's great! have taught calculus many times and at time they reach the back, the first row has Why didn't anyone ever tell us that?" the end ofeach course have arranged the already erased a page and a half. notes neatly in a folder and filed them in In order to give such insights and make a cabinet, I never look at them again. I The Naked Observer Principle. Throw in mathematics more interesting and acces• want the excitement of learning the sub• something quirky every once in a while to sible, I have developed a number of ject along with the students. stir things up. I like to remark that "to the teaching techniques. But when I began to untrained eye of the naked observer, it prepare a talk about the "secrets of my Grandmothers and Advertising appears that ...." Sometimes this flies right success," Irealized that my techniques are by, but ninety-nine times out often, some• probably used by most concerned teach• Using down-to-earth language helps stu• one catches on. ers, that my secrets are really open secrets. dents learn. Once they are comfortable with a new concept, we can become more Truth in Advertising. Amore serious prin• Goose Bumps formal. For example, I paraphrase the ciple. Sometimes we present an idea in comparison test for series ofpositive terms If you forced me up against a wall and one form, but without warning, apply it in by "smallerthan small is small; bigger than made me express in just one word the se- different form. Take the Mean ValueTheo• big is big." When freshman are struggling rem. It is usually stated as ~------August 1994 FOCUS lfib) - fia)]/(b - a) =r (c) elling in France, is not even aware that sentence. Where appropriate, use equa• one should speak French? A similar illit• tions instead of English, but do not go to but used in the form eracy in the language of mathematics is the other extremeand shun words entirely; fib) - fia) =r (c)(b - a) widespread, and we do very little about it. keep the reader informed of what you are doing. Avoid pronouns as in "Differenti• Mathematically, these are equivalent. But Recently I asked a class of sophomores to ate it, then set it equal to zero and solve it." psychologically, to the untrained eye of derive and explain on paper the formula Rather, differentiatefix), set!' (x) 0, and your naked freshman, they may seem very for the area of a sector of a circle. The = solve for x. Read over what you write. My different. The first is a curious fact about results were appalling. I asked a class of guidelines were published in the College a tangent being parallel to some chord. future math teachers to define factoring. Mathematics Journal, November 1989. Cute, but so what? The second form, how• A typical response: "Factoringis when you ever, provides an estimate for the way a break a number down into smaller num• Now, I don't want to make false claims of function varies from one point to another, bers." No mention of the words "product" success, especially since I advocate truth which is the basic concern of differential or "factor." I asked a class of juniors to in advertising. Writing is hard. Some stu• calculus. That's why the theorem is so express in mathematical notation a se• dents are so non-verbal, they never useful. I think we should not slide over quence that has period 4. Very few had improve. The majority, however, show this important point. any idea; subscripts are a total mystery. progress-not to the extent that I would Such examples show that we are neglect• like, but significant relative to their low We need Truth in Advertising also in the ing an important part of our students' starting levels. One claim I can truthfully definition of linear independence. Many education by not asking them to write. make though: writing focuses students' texts define a set of vectors {v I' V2' ••• , Vn} They need the ability to formulate defini• attention. It makes them aware, often for to be linearly independent if CIV + C + I 2V2 tions, state theorems correctly, use proper the first time, that mathematics is very ... + cnV = 0 implies c = c ... c = O. For n i 2 n notation and vocabulary, and write out precise, that there is a difference between students wrestling with abstraction for the logical solutions to problems. terms and factors, sequences and series, first time, that's hard. It is really a slick expressions and equations, that you don't way of saying that the vectors are linearly I became concerned about writing in the multiply a number by 10 by "adding a independent if none of them can be ex• mid 70s when my department asked me to zero." pressed as a linear combination of the revive an unsuccessful course for math others. So why not define linear indepen• majors intending to teach high school. It Most important, writing makes students dence that way? That's what I do, but then seemed obvious that there are at least two think. It forces them to reexamine what I admit that given an explicit set of vec• necessary conditions for good teaching: they know and sometimes realize that they tors, I don'twant to sit around all weekend you have to know something, and you must don't know what they know. trying every combination. That's the ad• be able to communicate it. Since math vantage of the slick definition; it's not the courses generally ignore communication, Semi-Open one that naturally comes to mind, but it's I devised a course that is fairly modest in I am not the only one who thinks writing more efficient. contentbut requires some serious writing. is important. Paul Halmos in the College Each homework assignment includes three Can Anyone Speak Mathematics Journal, September 1993, starred problems to be written up care• says, "I write notes to myself, explicitones the Language? fully, as if for a note in a journal. The with sentences .... I think by writing ... as writing is not to be directed to the instruc• So far, I have been discussing teaching if I were conducting a conversation be• tor, but to a member of the class who has tween me and myself." Paul Davis'sarticle methods that I am sure all serious teachers been sick and needs to learn the material. use. Now I'd like to mention one that is "Some Glimpses of Mathematics in In• Above all, it must be reader friendly; the dustry" in Notices ofthe AMS, September not so widely used: asking students to write most important person involved in the mathematics. By "writing mathematics" I 1993, explains what industry is looking homework is not the instructor or the stu• forin ourgraduates, and asserts that "teach• mean writingtechnical mathematics: equa• dent, but the reader. tions, exponents, subscripts, and good ing communication skills-writing, mathematical exposition. I do not mean This is a tall order. It means starting at the speaking, listening-is essentiaL" reports on the life of Gauss or essays on beginning, defining terms, using appro• Certainly writing is needed, but it is only the role of statistics in today's world. priate notation and vocabulary, proceeding one of many methods to help students Writing about mathematics is good; writ• logically, etc. To help my students with learn. I have devoted a good bit of space in ing mathematics is better. this kind of assignment, I distribute a set this essay to writing because it is a semi• of guidelines which Irequire them to sleep Unfortunately, many students have almost open secret, less known than my open with under their pillows. Theseguidelines secrets. no facility in the language of mathematics include some very basic rules for civilized although they have been exposed to it since mathematics