Mathematics Teaching and Learning by Jon L. HigginsReview by: Gerald R. RisingThe Arithmetic Teacher, Vol. 20, No. 7 (NOVEMBER 1973), p. 608Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41188361 .

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Children Using Mathematics. K. L. Gardner, J. A. Glenn and A. I. G. Renton, eds. New York: Oxford University Press, 1973, 128 pp., $2.50, paper. L, T A summary of primary school mathematics

content in English schools with some pedagogical comments.

What is the value of a book like this? The outlined content is standard. The suggested teaching devices appear in most texts. The com- ments on such basics as development psychology are so brief that they more caricature than characterize the issues. This is very thin gruel.

The Development of Operational Thinking in Primary School Children. Barnabas Otaala, New York: Teachers College Press, 1973, 177, pp. $3.95. L I have only one reservation about this report:

the title is misleading. The subtitle, which does not appear on the front cover, is much more informative: "An Examination of Some Aspects of Piageťs Theory Among the Itesco Children of Uganda."

The book is evidently an outgrowth of Mr. Otaala's graduate paper on this topic done at Teachers College. The experiment is clearly presented and the implications carefully analyzed. A serendipic role that the monograph might play is as a model for thesis writers.

Mathematics Teaching and Learning. Jon L. Higgins, Worthington, Ohio: Charles A. Jones Publishing Co., 1973, viii + 228 pp. *, T This is a most interesting methods text that

provides a serious student with good knowledge of a variety of psychological frameworks (learn- ing theories) from which he may draw his philosophical basis for instruction. The units focus on intelligence, Piaget, SR learning, gestalt and heuristics, and concept learning. Each is very well done.

I have little with which to quarrel here. My concerns relate only to the clientele. The book should be taught by a high quality instructor who can extend the content and help students to apply it to other specific aspects of their instructional program. And I think that this text should not be used at the time students are

either student teaching or making final prepara- tions for student teaching; then their focus is so tight on "practical" maintenance activities that this content would be largely wasted. Rather I see the book as more appropriate to a graduate course or even a lower division course - I be- lieve students would be better prepared emo- tionally for this content.

"Some Computational Strategies of Seventh Grade Pupils." Francis G. Lankford, Jr. Mimeographed. Charlottes ville, Va. : Center for Advanced Study, University of Virginia, 1972.

*, I, L

Here is an example of significant research not only well done and well reported, but also of immediate practical value to the classroom teacher. I encourage teachers to obtain this docu- ment and to devote the hour or so necessary to read the heart of the report (pages 20-41). At the same time I encourage members of the re- search community to turn to this study by a recognized statesman of mathematics education for a model of what we should be doing and how we should be doing it.

Professor Lankford's study of recorded oral comments of 176 students performing on a straightforward 36-item computation test sup- ports all three of his working hypotheses: (1) "Computational strategies ... are highly indi- vidualized and often do not follow the orthodox models of textbook and classroom." (2) "There are observable differences in ... computational strategies" between successful and unsuccessful computers. (3) "Clues for remedial teaching of computational skills may be derived from an examination of the patterns of ... unsuccessful computers."

The tone of the report can only be suggested by a few quotes: "With high frequency (74) pupils chose, or made, doubles to add. In 64 -f- 78, for example, pupils would say '8 and 4 are 12; 6 and 6 are 12 plus 1 is 13, plus 1 (carried) is 14.' " "A prevalent practice was to add numera- tors and place the sum over one of the denomina- tors, as in % + % = %: '5 + 3 = 8. You don't add the bottom numbers because 2 will go into 4.' " "Some surprising whole numbers were de- rived for answers, as in 3á - V2 - 22 ('2 take away 4 is 2; 1 take away 3 is 2')."

Thanks from the Editorial Panel

Ann McAloon completed her term as a member of the Editorial Panel of the Arithmetic Teacher in May 1973. Thank you, Ann McAloon, for your contributions to the continued progress of the AT.

The Editorial Panel

608 The Arithmetic Teacher

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