Helping Your Child Learn the New Arithmetic by David EnglerReview by: James R. SmartThe Arithmetic Teacher, Vol. 9, No. 5 (MAY 1962), p. 294Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41184636 .

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the results of either equating or relating ratio and fraction and the consequent difficulties injected into the study of per- centage. The interested reader is referred to book 1, page 208; book 2, page 163; and book 3, page 85. Both books 1 and 2 treat per cent as a fraction, and both identify the traditional three cases. Book 3 states, "Percentage is a development of ratio comparison which emphasizes 100 rather than 1 as a standard of comparison" (p. 227).

Many aspects of book 3 are of the nature to be expected in the year 1961. It is intended for students "not prepared to begin the study of algebra." In this ob- jective it might have some promise of suc- cess with a limited category of students, for instance, the college-capable student not quite mature enough to begin the study of algebra with his classmates. It also deserves consideration in the type of college course for which books 1 and 2 might be selected; but, like them, it would not be adequate as the sole college prep- aration in mathematics for prospective ele- mentary teachers.

Clarence H. Heinke Capital University

Columbus, Ohio

Helping Your Child Learn the New Arith- metic. David Engler. New York: Cri- terion Books, Inc., 1961. Cloth, 156 pp., $3.95. Arithmetic is taught differently now

than it was when most adults were in school; hence a book designed to acquaint parents with the newer arithmetic pro- gram should be considered seriously. This book presents a survey, by grade levels, of teaching arithmetic for understanding, followed by suggestions of how parents may give additional help at home in ex- plaining meanings.

Some good features make the book bet- ter than I expected. The lucid explanation of the basic philosophy of why schools now teach arithmetic for meaning and readily

understood explanations of many of the expanded algorisms deserves praise. Other strengths include good hints for teaching problem solving, excellent bibliographies, ideas for simple homemade devices to help explain meanings in arithmetic, and many practical suggestions for real-life family situations in which parents can stimulate the application of arithmetic.

This is a book written for intelligent parents. In general, the author does a nice job within the limited scope. Cer- tainly, however, the vocabulary is not always technically correct by modern standards. In fact, the author has virtually ignored developments in arithmetic educa- tion in the last half-dozen years. It is a shame the book was not published earlier, for the title will be very misleading. For example, nothing is included about equal ratios, the use of equations, enrichment top- ics, or experimental programs in arithmetic.

Occasionally, the author presents ma- terial which might be confusing to parents. Examples are as follows : absolute and rela- tive value on page 19, the collective idea on page 27, the use of exchange, and the emphasis on the trick of looking for "of" in percent problems. Other questionable inclusions are the discussion as to whether zero is or is not a number, the use of the word "inverse" without definition, and the assumption (pp. 24 and 73) that the equal additions method of subtraction is the most common one for adults. Yet, the book does manage to give parents a good idea of much of basic arithmetic from a point of view emphasizing meanings. Though the author is uncritical of modern teaching practices, and his suggestions by grade level may no longer parallel the arithmetic program in many schools, the elementary teacher could recommend the book to parents if she warns them to be cautious. The volume might also be used as supplemental reading in a methods course.

James R. Smart San Jose State College San Jose, California

294 The Arithmetic Teacher

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