writing. For example, honor Thank you for allowing me to share all of eighth or ninth grade. Can you imagine the equal sign. Do not write n2 =16 =n = these ideas with you. someone who has taken four or five years 4 or say that an n-gon equals (n - 2)180 of French yet cannot speak or write a degrees. Write in sentences; a +bis afrag• Justin J. Price is professor ofmathemat• simple sentence in French, or when trav- ment, not a sentence; a + b = 15 is a ics at Purdue University. ------@ FOCUS August 1994 Henry L. Alder It is a great pleasure to feature on these 1994 SECTION AWARDEES pages the recipients of the I994 Awards for Distinguished Teaching. The Committee on Awards for Distin• guished College or University Teaching of Mathematics is now in the process of nomi• nating at most three of these distinguished teachers for the third annual national awards. The Board of Governors will act on these nominations at its meeting on August 14, 1994, in Minneapolis. The na• tional awardees will be honored and will James H. Wahab make presentations at the annual meeting David M. Bressoud William Dunham Allegheny Mountain Eastern Pennsylvania Florida in January 1995 in San Francisco. and Delaware At its meeting in Cincinnati, the commit• tee was informed of the generous action of Past-President Deborah Tepper Haimo to endow the national teaching awards with annual contributions of $10,000 over the next five years. To recognize this act, the committee recommended to the Board of Governors that these awards be called the Deborah and Franklin Tepper Haimo Awards for Distinguished College or Uni• versity Teaching of Mathematics. Carroll Wells DavidC. Lay Jerrold If. Grossman This recommendation was approved by Kentucky Maryland-DC-Virginia Michigan the Board of Governors. In addition, the committee approved the following resolution: The Committee on Awards for Dis• tinguished College or University Teaching of Mathematics expresses its deepest appreciation to Professor Deborah Tepper Haimo for her gen• erous donation to the MAA of an amount of $50,000over the next five years to provide funding for the MANs national awards for distin• Mark Krusemeyer Robert L. Devaney JaneM.Day guished teaching. By this action she North Central Northeastern Northern California not only continues her commitment tofoster excellence in teaching math• ematics at the college and university level already so amply demonstrated by the central role she played as presi• dent of the MAA inestablishing these awards, but also has taken a giant step in support of the current national efforts to elevate the teaching of mathematics to the highest level of excellence. The 1995 national award recipients will be Stephen Hilbert designated the first recipients of the A. Duane Porter JohnD. Neff Rocky Mountain Seaway Southeastern Deborah and Franklin Tepper Haimo Awards for Distinguished College or Uni- @Y------August 1994 FOCUS versity Teaching of Mathematics. The extraordinarily high quality of this year's FOR DISTINGUISHED ThACIllNG section awardees will make their nomina• tion a very difficult task. The committee wishes that it were possible for all mem• bers of the Association to read the folders on this year's Section awardees so that all could learn of the highly successful teach• ing skills used by these teachers. The fact that 25 of the 29 sections have selected a section awardee speaks well for the fact that sections are supporting the national effort to identify and reward this Ronald M. Shelton David S. Moore Lance L. Littlejohn nation's outstanding college teachers of Illinois Indiana Intermountain mathematics. The sections' efforts in es• tablishing procedures for nominating and selecting the award winning teachers deserve highest commendation. On September 26, 1994, section secretar• ies will be sent information on the nominations for the fourth (1995) section awards. These guidelines will be essen• tially the same as those for the 1994 awards. The only change in the nomina• tion form is one designed to simplify the requirements for documenting evidence of success in teaching by changing the If. James Lewis Richard Bronson Curtis N. Cooper second paragraph of page 2 of the nomi• Missouri Nebraska New Jersey nation form to read as follows: You are also requested to submit no more than 3 pages of evidence to docu• ment the nominee's extraordinary teaching success. Appropriate docu• mentation may vary greatly from institution to institution but may include summaries of peer or student evalua• tions of teaching, increases in numbers of mathematics majors or Ph.D. candi• dates, or student successes in mathematical competitions. Robert S. Smith Lisa A. Mantini Mildred Jane Johnson Ohio Oklahoma-Arkansas Pacific Northwest In addition, the letter asking section sec• retariesto solicit nominations forthefourth annual awards will include the following para• graph: Section selec• tioncommittees are encouraged to designate some or all of those not cho• sen as a section Mario Martelli Steven M. Shew Montie G. Monzingo Martin Isaacs award winneras Southern California Southwestern Texas Wisconsin candidates to be Please see Awards on page 15 ------@D FOCUS August 1994 ments for me, then call back and remind PERSONAL OPINION the students of their appointments. My first contact with the student would be AcademicAdvising as anAggressive Activity before the semester began, hopefully at William Yslas Velez least a month prior to the start of the se• mester. The first thing I would do is ask No question about it, in the area of math• Attendance was always a problem. Stu• what their majors would be. Secondly, I ematics, Hispanics in this country are dents would not show up for their would go over their schedules with them definitely underrepresented. We all know individual sessions and would skip for the coming semester. This proved to it, we are all concerned about it, and for evening sessions. Nevertheless, Idid learn be a tremendous service. Students can the most part the mathematics community something useful from this experience. make the oddestdecisions as to the courses has been ineffectual in its efforts to in• Students benefit from personal attention they plan to take. I am a firm believer that crease participation of Hispanics in and even good students perform better the average student should take a light load mathematics-based professions. when they have information on which to the first semester that he or she is on cam• base their decisions. I certainly do not have a solution to this pus. The transition from high school to problem; however, I would like to detail Clark Benson left for the National Secu• college, the change in the emphasis of the some modest successes I have had in in• rity Agency after that first year, and I course material, the lack of concern of creasing the number of Hispanic students continued with the same pattern for the many of our faculty for our students, and who chose career paths in science, engi• next year. The number of students in• the simple fact of recently acquiring free• neering, and mathematics (SEM). creased and it was getting harder to get dom are factors that in many cases prove students to show up for their appointments too much for students. Miserable grades Though my own focus has been increas• and to come to the evening group session; during a student's first semesterin college ing opportunities for Hispanics in SEM however, I continued talking to students, can have disastrous effects on his or her fields, my comments really have little to encouraging them to continue with