Teaching Mathematics in the Elementary School by Clyde G. CorleReview by: J. FRANKLIN FITZGERALDThe Arithmetic Teacher, Vol. 13, No. 5 (MAY 1966), pp. 412-413Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187149 .

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"p-+~q," or just "~q" may seem to be as good a negation of "p-^q" as the usual one. Again, however, a good instructor can correct this flaw quite easily, by treat- ing conditionals in the usual manner, and it should not deter one from using the book.

For those who are familiar with Crouch and Baldwin's Mathematics for Elemen- tary Teachers, this is a greatly expanded version of the earlier book. The develop- ment of the real number system and the geometry chapter are essentially the same. Other chapters (see first paragraph, above) are interspersed, and a section called "remarks on teaching" is annexed to each chapter. A few of the remarks on teaching are very good and will make up for the need to plow through a constant defense of the material presented in the main por- tion of the text.

Taken as a whole, the book is a good text with which to teach a course that this reviewer doesn't think ought to be taught.

STEPHEN S. WILLOUGHBY New York University New York, New York

Teaching Mathematics in the Elementary School Clyde G. Corle. New York: The Ronald Press, 1964. 385 pp., $6.75. This methods book discusses the follow-

ing mathematical topics: systems of nu- meration, operations on whole numbers, rational numbers, geometry, measure- ment, and consumer mathematics. Throughout these discussions there are references to pedagogy and to contem- porary school mathematics programs, problem solving, diagnosis, and evalua- tion. The book is designed for use as a methods of teaching textbook with ex- ercises that are not particularly imagina- tive.

The book has many mistakes, usually language-centered. Frequently, the re- viewer had the feeling that the end sought by the author was a worthy one, but the language used to express it is misleading. Although the distinction between number

and numeral can be overdone from the standpoint of practicability, and one does not necessarily expect to always find them used precisely, there are instances when not to make the distinction is rather cata- strophic. For instance, on page six the following statement occurs, "The teacher, therefore, who insists that five plus four must equal nine should know that five plus four equals one, one (one eight and one) when the number base is eight." (Five plus four always equals nine, unless the defini- tion of addition or some axioms are changed. The sum does not vary when the system of notation is changed; only the symbol may change.) A similar error is found on page 77 in this statement, "The multiplication facts change when the num- ber base is eight." (It is not the facts which change but the symbols used to rep- resent them that change.)

Pages 66, 111, and 112 reveal, respec- tively, "negatives of the natural numbers," "negative two," and " - " in the context of "-5," which is called a minus sign. These are inconsistent and do not stress the ideas of inverse, negative numbers, and binary operation of subtraction. Another misleading expression, that is used several times and illustrated on page 218 is "come out even" when referring to the quotient. The expression does not mean the quotient is an even natural number. In the discussion of rational numbers no distinction is made between "rational number" and "fraction." It seems "frac- tion" is both a symbol and a rational num- ber. One may change fractions or add them. Page 274 reveals that a particular segment is a diameter of a circle and that the measure of the same segment is also a diameter. In other words, a set of points is a number.

The parts of the book that discuss teach- ing are better than those that discuss mathematics. Some helpful suggestions are made for teaching specific topics. Chapter 4 has a good discussion on the teaching of addition of whole numbers through the use of sticks and the abacus. However, the

412 The Arithmetic Teacher

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use of expanded forms should have re- ceived some stress. The number line was used, but the role of "0" on it seems con- fusing. The treatment of subtraction in Chapter 5 is on a par with that of whole numbers. There is a rather mechanical treatment of integers. Chapter 6 treats multiplication of whole numbers in terms of Cartesian product. It does not try to justify the Cartesian product by showing the limitations of multiplication in terms of addition. The sticks, abacus, and num- ber line are used to illustrate specific multiplication problems. Page 132 has four typographical and mathematical errors. Chapter 7 has some helpful ideas for teaching division by use of sticks, abacus, and number line. But the chapter has many language and typographical errors. The book misuses " = " in the state- ment "67-ï-9 = 7 with a remainder of 4."

Chapter 8 is a good development of operations on rational numbers through

the use of circles and their sectors, and the number line. There are unfortunate uses of the words "distribution" and "regroup" on pages 186 and 198, respectively.

In final appraisal the reviewer does not believe this methods book is satisfactory as a text or reference book. The mathe- matical content is not adequate enough, if indeed it should be. Neither is the mathe- matical content accurate enough, which indeed it should be. The methods which are fairly standard do not take as much advantage of mathematical principles as they should. There is also little in the way of sequential development of an idea. Good ideas are often mentioned with in- sufficient or no development of them. The chapters on contemporary mathematics programs, solving verbal problems, and diagnosis and evaluation have merit.

J. FRANKLIN FITZGERALD School of Education Boston University

Books received (Continued from page 391)

Excursions in Number Theory, C. Stanley Ogilvy and John T. Anderson. New York: Oxford University Press, 1966. Cloth, 167 pp., $5.00.

A reference book for elementary and junior high school teachers who wish to extend their mathematical knowledge.

Fun with Figures, J. A. H. Hunter. New York: Dover Publications, Inc., 1965. Paper, 109 pp., $1.00.

A collection of 150 problems (teasers) for elementary school children.

Mathematical Challenges, compiled and anno- tated by Mannis Charosh. Washington, D.C.: National Council of Teachers of Mathe- matics, 1965. Paper, 135 pp., $0.80.

A collection of problems for students in grades 7 through 12.

Mathematics for Teachers of the Middle Grades, J. Maurice Kingston. New York: John Wiley and Sons, Inc., 1966. Cloth, 322 pp.

Designed to provide a minimum amount of background material needed Ъу teachers of grades 4 through 9.

Numbers and Arithmetic, John N. Fujii. New York: Blaisdell Publishing Co., 1965. Cloth, 559 pp.

A college text on arithmetic with emphasis on both structural concepts and practical computational, skills. The book is intended to be used in a pre-algebra review course.

Series of Informational Pamphlets about Ele- mentary School Mathematics: No. 1 - Number and Numeration; No. 2 - Operations: Basic Number Processes; No. 3 - Operations with Fractions; No. 4 - Problem Solving; No. 5 - Geometry and Measurement. Publications Distribution Unit, Education Building, Albany, New York 12201: New York State Education Department, 1963-65. Paper, $0.25 each.

Pamphlets written to aid elementary school teachers of New York State imple- ment the mathematics curriculum.

May 1966 413

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