Children Discover Arithmetic: An Introduction to Structural Arithmetic by Catherine Stern;Margaret B. SternReview by: Gerald R. RisingThe Arithmetic Teacher, Vol. 19, No. 1 (JANUARY 1972), p. 47Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187891 .

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Children Discover Arithmetic: An Introduction to Structural Arithmetic, rev. and enl. ed. Catherine Stern and Margaret B. Stern. New York: Harper & Row, 1971. Pp. xv + 412, $10.00. *, I, T. No classroom from nursery school through

third grade should be without Stern apparatus! These blocks and associated equipment - only superficially like large Cuisenaire rods - should be available to children for experimentation even when they are not made part of the basic in- structional program.

The Sterns's book details their total approach to arithmetic through use of these specific con- crete materials. Any teacher who has access to the apparatus (Structural Arithmetic materials, Houghton-Mifflin Co.) will find in this book a rich source of ideas for their use incidentally or extensively. And all the formal contemporary programs cry out for this kind of supplement: many recommend it specifically!

Two unfortunate aspects of this book are its extreme advocacy and its partisan attacks on the straw men that are made to characterize "new math." I would ask the Sterns their own ques- tion: "Is this the New Math?" But these minor irritants do not detract in any appreciable way from the strong features of the book.

Pic-a-Puzzle: A Book of Geometric Puzzle Pat- terns. Reuben A. Schadler and Dale G. Sey- mour. Palo Alto, Calif. : Creative Publications, 1970. Pp. 127, $3.00. *, I, T, С The millions of elementary school teachers

who skip the geometry chapters in their texts should be forced at gunpoint to distribute copies of Plate 1-25 (primary) or Plate 11-23 (inter- mediate) from this book to their students. Their attitude toward geometry might change as stu- dent excitement mounts. That all-important les- son - that students learn through eyes and through activity - just might be communicated to them.

This book provides a rich source of geometric puzzles and, more important, an opportunity for divergent thinking in creating new puzzles. It also includes a very clear development of basic transformations that is suitable for middle grades. How delightful to see ideas so often beclouded by jargon at the college level pre- sented so simply and directly by example!

Highly recommended. Teachers will use the content as supplementary, when in reality it aims at such foundation ideas as conservation and the meaning of area.

And hats off to Creative Publications, who have joined in providing books like these for the classroom teacher. They are playing a useful role that major houses are not in a position to duplicate.

Your Move. David L. Silverman. New York: McGraw-Hill Book Co., 1971. Pp. 221, $6.95. L, T.

Many mathematicians see in games oppor- tunities to encourage logical thinking and strategy development and to display such con- cepts as isomorphisms (related structures). Teachers, on the other hand, are usually inter- ested only in the drill-and-practice contribution of quite another category: nonstrategic games. The games in this book fall in the first group.

Of the 100 game problems, I found that a quarter could be used to advantage in an ele- mentary school classroom, but for many of these the classroom teacher would need assistance to take advantage of the pedagogical values. An in- service workshop explaining mathematical values would make the book of more use. Recom- mended problems: 1, 3, 4; 25-29, 48, 72 (tic-tac- toe related); 30 (hex); 33 (go-moku); 34-37, 46; 49-51, 55, 56 (nim related); 54, 62 (number properties); 76, 78. Worth special note is prob- lem 69, a true-life situation in which an appen- dicitis victim is alone in a remote cabin with a dead phone.

Math without Tears. Roy Hartkopf. New York: Emerson Books, 1971. Pp. 247, $5.95. I.

A mathematics populanzer relaxed, informal, and good-humored. Purists would be put off by a lack of precision in language, but an intelli- gent layman, with a minimum of effort, can learn a little (or a little more) about mathe- matics - in particular about graphs, logarithms, and differential calculus. The applications ex- amples are interesting and to the point. Skip the trigonometry chapter. Finally, who could write a poor review of a book that has as one of a total of only two exercises: "Make up a graph which will convince your employer that, taking both the increases in your salary and the in- creases in the cost of living into account, you are far worse off than you were rive years ago.

The Growth of Understanding in Mathematics: Kindergarten through Grade Three. Kenneth Lovell. New York: Holt, Rinehart & Winston, 1971. Pp. xii + 204. I, L, T, C.

Kenneth Lovell is probably the best-known British advocate for the theories of the Swiss psychologist Jean Piaget. This book considers the primary school mathematics program as it relates to those theories and Lovell's own minor modifications of the Piagetian stages of intellec- tual growth. He encourages student activity and offers suggestions for specific sequences of tasks related to topics like set, number and numera- tion, operations and mathematical sentences, space, relationships, and mappings and pictorial

January 1972 47

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