their self-esteem, grade point average, and abil• do with this particular population. The mathematics and science courses. During ity to obtain scholarships and summer methods and ideas I wish to present are advising sessions, I encouraged some to internships. applicable to the entire student popula• join the student chapter of The Society of tion. It is worthwhile to point out that at Many of the students that I saw were first• Hispanic Professional Engineers, a group present Ihave over 35 minority mathemat• year engineering majors. These students for which I had recently become faculty ics advisees, six of which graduated in had already been to see their engineering advisor. May 94. I expect that during the next aca• academic advisors. The advice that they demic year, I will see even more of these I was getting tired of students not showing were given was to take calculus, chemis• minority students graduating with degrees up for their appointments and not coming try, a course in computer programming, in mathematics. to the evening sessions. I found myself English, and possibly one other course. I spending too many depressing hours try• don't think that more than ten percent of Six years ago, Clark Benson and I (at the ing to contact students by phone. The the students could successfully complete time, Clark was a faculty member at the increase in the number of students, as well such a course of study. This proposed University of Arizona, but he is now at the as my frustration, forced me to change the course of study is, in my opinion, elitist. National Security Agency) decided to focus of my contacts with these students. Its effect is to convince the majority of contact all of the minority students who In the third year of my efforts, I gave up students not tostudy engineering. Students were enrolled in first semester calculus. the evening session since I could never who, with a little time, would make very [Throughout this report, "minority" means get enough students to show up. I was also good scientists and engineers, are turned Hispanic, African-American, or Native being swamped by the number of minor• away at the door to these careers before American.] This was an easy task as there ity students who were enrolled in our they have a chance to peek in. were fewer than 25 such students. Our calculus classes. In Fall 1991, we had over contact with them would be as follows: My next topic of conversation with the 200 minority students enrolled in the first student was to discuss the choice of major A) Wemet with each student individually, two semesters of our calculus sequence. with them. At this stage in their careers, each week, for half an hour. During this Clearly I could not meet with this many most students are not aware of the vast time we went over their homework with students on a regular basis. possibilities. Students have heard of engi• them, went over copies of old exams that I decided to meet with as many students as neers, so students who are good at we had saved, and discussed their progress possible for short periods of time and to be mathematics and science usually choose with them in the course. more focused in my contacts with them. this major. One common response to the B) Once a week in the evening we met The following was the plan: I would meet question as to why they chose engineering with the whole group of students and dis• with minority students who were taking is that they were always good at, or always cussed the topics that they were presently first or second semester calculus and hire liked mathematics, and engineering is studying. In particular we stressed test• a student assistant to do the phone con• where mathematics is studied. taking strategies. tacts for me. The assistant's responsibility This point in the conversation allowed me was to call the students and set up appoint- to talk about the mathematics major. At @------August 1994 FOCUS the University of Arizona, the mathemat• We presumably give better advice; how• school teachers? Certainly, we would like ics major has many options-pure ever, a recent incident makes me doubt to see these students teaching mathemat• mathematics, applied mathematics, prob• our own desire to provide sound advice to ics since they have taken a large number ability and statistics, computer science, our university students. At a recent math• of mathematics courses, but these same economics and finance, education, and ematics meeting, I wastalking with agroup students must now return and spend at least engineering mathematics. This flexibility of mathematicians and I brought up my a year obtaining the credentials to teach in makes the mathematics major attractive. aggressive techniques, in particular, that I high school. We need quicker transition of More importantly, so many options lend discourage minority students from choos• these students into the high school class• emphasis to the significance of including ingateaching major early in theirfreshman room. mathematics in the student's course of or sophomore years. I was surprised by The other very real danger in advising is study. This is a point that I stress. Math• my colleagues' reactions and opposition. the way the subject matter is organized in ematics is the key to opening the door to Essentially, they were opposed to my mathematics. I have seen many students a universe hitherto unknown to the stu• methods for three reasons. do quite well in the mathematics courses dent. I. They considered it unethical to impose offered during the first two years--calcu• Many of the students that I have spoken my views on these students. Ius, differential equations, and linear with do not have a clear idea as to what algebra. Then they hit a brick wall, en• 2.There is agreatneed forgood high school direction to take, and here again I stress countering our junior and senior level mathematics teachers, and students should the importance of the choice of calculus. courses in algebra and analysis. For many not be discouraged from this profession. While the student is unsure of his or her of these students, it's as if they have begun major, it is sensible to take calculus since 3. There is a tremendous need for high the study of a completely different sub• this choice keeps open many career op• school minority mathematics teachers, and ject. But it is worse than this when some of tions. I should encourage these students to go these students realize they are not good at into this profession. "real" mathematics. What is a student to I should point out that in these conversa• do? What advice can be given in these tions with students, it is not my intention This makes me wonder what it is that situations? Students have to be monitored to tum them into mathematics majors, nor university professors are telling their stu• very closely as they make the transition do I encourage them to switch their major dents. from lower to upper division studies. to mathematics. My aim is to pass on to I find the last reason the most onerous. them the enthusiasm that I have for my I would like to close with some recom• When I was an undergraduate I was en• chosen subject of study,to encourage them mendations to the mathematics couraged to become a high school Spanish to pursue their own academic interests, community. teacher (not mathematics because this was and hopefully to include a good course of presumably too hard for Hispanics) be• I. View your undergraduate mathematics study in mathematics, whatevertheir cho• cause I could be a role model for the majors as an integral part of the