BRITISH COLUMBIA ASSOCIATION OF MATHEMATICS TEACHERS

NEWSLETTER

VOLUME 14, NUMBER 6 SEPTEMBER 1973

BCAMT EXECUTIVE 1973-1974

Past President J. Michael Baker 11225-87th Avenue Delta 594-8127 (home) 588-1258 (school)

Vice-president Roger Sandford R.R. #1, Tzouhalem Road Duncan 746-6418 (home) 749-6634 (school)

Treasurer Bill Dale 1674 Tull Avenue Cou rtenay 338-5159 (home) 334-2428 (school)

N.W. NCTM Conference Organizer R. Mctaggart 4780 McKee Burnaby 1 434-0716 (home) 736-0344 (school)

NCTM Representative Tom Howitz 2285 Harrison Drive Vancouver 16 325-0692 (home) 228-5203 (UBC)

President Alan Taylor 7063 Jubilee Street Burnaby 1 434-6315 (home) 936-7205 (school)

Secretary Mrs. Floreen Katai #310-706 Queens Avenue New Westminster 526-1163 (home) 943-1105 or 943-1106 (school)

Publications Chairman Bill Kokoskin 1341 Appin Road North Vancouver 988-2653 (home) 985-3181 (school)

Summer 73 Conference Organizer Walter Szetela 4931 Stevens Drive Delta 943-7159 (home) UBC

Elementary Representative Mrs. Grace Dilley 2210 Dauphin Place Burnaby 2 299-9680 (home) 588-5918 or 581-0611 (school)

In-service Specialist Dennis Hamaguchi MacDonald Park Vernon 542-8698 (home) 542-3361 (school)

The B.C. Association of Mathematics Teachers publishes Vector (combined newsletter! journal). Membership in the association is $4 a year. Any person interested in Mathe-matics education in B.C. is eligible for membership in the BCAMT. Please direct enquiries about membership or articles to be published in Vector to the Publications Chairman.

Inside This Issue...

A MESSAGE FROM THE PRESIDENT . ...........1

NOTES FROM THE SUMMER CONFERENCE FOR GRADE 7 TEACHERS .............. 2

FIVE IDEAS GLEANED FROM THE

SUMMER CONFERENCE .................... 4 WHY TEACH EUCLIDEAN GEOMETRY ? ....... . . . . 7

OBJECTIVES FOR THE GRADE .10 . GEOMETRY COURSE ................... 11

MATHEMATICS CONTESTS IN B.0..... ... ..... . 16

BOOK REVIEW ...................... 17

SCHEDULE OF MEETINGS .................. 19

NEW BOOKS ACROSS MY DESK .............. 19

A Message from the. President With the start of a now year, mathematics educators in British Columbia are faced with an interesting and challenging task. The move toward decentralization in the educational field, combined with upcoming curriculum revision, will generate a greater need for teacher involvement. Awareness of course-content changes and different methodologies goes hand-in-hand with the effective development of a less-rigid curricu-lum. The BCAMI' intends to keep its finger on the pulse of change and to facilitate communication among teachers in the province.

As incoming president, I wish to extend greetings' to fellow members of the BCAMT. I seek your advice and active 'involve-ment in the area of mathematics education. Please feel free to contact me in this regard.

The present elected executive is. .compris.ed.o,f an. entirely new team. We are anxious to continue the good work of the previous executive and to expand the scope .of,our. involvement as needs dictate. Our major objectives for the year revolve around communication and in-service. Both of these aims have much in common, and consequently one enhances the other.

We hope to improve lines of communication in several ways. First, to enhance a balanced representation from all grade levels, we will appoint a member to the executive from both primary and intermediate areas. Once equal representation is assured, the next step will be to strengthen horizontal lines of communication between other teachers and those on the executive. To facilitate this interaction, we plan to hold several meetings during the year at various locations in the province. The time and place for these meetings will be published in Vector when details are finalized.

Improved 'two-way' communication between teachers and the Department of Education also holds a high priority. In keep-ing with the previous executive's attempts in this direction, we will continue to press toward streamlining the existing structure.

