Teaching Mathematics in the Elementary School, 2d ed. by Lola June MayReview by: Edith RobinsonThe Arithmetic Teacher, Vol. 21, No. 7 (NOVEMBER 1974), pp. 641-642Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41188642 .

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eludes considerable geometry work. The non- basic part of the text includes work with ratios and rates, proportions, finding percents, graphs, probability, integers, and graphing ordered pairs. The approach to teaching the division algorithm begins with the "modern approach" as used in the grade-4 text, but quickly is changed to the "old goes-into approach," called the place value method in this text. The divide, multiply, subtract, bring down steps are used. The "whys" are not considered; children are taught to divide by rules - for the reviewer this is not consistent with good mathematics teaching. The word prob- lems in this book seem to be particularly rele- vant and within the children's experiences as they are concerned with such things as visiting the airport, improving a park, paper drives, va- cations, and going to the zoo. The "Let's Go" section on flowcharting is good.

The grade-6 program reviews the work with whole numbers, fractions, and decimals of pre- vious grades; continues the rule approach to division as seen in grade 5; uses flow charts for some review topics; introduces as new topics some of the enrichment work in earlier books, such as prime factors, common multiples, lowest common multiples, ratios, percents, and others; extends fraction and decimal work introduced in grade 5; introduces multiplication and division of decimals; teaches division of fractions; in- cludes geometry concepts and constructions. Ex- tension topics include a variety of topics relating to transformational geometry, plane and solid geometry, mensuration, statistical graphs, prob- ability, and operation with integers.

The Teacher's Edition contains these general parts - "Count Muchmore and his Friends," an explanation of the code used for the books and the purpose of the cartoon characters used in the program; a list and description of the com- ponents of the Silver Burdett Mathematics Sys- tem; features of the Teacher's Edition; features of the students' textbooks; an explanation of the

Silver Burdett Mathematics System; a scope and sequence chart for grades 1 through 6; a list of the performance objectives in each of the six strards in the grade-6 program; the in- dividualized course and time schedule; and a glossary. Before each chapter there is a section giving the perspective, the performance ob- jectives, and information about teaching the chapter, including typical student difficulties, minimum student requirements, and a pretest. The margins of each lesson contain headings that flag the lesson parts. The pupil's page with answers is the predominant part of each teacher- edition page. In places are also found sections entitled "Teacher's Corner" and "Students' Cor- ner." The teaching strategies are very brief, and little help is given to the teacher on how to teach this program. A teacher who does not know how to teach elementary school mathe- matics will not learn how to teach from using this manual. No mathematical background for the teacher is given. It appears that the authors assume that all elementary teachers know how to teach elementary school mathematics and have a good mathematical background. This is far from reality!

Overall, the program appears to the reviewer to be a step backward. Too much emphasis is given to presenting facts, giving rules, and showing how to compute, with little attention given to developmental teaching and teaching for understanding. Little or no emphasis is given to using manipulative materials, learning by doing, and using good questions to lead pupils to make discoveries and generalizations. It is unfortunate that the teacher's manual is little more than an answer book.

Some good features are the teaching of metric measurement from grade 2 through grade 6, the emphasis on problem-solving strategies, and the inclusion of much geometry in the basic program. - Géraldine Green, Royal Oak Public Schools, Royal Oak, Michigan.

New books for teachers

Edited by Edith Robinson, University of Georgia, Athens, Georgia

For the methods course

Teaching Mathematics in the Elementary School, 2d ed. Lola June May. New York: The Free Press, 1974. xvi + 350 pp., $5.50 paperback, $9.95 hardcover.

The author's breezy enthusiasm for teaching comes through clearly in her writing, making this an easy and enjoyable book to read. May's well-known talent for creating interesting class- room activities is also apparent. In general,

November 1974 641

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she addresses herself to the teacher as an equal, with illustrations that look like anyone's free- hand sketches, and complete emphasis on chil- dren's learning. In particular, the frequent com- ments about what is easy and what is difficult for children are valuable to the teacher or prospective teacher.

Unfortunately, the book suffers from a lack of careful editing. For example, in the chapter on the meaning of fractional number, there are repeated references to the unit being partitioned into congruent parts; as a consequence of this stipulation, a rectangular region could not be partitioned into fourths by its diagonals. In the chapter on informal geometry, pupils are to be instructed to place four dots "so that none of them is in a straight line" (p. 263). Again (p. 210), %2 is to be written as

6X1/6X2.

And (p. 246),

1 X 1

5 X 6 ~(S^3;X2

Although some of these are clearly typographical errors, the fledgling or insecure teacher may ac- cept them at face value and strive to carry them out in the classroom. In turn, the pupil who believes that only congruent parts of a "geometric" unit can be accepted when con- sidering fractions may later be baffled in geom- etry when asked to prove that any median of any triangle bisects the enclosed region

о

/ i ' i^' ^У The book covers all the standard content of

elementary school mathematics, including a (new) chapter on the metric system and a (new) chapter on the role of the teacher. The latter is especially good.

Guiding Discovery in Elementary School Mathe- matics, 2d ed. С. Alan Riedesel. New York: Appleton-Century-Crofts, 1973. x + 657 pp. The critical factor in the choice of this book

as a text for a methods course will be, I believe,

the instructor's own definition of "discovery." For Riedesel, this is "guided discovery" as ex- emplified by Socratic questioning, pattern search- ing, group thinking, or the laboratory approach. In the opening chapter, these four methods are contrasted with an "explanatory pattern"; in most of the remainder of the text the four discovery patterns are applied to the standard elementary mathematics curriculum (along with a few extras).

Like the first edition, the second edition gives the reader the benefit of up-to-date information on research findings and recommendations con- cerning methodology. The exploratory activities at the beginning of each chapter together with the reference-related questions at the end ac- commodate both prospective and experienced teachers and should provide a basis for good class discussion. The generalities - homework, writing objectives, and evaluation - are taken up in chapter two; sequencing is handled within specific content chapters.

I found a few rather disconcerting typo- graphical errors, and have a personal bias against statements such as, "Larry has placed a set of four fish on the flannel board" and "Bob is a subset of the boys," for I see these as perpetuating the worst of the so-called new mathematics. However, overall, the book is a well-organized presentation of a particular theo- retical point of view.

In the classroom

Diagnostic and Learning Activities in Mathe- matics for Children. Richard Copeland. New York: Macmillan Publishing Co., Inc., 1974. 81 pp., $2.50. The book consists of thirty-two adaptations

of Piagetian tasks accompanied by some dis- cussion. Teachers may enjoy trying out some of the tasks with their pupils, for children's responses can be both astonishing and instructive to adults.

At the same time, readers should not be misled by the title or by the preface in which we are told that "Children's performance in these ac- tivities can serve as a basis for planning an appropriate instructional program in mathe- matics." This may very well be true, but the book fails to provide the necessary help. To cite an example, the purpose of Activity 11 is (p. 26) "to determine when children are able to solve problems involving multiplication of numbers." Many teachers would be interested in a diagnostic activity of this type, but the reader is not told what type of performance should be taken as evidence of the ability. The reader is told that stage-3 children can predict the number of straws necessary (20, for 2 sets of

642 The Arithmetic Teacher

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