depart• sen major will be. In fact, it happens students. ment. There should be activities which regularly that one of my mathematics undergraduates are essential for running. advisees will abandon the mathematics Many students coming to my university Computer laboratories are an especially major for another major, one more to his simply do not know of the opportunities attractive option. or her liking. When this happens I con• for someone with a mathematics back• sider my advising of them to have been a ground, and these students simplygravitate 2. Encourage funding agencies such as the tremendous success. That student has left to the teaching profession because they do National Science Foundation to provide with a solid foundation of mathematics know of that profession. This is especially funds to hire undergraduates for activities for a major that has caught his or her inter• true of young Hispanic women. It is my essential to mathematics departments. Just est. In many cases the student has taken responsibility to acquaint these students as the laboratory sciences have a need for more mathematics than the typical student with the myriad possibilities that exist. undergraduates, so must mathematics de• in that major, so that student will have an Though the teaching profession can cer• partments develop such a need. even better chance at success. tainly be a very fulfilling occupation, I do 3.Advising undergraduate students should not think that we should funnel our stu• I strongly believe that the mathematics be a priority in our departments. If, as a dents intoit untiltheythemselves areaware community has neglected our undergradu• community of scholars, we cannot con• of the opportunities that exist. ate mathematics majors. These students vince our undergraduates of the usefulness have chosen a very demanding field of There are some problems with my tech• of mathematics, then who else can? We study, and except for presenting them with nique as it applies to those students who should make an effort to contact every lectures, we have providedthem with little choose mathematics as their major. Stu• calculus student in order to provide neces• more. Even the information that would dents should be encouraged to get advice sary information for that student to allow them to choose between mathemat• from many faculty members. I have some• understand the importance of mathemat• ics and other fields is not given to these times misread the abilities of a student and ics in his or her curriculum. students. given poor advice. And what do we do 4. Increase summer internship opportuni• with students who graduate with math• One of our complaints in academe is that ties. There are many in the mathematics ematics majors and decide to become high high school counselors give bad advice. ------@ FOCUS August 1994

community who would welcome the op• portunity to work with undergraduates if Stroik To Deliver His Centenary Lecture there were funds available to support these activities. Wemust not forget the opportu• On September 30, 1994, Professor Dirk J. Struik will deliver his centenary lecture nities that industry offers. Be more "Mathematicians I Have Known," at Brown University. The event is co-sponsored by aggressive in convincing industry to hire Brown University, Providence College, and the American Mathematical Society. mathematics majors, as summer interns For information, call (40 I) 863-2708. For dinnerreservations, send $25 by September as well as permanent employees. 15th to Brown University-Struik Dinner, Box 1917, Brown University, Providence, 5. The transition from lower division to RI 02912. The lecture begins at 3:30 P.M. in Brown University's List Auditorium. upper division isa harrowing one for many of our mathematics majors. One of the main reasons for this is that "proofs" are part of the mathematical scenery of these upper division courses and in fact form a major part of the course content. Yet "proofs" are being de-emphasized in our calculus sequence. What can wedo tomake this transition easier?

William Yslas Velez teachesat the Univer• sity ofArizona.

C. compute the derivative of a function the past there was a large common core of AP Calculus Exams numerically; material in most college calculus courses. This homogeneity made designing the AP D.compute definite integrals numerically. To Include Graphing Calculus course relatively easy. Today the Not all graphing calculators have these situation has changed, and there are many Calculators capabilities as built-in features, but all can different calculus courses taught through• easily be programmed to perform them. out the country.Although there isstillmuch Anita Solow Students will be allowed to bring pro• common material in calculus courses, it is grammed calculators into the approached differently in many reform set• Beginning in May 1995, students will be examinations; calculator memories will tings. This makes it more difficult to create required to use graphing calculators on the not be cleared. In this way, the differences the AP Calculus syllabi. In addition, inte• Advanced Placement (AP) Calculus Ex• among the calculators can be minimized. gration of technology into the courses aminations. The multiple choice section creates pressure to change the syllabi. The decision to require graphing calcula• will be divided into two parts. Graphing Some topics that were part of a standard tors was arrived atafter lengthy discussion calculators will beneeded for some of the curriculum become obsolete with technol• and study. Important issues that were con• problems in the second part of the mul• ogy, while other topics gain importance. sidered included the decision's tiple choice section and on the (Of course, there are differing opinions acceptability to colleges and universities free-response section. They will not be about what these topics are.) allowed on the first part of the multiple that grant AP credit and/or placement, choice section. equity issues surrounding calculator use, Over 100,000 students take the AP Calcu• the cost of calculators, and the readiness lus examinations, with more than that The AP Calculus Development Commit• of high school teachers to use graphing taking the courses. One consequence is tee is a committee of the College Board, calculators. The main reason that graph• that a large number of students will be consisting ofthreecollege faculty and three ing calculators are being required is the entering colleges and universities with from high school. It has specified what the beliefthat the use of graphing calculators facility in using graphing calculators in capabilities ofthe technology are to be for can make the calculus course a better their mathematics courses. the test. Students will be expected to have course, with increased student activity and The AP Calculus program is not static. It a calculator to: discovery-based learning. has changed in the past and will continue A. produce the graph of a function within The next step, revising the syllabi for AP to do so in the future. What is perhaps an arbitrary viewing window; Calculus courses, will begin this fall. In different now is that the changes occur at B. find the zeros of a function; a quicker pace. @------August 1994 FOCUS