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In the area of in-service, our plans include the establish-ment of resource teams to become available throughout the province - this is one intended outcome of the recent summer workshop. We will also promote the establishment of 'think tanks' throughout British Columbia. A greater sense of direction and the means to accomplish it are expected out-

comes.

You are, as members of the BCAMT, welcome to attend executive meetings. The scheduled dates appear in this issue of Vector.

Respectfully submitted, 'Alan R. Taylor' President.

Notes from the Summer Conference for Grade? Teachers

by Floreen Katai

As an elementary teacher faced with teaching Grade 7 this fall, I found the summer conference in July very helpful. I would like to share with you some of the things I found use-

ful.

1. Read the 'AMENDED' set of objectives for the Grade 7 course of studies that the Department of Education will send out in September. There are omissions in the amended ver-sion, which are different from the interim one.

2. Try to get a copy of the 'CORRELATED CURRICULUM GUIDE'

for the four Grade 7 textbooks (Math I, School Math I,

Essentials of Math, and Contemporary Math) done by Ken

Pelling and Larry Evans from School District 71 (Courtenay).

Working on an LIP grant, these two math teachers were released from their teaching duties last spring to correlate and cross-reference the objectives from the interim course of studies with the above four textbooks. This guide should save you a lot of time in finding related topics in all four books.

For a copy, write to: Mrs. G. Davies, Elementary Supervisor, School District 71, Courtenay, B.C.

NOTE: They did a similar guide for Grades 4, 5, and 6 using the texts they assumed would be chosen for September, 1974.

3. All the sessions I attended that were evaluating the 'new' textbooks generally agreed on the following points:

a. Don't forget to use Contemporary Math for exercises as well as for some units.

b. Math I (Ginn) and School Mathematics. I (Addison-Wesley) are favored texts for covering the curriculum objectives.

C. Essentials of Math I (Ginn) does not meet the require-ments for the Grade 7 curriculum but is very good and popular with poor readers and low achievers.

d. Grade 7 and 8 teachers should consult each other regard-ing overlap in both curriculums and perhaps could come to some agreement as to content and texts for both grades.

4. The metric system is here to stay. Grade 1 and 2 teachers are being asked to teach it this fall. The 'new' texts for Grades 4, 5, and 6 that are to be used in Septem-ber 1 74 are to be written with the metric system only.

S. Jim Sherrill suggested writing to the following three groups for information on the metric system:

a. Steve Gossage, Metric Commission Chairman, 320 Queen Street, Ottawa, Ontario K1A OHS

(for progress on the metric system in Canada)

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II,

C.

Albert Mettler, Canadian Metric Association, P.O. Box 35, Fonthill, Ontario NCTM, 1906 Association Drive, Reston, Virginia 22091

(for learning teaching

metric)

($ 4 membership fee)

(for list of companies producing metric materi-als and for articles on the metric system)

6. FREE: a set of colored pictures on the history of measurement, write to the Ford Company in Vancouver.

Five Ideas Gleaned from the Summer Conference

by Roger Sandford

1. To practise converting fractions to decimals.

a. On a, 'guess my rule' basis, slowly reveal to the class, waiting a second or two at each number, the sequence.

1 1,1 1,1,2 1,1,2,3 etc. etc. 1,1,2,3,5,8,13,21,34

till even the slow ones recognize the rule. (It's called Fibonacci Sequence - don't tell anyone!!)

b. Ask them to calculate

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1 1 1 2 2 3 3 5 5 8

etc.

C. Have the class comment on the answers - would they like to discuss the result? Would they like to find the 20th and 21st member of the sequence and find the appropriate decimal as accurately as they can without doing any division!!!?

2. To practise averaging and graphing data.

a. Get a wooden block and make a dice (buy one!!! Steal one from the Monopoly set!)

b. Get the kid(s) to throw it and take the average of all the throws up to any particular throw.

C. Graph the average at throw 1, throw 2, etc. d. If you do it 50 throws, a weird thing will appear (on

the graph, I mean). e. Discuss why.

[Note - let the STUDENTS, organize the data according to their own methods, also the graph.]

