Elementary School Mathematics: Teaching the Basic Skills by William ZlotReview by: Edith RobinsonThe Arithmetic Teacher, Vol. 23, No. 7 (NOVEMBER 1976), p. 540Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41189083 .

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course. The reviewer hopes the comments supplied will enable readers to assay the texts against their own set of priorities.

Elementary School Mathematics: Activities and Mate- rials. George F. Green. 1974, 512 pp., $11.95. D. C. Heath & Company, 125 Spring Street, Lexington, Mass. 02173. A book for the thoughtful student, but not a theo-

retical book. Bits of good, practical advice stand out in stark simplicity: "Drill should not be used to teach an idea" (p. 23) and "Any activity is a game if the chil- dren think it's fun." (p. 142). Furthermore, if some matter is not discussed sufficiently, the exposition is so clear that any deficiency in the discussion should be recognizable by instructor or student. For example (p. 20), the italics in the following quote signal a possible need for distinguishing between use of an activity to justify a pronouncement and use of an activity for discovery:

As children observe that the result [of joining sets of size 2 and 3] is a set of five children, they are beginning to learn the desired fact.

The mathematical reviews prefacing each content chapter are concise and clear. Of particular note is the definition of computational algorithm (p. 162), which puts the matter neatly into perspective. You may or may not like the ensuing analyses.

The (content) scope of the book is broad, thus pre- paring the student to meet classes of older or accelera- ted students. Simultaneously, a large number of activi- ties are proposed for use in teaching. The requisite sacrifice is in the amount of detail provided for using any given idea. Although the accompanying ex- planation is completely unambiguous, it does not, for example, suggest appropriate wording for a question for third graders. In short, the text is written for stu- dents capable of translating the ideas into practice.

The author's style of writing is lively, and makes interesting reading. The activities suggested are also interesting, and incorporate all the usual devices (geoboard, abacus, and so on). More help is given for circumventing the difficulties that children have with mathematics than for remediating them.

Elementary School Mathematics: Teaching the Basic Skills. William Zlot. 1976, xiv + 494 pp. Dun-Don- nelley Publishing Corporation, 666 Fifth Avenue, New York, N.Y. 10019. The emphasis in this book is on the pupil and his

interaction with mathematics. Thus the term "basic skills" (see title), as it develops in the text, becomes what the pupil needs to know to succeed in arithmetic.

The mathematics, which is refreshingly clean, pro- vides the organizational framework for the text, but not in the sense of sterile formalism. Addition (of whole numbers) is introduced with descriptions of various physical situations; the similarity that can be perceived in these situations is symbolized by "a + 6," where a and b are whole numbers. Next, the ordered-

540 The Arithmetic Teacher

pair notation is presented (in an optional section), and finally the commutative and associative properties and the role of zero are discussed. Assignments of standard names to sums in which one addend is greater than 9 - that is, computation - finds its appropriate place in a later section on numeration. The result is that about 100 pages of the text are devoted to developing the concept of whole number and the concept of oper- ations and their properties before tackling the business of naming sums, products, and so on. This separation benefits the prospective teacher: in no way is it sugges- ted that numeration be postponed indefinitely for the pupil. The prerequisites for understanding operations and algorithms are carefully developed, but in their respective parts of the book, as distinct here as they are in actuality.

The text is rich in verbal problems. Their usefulness for motivating topics (in the mathematical sense) is fully exploited; the context of the problem exposes the need for certain processes, for certain agreements about symbols, and for certain agreements about what not to consider (a matter frequently overlooked).

When a mathematical definition is required, it is stated precisely, although not always in the same way as it might appear in a mathematics book. This con- forms with the overall theme that the mathematics is for children. Prime number, for example, is defined in terms of sequences; presumably, the children have had much experience with these sequences, so the defini- tion needs no further motivation.

Constant reference is made to difficulties that chil- dren have with arithmetic, and suggestions are offered for circumventing or remediating these. One of the nice features of the book is that this is managed with- out interrupting the flow of the total development. Research related to mathematics learning is alluded to, but space is not expended on fruitless discussion of gray areas.

The principal drawback to the text is its limited scope. Most of the book is devoted to the system of whole numbers and thexsystem of rational numbers. Certain measurement topics are introduced in con- nection with the development of the rationals. Geome- try, relations and functions, and probability and statis- tics do not appear.

Exercises at the ends of chapters are interesting and thought-provoking. The reference lists are extensive and incorporated into exercises. I found no typo- graphical errors, and the only misleading portions were in connection with the ideas of sets. For example (p. 74), "Sam has a set of 4 posters . . ." perpetuates the notion that a set is something that can be handled.

Helping Children Learn Mathematics: A Competency- Based Laboratory Approach. Gregory R. Baur and Linda Olsen George. 1976, 406 pp., $10.95. Cum- mings Publishing Company, Inc., 2727 Sand Hill Road, Menlo Park, Calif. 94025. Whether or not you like this text will depend largely

on your commitment to a competency-based methods course.

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