CD-ROMfrom page 5 explanation or shows more steps, the page Finding the Derivative by the Limit Process becomes denser and more foreboding. Fmdthe derivativeof f(x) = x3 +2x. Thenuse the re3Ult to Thus, in a printed text, it is easy to lose findthe slope ofthe graph off whenx = -1. sight ofthe forest because ofthe presence SOLUfrON of so many trees. Beforeviewing the fonowingsteps,try supplyingthem As an example, considerthe screen shown yourself. in Figure 4. This example asks the user to fl(X) = lim f(x +i1x) - f(x) = find and use the derivative of a function. .6x....O i1x I----l,:-+-J'-I---t-+---+x By keeping the parent screen simple, the Usingthe derivativef'(x) =3x2 + 2, you can concludethat basic idea ofthe example remains promi• the slope ofthe graph of f whenx = -1 is nent. The overall strategy-finding and /,(-1) = 3(-1)2 +2 = 5 evaluating the derivative-remains clear. as indicated inthe graph. The actual computation of finding the derivative by the limit process is of sec• ondary concern and can be accessed by selecting the "steps button," as shown in Figure 5. Other observations about the derivative and the tangent line can be ac• cessed by selecting the "explore button." The alternative of presenting the entire Figure 4 The problem of not being able to see the forest for the trees can be solved in a CD-ROM text• example on a screen that can be scrolled is book by designing parent screens that present succinct overviews of essential concepts. From the parent much less useful because it clouds the screens, any number of child (or grandchild) screens can be accessed to provide further insight or clarifi• primary goal of the examples with many cation. For instance, the essence of the example in this screen is finding, evaluating, and interpreting a secondary mechanics. derivative. The mechanics of actually using the limit process to find the derivative, while necessary, would clutter the screen and make the example appear more complex than it is. The Future: What does the future hold for textbooks and education?Although no it seems clear that the benefits ofCD-ROM one can answer this question completely, textbooks will make their presence more and more common. With improvements in portable computers, one can imagine luur.u tivr f rlr ulu: V,'r'.IiJlI III """""r that CD-ROM textbooks will become commonplace. Already, publishers have !,(x) = lim f(x +i1x) - f(x) .6x....0 i1x begun making substantial investments in = lim (x + i1x)3 + 2(x + i1x) - (x3 + 2x) majorCD-ROMtextbooks. Thefirst com• .6x....0 i1x prehensive CD-ROM textbook, The = lim x3 +3x2i1x +3x(i1x)2 + (i1x)3 +2x +2i1x - x3 - 2x Enduring Vision-a United States history .6x....0 i1x text by D. C. Heath-was introduced to the marketin 1993. Many others are forth• = lim 3x2i1x+3x(i1x)2 + (i1x)3 +2i1x coming, including the CD-ROM textbook .6x....0 i1x mentioned in this article, which was de• = lim ~[3x2 + 3x.dx + (i1x)2 + 2 1 veloped by Meridian Creative Group. .6x....0 IJ4 = lim [3x2 + 3xi1x + (i1x)2 + 2] .6x....0 Roland E. Larson is a professor ofmath• ematics at Penn State University at Erie. = 3x2+2 Thefifth edition ofhis calculus text, Cal• culus, with D. C. Heath and Company, is available in printed and CD-ROM ver• sions. The CD-ROM version was coauthored with Ann R. Kraus. "~"~I f1~fl -~/t

Figure 5 This is one of the child screens of the parent screen shown in Figure 4. By selecting the "steps button," a user is able to view a screen whose sole purpose is to show how the limit process can be used to find the derivative of fix) =x3 + 2x. After digesting this screen, the user can return to the parent screen and the essence of the example. FOCUS August 1994

Rewards from page 3 traditional research articles in refereed communication with the administration, and appreciation from colleagues and the In teaching departments, the report says, journals. The committee's site visits re• chair. "The most common reason for low "These changes were recent enough to vealed that most departments do not have quality of life in departments was lack of cause consternation among junior faculty a working definition of scholarship. Al• appreciation of the department by the ad• members over exactly what was expected though there seems to be agreement that ministration," the report states. of them inorder to gain tenure and whether scholarship implies some sort of active these expectations were changing as they engagement with the discipline, there are Recommendation and Guiding Prin• varying views on exactly what kinds of progressed toward tenure." In research ciples departments, the new emphasis on teach• activities should be considered scholar• ing was "more evident in the rhetoric than ship and how they should be rewarded. Because of the great diversity of institu• tions and departments, the report avoids in the actual policies, [but] this emphasis Lack of communication between various making pronouncements about what de• is definitely working its way into the re• organizational levels is a major problem partments should do. However,itdoes state wards structure." at many institutions, the report notes, and one general recommendation: "The rec• one that can hamper efforts to change the The report outlines a number of difficul• ognition and rewards system in rewards system. Often there is a lack of ties associated with making changes in the mathematical sciences departments must understanding about the relative values rewards structure. First, there is little con• encompass the full array of faculty activ• that institutions placed on teaching, re• sensus within the mathematical sciences ity required to fulfill departmental and search, and service. "One assistant community about how to evaluate many institutional missions." In addition, the professor told us that teaching was abso• professorial duties. Research emerged as report sets forth six Guiding Principles to lutely the main consideration in the tenure the activity that faculty are most comfort• assist mathematical sciences departments decision," the report says, "while another able about evaluating, but, the report says, in considering changes in their rewards in the same department told us the main "even thiscame under attack insome quar• systems. ters. It was felt that a certain amount of consideration was research." There are publication, as well as invitations to con• often disparities in goals: "In some places Three of the Guiding Principles have to ferences and giving colloquiums and it was apparent that the department and do with what kinds of activities should be seminars, could be achieved through the administration were working on to• rewarded. The report points to research as cronyism." However, the report notes, tally different agendas, and neither knew the fundamental raison d' eire of the disci• whatever the problems are with evaluat• what the other's was." pline and states that research should be among the primary factors of importance ing research, they have not prevented The fewest communication problems were in any rewards system. There must be in• research from gaining high importance in found in institutions with the most effec• ternal strength in core areas of the the rewards system. tive department chairs, the report says. discipline as well as "lively connections Acting as the interface between the de• With teaching, the situation is the oppo• to other disciplines and to business and partment and higher administration, chairs site: perceived difficulties with evaluating industry," the report states. In addition, can have a great deal of influence over the teaching, the report states, "emerged as a "No distinction should be made in the re• well-being of the department. "Unfortu• fundamental stumbling block in efforts to wards system between research in the core nately," the report notes, "chairs increase the importance ofteaching in the areas