3. To practise subtraction of fractions.

1 1_ 3 5 1 1_ 5 7 1 1_ 7 9 1 9 11

0-0 = 0-0= 0-0=

4. Open ended question on a one-way street plan.

How far is it in city blocks of pavement from any junction to another? Does the distance vary according to where you start?

Etc.

S. Suggestion to the librarian of your school if you are going to give library assignments.

Historical Topics for the Mathematics Classroom

31st Yearbook NCTM Tom Howitz - $8.25

University of British Columbia Vancouver

You know where.

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Wh y Teach Euclidean Geometry? by Bruce Ewen

Eight yearsago, when Moise Downs had been in use for al-most a year, I fancied that my apprenticeship as a teacher had progressed to the point where I might comment in writing. I thought that this method might have greater consequence than the usual staffroom bitching. The then-editor of the BCAMT newsletter printed my comments in May 1965 with the prior warning: 'I am not in agreement, but it is an interest-ing (I'm sure he meant curious) comment.' I still wonder if it was my last sentence to which he referred. I wrote: 'Taught without an opinion on the teacher's part, the subject will be as lively as a can of last year's bait.'

Since that first effort, I have been propelled into a program of study and work which is unfortunately not a part of any degree program. But if you claim to be a teacher, the most important thing you can teach is how to study. You do this best if you are a practitioner of the art.

The significant result of this study is a set of questions and a set of answers which are satisfactory to me. Your set of answers may not be the same as mine, for you're a different person, but you must face the same questions and try to find your satisfactory set of answers before you may consider yourself an effective teacher. And you may not like it any more than I do that you are constantly questioning that effectiveness.

These are my questions:

Why do you teach Euclidean geometry (or any other piece of subject matter)?

What is it you are doing for your student when you say you are teaching geometry?

Do the materials you use enhance or diminish your ability to do these things?

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You will recognize that these are the questions of philosophy, method, curriculum. They are in the order in which they must be answered if they are to make any sense. And the first is

a matter of opinion - your opinion.

There do we get the opinions we call 'philosophy in educa-tion.' There are three main sources, but only one has pro-vided a clear line throughout history, and only this one is complete in that it offers guidance in matters of method and curriculum. The others have served to produce modifications at some times and in some places, and those modifications have often been temporary.

The first source is Plato. He incorporated into his philo-sophy the Pythagorean concept that number exists prior to human thought - it is consistent with Plato's ideas on the nature of reality. From this it follows that human activity must be directed toward the discovery of the truth about number and form. The best modern exposition of this opinion

occurs in the Apologia by the mathematician Hardy. From this opinion flows the methodology of search-after-truth, each step based upon previously accepted steps, no statement permitted which is not firmly based upon doctrine, the definition-theorem-proof sequence with which we are familiar - all of which Plato received ready-made from Euclid. This is the form and method used in the arguments of the Dialogues. Most of us follow this opinion even when we claim a different philosophical bias; the consistency of philosophy, method and curriculum makes it easiest to do so. The practices of Plato's first academy were emulated in the British schools from which we derive our methods and practices.

The logicians are our second source of opinion. Aristotle criticized Plato's concept of reality, and in more modern times mathematicians have had their go at the a priori posi-tion of number, arguing that logic itself takes priority. Thus Birkhoff substitutes a new logical structure for the 'self-evident truths,' and Russell places arithmetic upon a new foundation. But in doing so, they have not attempted to produce a new educational methodology to correspond to the new philosophy. Their effect upon curriculum has been to increase its weight. It is interesting to note that if you accept the logicians' view, you must abandan the notion that logic is a method of argument in search of truth first

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practised in writing by Euclid and his teachers; logic must occupy a position corresponding to Plato's reality.

Our third source of opinion is a sometime thing. From time to time since the beginnings of political democracy and mass education, groups which call themselves revolutionary or humanist or whatever have influenced our opinions for a while. We are now in the midst of a period when these people are much heard. Traditional philosophy, method and curriculum are vigorously attacked, often with good cause. But the problem of formulating philosophy with consistent method and curriculum, all consistent with the emerging society they claim to see, is less attractive than the politics of the attack upon the traditional. They often seem like soldiers who enjoy the battle without caring about the consequences. Can a new philosophy exist for mathematics education? Lance Hogben will tell you that mathematics arises out of man's long struggle out of ignorance; its structure and form are his inventions; applied math gave rise to pure math - all in direct contradiction of the platonists and logicians. He found several sensitive spots in traditional mathematical philosophy, which you will find if you do read Hardy. Method and curriculum to correspond are not forthcoming.