of mathematics and that in applied commonly have no systematic training to rewards structure." In particular, the stu• areas." The report suggests that joint ap• prepare them for this role." An interesting dent evaluation questionnaire-thesingle pointments, with joint evaluations, can finding about chairs emerged from the most frequently used method of evaluat• help interdisciplinary research to thrive. ing teaching-was viewed with great survey. Faculty and chairs were asked suspicion. The report quotes one faculty whether salaries reflect differences be• Two other primary factors of importance member's assessment of what usually tween excellent and average teaching. In in any rewards system are education and happens with student evaluation question• every type of institution, the percentage service. Although there may be more or naires: "If the student fails, I fail." When of chairs who answered "yes" was close to lessemphasis on research depending upon it comes to evaluating activities such as double that of the faculty. the department and the institution, teach• ing is a major responsibility in every service to the institution or to the profes• What kinds of rewards do faculty want? department. Therefore, the report states sion, "There was usually not even an The report states that, when it comes to that, inalldepartments, "the teaching func• attempt formally to measure effective salary raises, most faculty prefer a rewards tion should be viewed as a primary work." system that combines across-the-board responsibility of all faculty and should be and merit salary increases. In addition, the Another barrier to changing the rewards rewarded and recognized accordingly." report says that the general "quality of life" system is the uncertainty about what Departments should help faculty and in the department emerged as a reward should be included under the rubric"schol• graduate students improve their teaching much valued by faculty. Quality of life arship". The report notes that this by having those acknowledged to be ex• rewards can take many forms, tangible and uncertainty is less pronounced in research• cellent teachers share their expertise or by intangible: offices, classrooms, parking, oriented departments, where scholarship calling upon such campus resources as clerical help, computer facilities, conge• is usually assumed to mean publishing teaching centers. niality within the department, good @------August 1994 FOCUS In the realm of service, the report points to a wide array of responsibilities connected Awardsfrom page 9 a variety of activities that are crucial to to research, to students, to their institu• departments and their institutions and tions, to the profession, and, depending renominated the following year. For which should be valued as important com• upon the department and the institution, those so designated, a letter should be ponents of a rewards system. These to the local community and the nation. written to the nominator asking him or include: chairing the department, manag• "The optimal strategy for meeting these her whether the nominator is willing to ing the undergraduate or graduate varied departmental responsibilities is not renominate the candidate, whether he programs, serving on departmental or in• to expect all faculty members in the de• or she is still eligible, and, if so, to stitutional committees, recruiting and partment to do all things at all times," the update the file if necessary, but not re• mentoring minority and women students report notes, "but rather to match faculty quiring a new file to be submitted. and scholars, and assuming leadership work with faculty interests .... But, in or• Last year, some sections had been con• roles in professional organizations. der to work, this approach must be cerned that, while the candidates who were accompanied by a rewards system that Scholarship should also be an important nominated were outstanding, the number recognizes excellent contributions to all factor in any rewards system. The report of nominations had been smallerthan they facets of the departmental mission." In suggests that every faculty membershould would have liked. This year, it appears this addition, a hallmark of academia is that be engaged in some form of scholarship. has been much less of a problem, perhaps not everyone need fit into the same mold. In some departments traditional research as a result of the publicity given last year "[R]atherthan codifying every aspect of a may be the primary mode of scholarship, to the example set by the Northeastern rewards system," the report declares, "de• while in others it might be more appropri• Section which sent out a flyer in March partments should formulate clear and ate to adopt a broader definition of urging any member ofthe section to "send flexible policies." scholarship that encompasses such activi• aone-page letter in support of an outstand• ties as writing textbooks and expository The rewards system should be consonant ing teacher and the Section Committee will papers, public awareness efforts, curricu• with the departmental mission and the ask the candidate's department chair to lar development, improving teaching mission of the institution, the report states. complete the nomination form." To assist methods, and research in mathematics Departments must examine whether the further the effort to obtain more nomina• education. The report also suggests that needs of their constituencies are being met tions, the committee this year encourages rewards systems be flexible enough to and must make the rewards structure re• anyone, in particular its own members, to allow faculty to shift to different forms of sponsive to those needs. In addition, clear call department chairs and others to urge scholarship during their careers. Noting lines of communication are important. All them to make nominations. that no one definition of scholarship will concerned-faculty, chair, and adminis• The committee hopes that the above indi• be right for every institution, the report tration-should know and understand cated simplification of the requirements includes in an appendix a proposal for a what is valued and rewarded. The report for documenting evidence of success in definition of scholarship that could be used particularly stresses the importance of the teaching and the suggested procedure for as a platform for further discussion and department chair in the implementation renominations the following year will refinement within individual departments of any rewards system. "Care in the selec• make it easier for chairs to nominate de• and institutions. tion and training of the chair isan important serving candidates. The national factor in the health and well-being of the For a rewards system to work, there must committee urges all members of the Asso• department," the report states, suggesting be accepted methods for evaluating vari• ciation to think of worthy candidates for that the mathematical sciences commu• ous activities. Inparticular, the report notes these awards and nominate them to the nity should organize more workshops for that the lack of such methods can prevent appropriate section committee. Even if chairs and other training and development some professorial activities from being your candidate should not be selected as a mechanisms. properly rewarded. For example, the re• recipient of the award, remember that a port says, "The perceived inability to Distribution nomination by itselfisa distinct honor and evaluate teaching isone ofthe major stum• also that there is now a simple procedure bling blocks to making teaching an integral Those wishing copies of the report should in place allowing the candidate to be nomi• part of the rewards system in mathemati• write to the American Mathematical So• nated again if not selected the first time. cal sciences departments." The report ciety, 1527 Eighteenth Street NW, The larger the pool of outstanding nomi• states that departments should not allow Washington DC 20036; e-mail: amsdc@ nations, the easier it will be to maintain imperfections in evaluation methods to math.ams.org. The report (without accom• the high quality of the awards, so success• impede progress inbroadening the rewards panying figures) is also available on fully established by the first three sets of structure. National leadership on the issue e-MATH. Toaccesse-MATH, type: telnet awardees. of evaluation would help, the report says, e-math.ams.org. The login and password proposing that the professional societies are e-math. For more information, send e• Henry Alder is chair ofthe Committee on could assess evaluation methods currently mail to support@e-math. ams.org. AwardsforDistinguishedCollege or Uni• in use and provide guidelines, models, or versity Teaching ofMathematics. suggestions. Allyn Jackson is Associate Managing Editor, Notices of the American Math• Mathematical sciences departments have ematical Society. FOCUS August 1994 NETWORKS IN FOCUS Navigating the Network with NCSA Mosaic Frank M. Baker This article first appeared in the Educom an interactive, scrollable, online book. You on a machine at an Internet site answering Review, vol. 29, no. J, and is reprinted can move around within complex docu• queries sent by NCSA Mosaic clients, here with permission/rom EDUCOM. ments, as well as from document to which may be located anywhere on the document across the network, simply by Internet. To users, the client looks like any As he was leaving for a meeting in clicking on these hyperlinks. You use the other application on their machine, only Asheville, John remembered reading same interface fornavigation and fordocu• this one has immediate access to informa• somewhere that the North Carolina De• ment viewing; you can even retrieve tion all over the world. The pieces of partment ofTransportation had announced information from Gopher, WAIS, and information sent from servers to clients plans to rebuild and extend parts of 1-26. anonymous FTP servers without moving are known simply as documents, which John barely had enough time as it was; if to a different application for each one. may contain plain text, formatted text, much of that stretch ofroad was currently graphics, sound, and other multimedia under construction, he would need to call NCSA Mosaic and the data. and say he would be late. Going to his WorldWide Web desktop computer, John used NCSA Mo• An Integrated System saic, a new Internet interface, to find the The Internet has grown up during the past North Carolina Department ofTranspor• two decades as a loosely federated world• The NCSA Mosaic system is an integrated tation highway construction projects map wide collection of information resources set of browsers, viewers, servers, gate• and was happy to see that the plans af• and services. NCSA Mosaic itself is part ways, and filters that allow you to approach fected only one short section of the of the WorldWide Web environment, a the Interuet as one consistent information highway south ofAsheville. John selected system for maintaining distributed source. At the simplest level, the NCSA "1-26 improvements south of Asheville" hypertext that originated at the European Mosaic clients provide navigation and and read the project plan. Aside from the Laboratory for Particle Physics, CERN, document viewing capabilities for brows• work on one bridge, all the lane closings in Geneva, Switzerland. Initially devel• ing the information universe of the would be at night; he should still be on oped to keep track of researchers' Internet. As your interest, needs, and skills time. information and to provide an easy method develop, the configurable addition ofex• ternal viewers allows easy and The past several months have seen un• of sharing information among scientists, straight-forward expansion to handle vir• precedented coverage of the Internet in the Web has grown into one ofthe world's tually any specific type of data. This the popular press. Until now,though, navi• most widely used tools for information publishing, discovery, and retrieval. flexibility will allow you and NCSA gating the network has been an exercise Mosaic to keep pace with the quickly in frustration for even the most ambitious The Web employs several established or evolving world ofmultimedia and allows networker. Now a new software program developing standards to make it as univer• NCSA Mosaic to be custom configured promises to make Internet access easy and sally usable and reliable as possible. Ituses for any working environment. transparent for the everyday user. a standard naming convention-knownas The NCSA Mosaic system is a completely NCSA Mosaic, developed by the Soft• the Uniform Resource Locator or URL• open framework; you can enter at your ware Development Group at the National to locate individual pieces of information most comfortable level, progress through Centerfor SupercomputingApplications, sitting on machines anywhere across the the use of various viewers, learn to create is a window on the ever-expanding world network. Clients and servers use a stan• your own hypertext documents, set up your of on-line information. As a distributed dard transfer protocol-known as the own server, engage in multimedia collabo• hypermedia browser designed for infor• HyperText Transfer Protocol, or HTTP• ration with colleagues in distant locales, mation discovery and retrieval, NCSA to send and retrieve documents across the develop scripts for specialized informa• Mosaic provides a unified interface to the Web. Documents on Web servers are for• tion filtering and presentation, and develop diverse protocols, data formats, and in• matted with a standard markup language gateways to unique information resources formation archives used on the Internet. known as the HyperText Markup Lan• guage or HTML. The HTMLspecification and integrate them into the NCSA Mosaic With NCSA Mosaic's hypermedia-based includes the hyperlink format that allows information space for otherusers. In short, interface, electronic links known as users to move around the Internet byjump• the possibilities are endless; you can think hyperlinks are embedded in richly format• ing from one document to another. ofNCSAMosaic and the Web as allowing ted documents that can include full-color the progressive customization of your own images and sounds. NCSA Mosaic pre• Building on the Web's initial structures, information space, and that of your group. sents these documents like the pages of NCSA Mosaic uses a client/server model for information distribution. A server sits @------August 1994 FOCUS