Most of us who teach mathematics are platonists. We have to be: only here do you find a philosophy with its consistent methodology and curriculum. But it's embarassing to admit it in this age of 'education for. every man's child.' Plato's education was not for every man's child; it was for the wealthy and powerful, and its purpose was the maintenance of the state based upon the wealthy and powerful. Plato made no bones about it. As for 'nurturing independent thinking,' there is one independent thinker in the Dialogues - a teacher - who in the end must justify his own death in the interests of the state.

I teach Euclidean geometry because it is difficult to under-stand history without an understanding of Plato's blueprint for a successful state - every successful ruler in the West since the Year One has studied it. It's difficult to under-stand Plato without an understanding of Euclid and his method of argument. It is difficult to read St. Paul without experience with Euclid. This has been important to me, and I have no reason to expect it will be different for my stu-

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dent. Euclid is one of the keys to understanding of 'where

it's at' for mankind.

My student's ability to participate in a democratic society will depend upon his ability to examine a proposition and place his ideas in understandable sequence. If he cannot do this, he can only be a spectator in society. It is therefore the student's ability to participate in the argu-ment which is the central issue; the objects of the argument (the points, segments, circles) are not the issue in Euclidean geometry. But it makes no sense to teach the argument unless and until the student has an understanding of the objects. The fundamental concepts, their applications, and the language used must all be part of the student's

experience before it makes sense to teach Euclid as a structured system.

Curriculum decisions are not hard to make when these specifics are set out. Certainly I would not choose Moise Ei Downs. The mechanical Euclid is there all right, but his propositions are hashed about to please the logicians and analysts. 'The whole is greater than its parts' comes out: 'If a = b+c and

if b 0, then a > c.' 'A straight-line segment is the short-est distance between two points' becomes 'AB CD.' Nothing has been added but words; the flavor is gone, and clarity

suffers.

Those of us who would call ourselves progressive teachers and educators must soon get about the homework of setting out constructive principles of philosophy, methodology and curriculum guidance which are different from each other and demonstrably different from those of the traditionalists. If this is not done, the traditionalist need only wait; he will win by default. As of today, the so-called progressive educator, in mathematics and elsewhere, stands without any philosophical clothing, as naked as the emperor in Andersen's

story.

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Objectives forthe Grade 10 Geometr y Course

by Dr. David Robitaille, University of British Columbia

In a previous edition of Vector, I presented and discussed the results of a questionnaire concerning objectives for the teaching of high school geometry. That paper dealt mainly with teachers' stated objectives for the present Grade 10 geometry course and some of the implications arising from these objectives.

In British Columbia, as well as many other places in North America, a good deal of controversy surrounds the question of the future of the high school course in deductive geometry. Unfortunately, this discussion is too frequently centered around the selection of appropriate content and not frequent-ly enough around the more fundamental question of objectives to be attained. Speeches are made and journal articles are written listing the merits of the vector approach to Euclid-ian geometry or transformational geometry or non-Euclidian geometry, or any of a number of alternatives. Rarely do we read or hear recommendations concerning the aims of the course.

Process Objectives vs. Content Objectives

It will be useful for the discussion which follows to dis-tinguish between two types of objectives: process objectives and content objectives. The term 'content objectives' is self-explanatory. It refers to the knowledge components of the geometry curriculum which we expect our students to master sometime during the course. Content objectives for the Grade 10 course would include the following, among others:

1. knowledge of facts and terminology 2. knowledge of basic principles and rules 3. knowledge of definitions, axioms, and theorems 4. ability to reproduce proofs of certain theorems

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5. ability to perform basic geometric constructions.*

The term 'process objectives,' as it applies to the teaching and learning of geometry, refers to those skills and abilities teachers have in mind when they say they are teaching geometry in order to develop their students' powers of logical think-ing. Process objectives pertain to higher-order cognitive behaviors. Among the many possible process objectives for

deductive geometry are the following:

1. ability to follow a line of reasoning

2. ability to analyze data

3. ability to construct a valid proof

4. ability to criticize proofs S. ability to make and test generalizations.*

etc.