External Viewers ing Clients from the NCSA FTP Server.) ments, you should first learn about Installing and running an NCSA Mosaic HTML-the formatting standard for There are myriad types of data available hypermedia documents in the Web envi• on the Internet, many of which must be binary is straightforward. The procedures differ slightly across the X, Macintosh, ronment-and URLs-the scheme for stored, read, and interpreted in a unique consistently naming documents accessible manner. Though NCSA Mosaic is not and MS Windows platforms, but they are installed like any other application on their on the Web. You will find hyperlinks to designed to read and interact directly with HTML and URL primers at the very end all of them, the system relies on external respective platforms. The installation pro• cedures are fully described in the readme of the NCSA Mosaic Demo Document viewers in order to work with the widest mentioned earlier. Those primers in tum possible variety of image, audio, video, files referred to in "Downloading Clients from the NCSA FTP Server" and in docu• point to more advanced information and typeset data formats. These external sources. viewers are separate programs that are mentation that can be found once the files invoked when necessary to display cer• have been downloaded and uncompressed. Current Release Levels tain types of data. To use NCSA Mosaic as an Internet In Novemberand December 1993, NCSA browser, the system on which it is installed With the external viewers, users are not released the following versions of NCSA must be fully connected to the Internet. limited by the NCSA Mosaic (anyone can Mosaic: use any viewer that will work with NCSA This is because the first thing NCSA Mosaic to view any type of data). Plus, as Mosaic usually does when you run it is NCSA Mosaic for the X Window System new viewers and data types appear, they download one of the NCSA Mosaic home Version 2.0 pages (the start-up document) from an can be easily integrated into the NCSA This version can be used on almost any NCSA server. If NCSA Mosaic executes Mosaic environment without rewriting the modem UNIX-based graphics workstation but you get an error message instead of a application software. For example, the (e.g., Sun Spare, IBM RS/6ooo, DEC 5000 home page, the problem is most likely in various NCSA Mosaic clients can use the or Alpha, Silicon Graphics IRIS). following external viewers: your Internet connection; you will have to get that connectionestablished before you NCSA Mosaic for the Macintosh Version Iviewfor the Microsoft Windows client can use NCSA Mosaic to navigate the 1.0.2 a Windows utility that plays GIF, JPEG, Internet. NCSA Mosaic can also be used This version can be run on any Macintosh, and TIFF images.as well as images re• as a collaborative tool within a working including SEs and Classics, running Sys• corded in several other formats group without an Internet connection, but tem 7.0 or higher. Ulaw for the Macintosh client a such applications are beyond the scope of Macintosh utility that plays audio data this article. NCSA Mosaic for Microsoft Windows Version 1.0 xvfor the X Window System client an X Where Can I Go From Here? utility that displays GIF, JPEG, and TIFF This version can be used on any Intel Once you have successfully installed images as well as images recorded in sev• 80386SX-based PC (or better) running NCSA Mosaic, you should spend some eral other formats. Microsoft Windows release 3.1 or later. time becomingfamiliar with the interface. This client will run with 4 Mb, but NCSA These are just a sample of the available The NCSA Mosaic Demo Document, recommends a minimum of8 Mb of RAM. viewers. NCSA makes several standard available via a hyperlink in the NCSA viewers available, but the system can be Mosaic Home Page or via a menu selec• NCSA Mosaic is being continually devel• configured to accommodate other view• tion, provides an overview of NCSA oped. The most up-to-date versions can be ers. Mosaic's capabilities with hyperlinks to a accessedby checking NCSA's FTPserver. wide variety of information sources. As Setting Up the Client E-mail queries concerning these releases you browse the information universe, you can be sent to the following addresses: can access material through other menu NCSA Mosaic is implemented for three Macintosh [email protected] types of platforms: selections and other home pages. Windows [email protected] X Window System Serving Information X [email protected] Macintosh To distribute information via the WorldWide Web, you will want to set up Downloading Clients from Microsoft Windows. an HTTP server. The HTTP protocol is the NCSA FTP Server Each implementation takes advantage of stateless, lightweight, and extremely fast, the strengths of its respective platform, but provides capabilities not found in ear• NCSA Mosaic can be acquired from but they have all been implemented to lier protocols, such as FTP. HTTP servers NCSA's anonymous FTPserver. Youmust preserve as much cross-system compat• are currently available from various Web first execute the following FTPcommand: ibility as possible. All three clients can be sources for UNIX, Macintosh, and ftp ftp.ncsa.uiuc.edu downloaded for personal use from NCSA's Microsoft Windows systems. anonymous FTP server. (See Download- Enter anonymous at the login prompt and If you wish to publish hypertext docu------@ FOCUS August 1994

press Return. Enter your e-mail address UNIFORM RESOURCE LoCATOR (e.g.,[email protected])atthepassword prompt. The UniformResourceLocator(URL)is the standardaddressing mechanism used to locateandretrievedocuments fromanywhere on theWorldWide Web. AURLconsists If you have never downloaded files from ofthreeparts:acodeidentifyingthetransferprotocolto beused,anaddressidentifying this server, download and read the file the machine on which the file resides, and a full pathname locating the file on that README. FIRST. machine. You will find NCSA Mosaic executables Forexample,the HomePagefor NCSAMosaicfor theMacintosh is in the HTMLfile in the following directories. Initial instal• /SDG/SoftwarelMacMosaiclMacMosaicHome.hbnlonNCSA's WorldWideWebserver. lation instructions can be found by reading When it starts up, NCSA Mosaicfor the Macintosh usually retrieves this document the indicated readme file for each client: automatically using the following URL: Macintosh executable /Mosaic/Mac/ http://www.ncsa.uiuc.edulSDG/Software/MacMosaiclMacMosaicHome.html L ..::'..J1 II I Macintosh readme /Mosaic/Mac/ I NcsA's Webserver I NCSAMosaic.I.O.2.README Codefor the H1TP protocol The pathnameof the file containingthe document NCSA Mosaic and HTML shield users from URLs most of the time. The URL is Windows executable /MosaiclWindows/ embeddedin the HTMLdocumentsourcecodethatgeneratesa highlighted hyperlink. Windows readme /Mosaic/Windows/ Whena user views a documentand selectsa hyperlink, NCSAMosaicuses the URL readme.now in the sourcefile to automatically retrievethe indicateddocument. X executable /Mosaic/Mosaic-binaries/ HYPERTEXT MARKUP LANGUAGE X readme /Mosaic/README.Mosaic Documents designed to be read on the WorldWide Web are usually formatted with the Please note that these clients are copy• HyperText Markup Language (HTML). HTML provides the ability to print formatted righted but free for noncommercial use; lists, titles and subheadings, inline images, bold and italic text, hyperlinks, and more. NCSA and the University of Illinois re• It also provides the ability to point to images that can be viewed through an external tain the copyright but will allow anyone viewer, audio files, or movies that can be played if a user has the appropriate software retrieving the software from the FIPserver and hardware installed. to use it personally without any further license. Anyone who wishes to use or dis• The first section below is a simple HTML selection that illustrates the title, level-one tribute the software commercially must heading, emphasized text, and paragraph commands. The formatted output appears at first obtain a license. The full NCSA the bottom. Mosaic copyright notice can be viewed