The distinction between process and content objectives is an important one. It allows us to discuss the future of the deductive geometry course along two dimensions and, simul-taneously, alleviate the confusion that arises when the two

concepts are intermingled.

In my opinion, discussion of process objectives is more funda-mental than is discussion of content objectives. The basis for this opinion is that decisions regarding process-objec-tives should precede and underlie any discussion of content objectives. Decisions regarding appropriate content for the course should be made in the light of the process objectives

selected.

Development of 'Logical Thinking' Abilities.

The questionnaire results mentioned earlier can be summarized by saying that teachers' major objective for the Grade 10 geometry course is the development of their students' abili- ties to think 'logically' by which they seem to mean 'deductively.' This. is a valid process objective even though some might quarrel with the terminology used. On the other hand, the objective as stated is extremely vague and gives

*Most of these objectives are selected from Wilson, 1971,

p. 646.

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rise to a number of questions:

1. What skills, abilities, and so on are components of this ability to think 'logically'?

2. How do we measure the degree of student attainment of this objective?

3. Can we convince our students of the importance of attaining such an objective?

Let us examine these questions in some detail and attempt to begin to answer them.

We do not appear to have done very much toward obtaining an answer to the first question. Actually, we seem to be in the position of hoping that, in our geometry classes, 'more is caught than is taught.' What we teach and, to a greater degree, what we test for seems to deal almost exclusively with geometric facts and replication of established results. In a way, our position is akin to that of the parent who decides not to assist his five-year-old to tie his shoelaces. The parent hopes that in so doing he will be contributing to the child's learning the basic skill of shoelace tying and, concurrently, he will be assisting in the child's development of a sense of independence. The former is an important and easily-measured objective; acquisition of the latter is virtually impossible to measure, at least in the short run.

On the other hand, considerable work has .been done in the last decade or two in the areas of identifying cognitive behavior levels, including the higher-order ones we are discussing here, and of suggesting means of measuring them. These studies have resulted in a number of taxonomies of objectives, both cognitive and attitudinal. The first of these, and perhaps the most famous, is the taxonomy of edu-cational objectives developed by Benjamin S. Bloom (1956). More recently, two taxonomies of objectives have been developed by mathematics educators for use in the specific area of mathematics. These are taxonomies of Avital and Shettleworth (1968) of the Ontario Institute for Studies in Education (OISE) and those of Wilson (1971) who deals speci-fically with secondary school mathematics.

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This is not the place to discuss the various taxonomies in detail. Teachers of geometry as well as all those who are interested in preserving the place of geometry in the secon-dary school curriculum would do well to familiarize themselves with one or more of these taxonomies. Not only do the tax-onomies aid in identifying the components of an ability such as 'logical thinking,' but also they provide examples of test items which can be used to determine whether or not the desired behaviors have been acquired. For example, Wilson (1971, p. 685) suggests the following question to test a student's ability to make and test generalizations:

On your paper draw three triangles: one with acute angles, one with one right angle, and one with one obtuse angle. Using straigtedge and compass,

bisect each angle . of each triangle.

What relationship do you observe between (sic) the three angle bisectors of each triangle? Do you think this would be true for every triangle? Why?

All the foregoing is intended to demonstrate that it is feasible to operationalize our 'logical thinking' objectives. It will by no means be a simple task, and this is undoubtedly why our test items in geometry have so often emphasized the lower-level cognitive behaviors. However, if we are to im-prove the teaching and learning of geometry, there is no doubt that we must begin to move in directions such as the

one suggested above.

Student Awareness of Course Objectives

It is of fundamental importance to the teaching-learning process that students be aware of and, to some degree, accept the objectives of a course. If students know what is expected of them, what behavioral changes are supposed to take place as a result of a given course, then they are more likely to succeed. 'He must accept and to some degree understand the goals if he is to exert the appropriate learning effort.' (Bloom, Hastings and Madaus, 1971, p. 9.) Or again, the same authors state that 'We believe that at the beginning of the year the teacher should make explicit to himself as well as to the students the changes that are expected to take place in them as a result of the course.'

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(Page 9.)

Most teachers will agree that it makes good sense, generally speaking, to ensure that their students are aware of the objectives of a particular lesson or even a unit. However, many balk at the idea of stating objectives for an entire course to their students. The logic of this position escapes me.

Stating objectives for a year-long program of study does impose some constraints upon the teacher. Telling students in advance that our objectives for the course include those listed as process objectives earlier in this paper would affect the teaching and testing programs that took place during the course. For example, it might force teachers to stop teaching geometry in what might be called an ex post facto manner. By this is meant that we too often present theorems not as problems to be solved but as problems whose solutions are known and need only be studied. It might, on the other hand, force us to teach the course from a problem-solving point of view where we make use of deductive reason-ing to establish intuitively derived results.

Conclusion

The thesis of this brief paper is that we need to spend more time discussing our objectives for a course in deductive geometry before we plan any content revision. In this regard, it seems useful to distinguish between content objectives and process objectives. Decisions regarding process objec-tives will have subsequent impact not only on our choice of content for the course but also, and more importantly, on the methodology used in teaching geometry.

References

Avital, S.M. and Shettleworth, S.J. Objectives for Mathe-matics Learning. (Bull. No. 3) Toronto: Ontario Institute for Studies in Education, 1968.

Bloom, B.S. (Ed.) Taxonomy of Educational Objectives: The Classification of Educational Goals. Handbook 1. Cogni-tive Domain. New York: McKay, 1956.

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Bloom, B.S., Hastings, J.T. and Madaus, G.F. Handbook on Formative and Sunnative Evaluation of Student Learning. New York: McGraw-Hill, 1971.

Wilson, J.W. Evaluation of Learning in Secondary School Mathematics. In Handbook on Formative and Suminative Evaluation of Student Learning. New York: McGraw-Hill, 1971, p. 643-696.

Mathematics Contests in B.C. by Dr. Donald J. Miller, Department of Mathematics, University of Victoria

Some time in December an invitation and registration form will be sent to each secondary school for both the Junior Mathe-matics Contest and the Annual High School Mathematics Examin-ation. These invitations will also contain the aims of both

exams.

The dates for the 1974 competitions have not been set, so far, and the registration fee for the MAA contest may change

next year.

Last year, as regional chairman of the Canadian Mathematics Olypiad, I was allowed to nominate 21 candidates to compete in the contest. On an experimental basis, it was possible for a high school principal to nominate a candidate for a token fee of $2. I do not know what the policy will be for this coming year. The prizes for last year's Olympiad are:

First Prize = $11500

J London Life Insurance

Second Prize = $1,000 Company of Canada Scholar-

Third Prize = $ 500 ships

Fourth Prize (5)= $ 200 each Canadian Mathematical Fifth Prize (10)= $ 100 eachi Congress Prizes

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I should know the dates for the MAA contest some time in September. I will also ask Professor Kennedy to keep you informed on the Junior Math Contest.

The top three in the MAA contest in B.C. for 1973 are:

First David Simpson, Steveston Senior Secondary, Richmond

Second Kelvin Ketchum, Killarney Secondary School, Vancouver

Third Ken Dunn, Vernon Senior Secondary School, Vernon

Book Review by Bruce Ewen

THE CALCULUS - AN INTRODUCTIONS by Hugh Thurston, (1973), Prentice-Hall, $12.95.

As a teacher of Grade 12, I find it important to know what my successful students will cope with in the following years. This has been of special personal interest to me recently in that my own children have been studying at UBC. When I have read their texts, I have usually been more critical than complimentary. I must admit that I approached Thurston's Introduction with a negative attitude inspired by other introductions I have seen.

A text must be readable to the student for whom it is intended. Then it must be at least comfortably readable to me. Once I provided myself with a list of the letters of the Greek alphabet, I was pleased to find that Thurston had passed my first test; moreover, there is a person to be found behind the writing - a person willing to ask and answer . the question 'what good is it?' in terms meaningful to most.

A good text will seek a balance between the intuitive and

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the logical. Thurston demonstrates that he is keenly aware that the point of balance must have reference to the student's intuitive power, not the teacher's. In the early stages, all his lessons are brought out of discussions which can have meaning to a student, and later lessons are based on these together with further discussions. When he chooses to present a summary in logical form, he makes it clear that he is doing so, and he makes clear the difference between the formal statement of the argument and the common-sense or intuitive equivalent. This is indeed a refreshing change from the method of teaching which begins with a definition and proceeds from there without regard to whether the student has understood the definition. I can remember struggling through the epsilon-delta definition of a limit before entering the study of limits. Thurston gets: . around to the definition at. a point where the student already has consider-able experience with the idea, and when he does, the language chosen is by contrast remarkably easy, easily within the power of my students.

Thurston's text finds a good balance between theory and practical usefulness. Much of his theory is developed in discussion of practical problems.. His choice of examples and exercises cover a wide range of applications. For this reason alone I would recommend that Grade 12 teachers get a: copy of this book.

Thurston chooses some notation that will be unfamiliar to you, but he carefully sets out equivalent notations and why he chooses his. For instance, the sigma notation is used to de-note both the sequence and its sum, which may bother those who have punned: 'Sigmafies summation.' And I must admit I blanched a little when reading 'y=arctan.' Not arctan x, just arctan.

Should I choose to criticize Thurston's approach to any topic, it would be the finding of the derivative for y=ln x. Here his treatment is quite standard, when it would be more in keeping with his previous lessons to ask the question 'Can we find a function which differentiates itself?' Out of this question he could develop y=eX from either an

intuitive or a logical point of view, and the derivative of

y=ln x would follow easily, just as the derivative of y= arcsin follows from being able to differentiate the sine function.

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Above all, this text demonstrates that it is possible for mathematics to be written with a concern for the student taking precedence over a concern for the subject itself. Thurston should be congratulated and urged to go further.

1973a 74 Schedule of. Meetings The BCAMT executive has tentatively planned to hold at least five meetings this coming year. Any. interested members of the BCAMT may attend. .

September 8, 1973

October 5 or 6., 1973

January 19, 1974.

March 25, 1974

June 1 2 1974

at 10:15 a.m. - B.C. Teachers' Building

at NW Conference

at B.C. Teachers' Building

Annual General Meeting

at B.C. Teachers' Building

New Books across My Desk 1. MATHEMATICAL PURSUITS ONE, Wigle, Jennings, Dowling,

Macmillan Co. of Canada, Toronto, 1973. 356 pages - $6.95 - aimed at the Grade 9 level for average and above students.

2. TOPICS FOR MATHEMATICS CLUBS, jointly published by MU ALPHA THETA and the NCTM. 106 p. , $2.80 per copy for NCTM.

19 . PSA 73-108/bs

PLEASE

RENEW YOUR MEMBERSHIP IN THE B.C. ASSOCIATION OF MATH TEACHERS - LAST YEAR'S OFFICERS TRIED TO SERVE YOU WELL

I. Tried to have the classroom teacher's voice on mathematics heard by the Minister of Education by submitting a brief.

2. Encouraged teachers to join them in their various projects.

3. Organized two most successful summer conferences.

4. Made lists of resource people for in-service chairmen.

5. Opened up a dialog with the revision committee for representation of the B.C. math teachers.

6. Worked like dogs on your behalf for both the secondary and the elementary teachers of B.C.

THIS YEAR'S OFFICERS HOPE TO

1. Continue the good work of last year.

2. Start a think tank on classroom math problem areas manned by practising math teachers (if you would like to offer your help write do BCAMT at the BCTF).

3. Begin leadership workshops to begin math PSA chapters in remote areas of the province (like Vancouver?).

4. Encourage an even better BCAMT Journal/Newsletter.

5. Encourage more math workshops.

DO JOIN US - WE NEED YOUR SUPPORT, AND MORE IMPORTANTLY YOUR PROFESSIONAL HELP,

TO DO MORE FOR YOU AND YOUR STUDENTS.

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