Teaching and Learning: A Problem- solving FOCUS, Frances R. Curdo, ed. 1987, viii + 116 pp., $12 paper. ISBN 0-87353- 240-6. National Council of Teachers of Mathe- matics, 1906 Association Drive, Reston, VA 22091. This book is an anthology of seven papers concerning the problem-solving process in mathematics, plus a chronological bibliography of Plya's work in mathematics education. The focus of the book concerns the work and views of the late George Plya (1887-1985). These papers were presented at the 65th Annual Meet- ing of the NCTM.
Although the papers may possibly be read in any order by a person previously familiar with the work of George Plya, they are arranged in a general order that reflects a framework for a review of problem solving. The first paper is a classic presentation by Plya himself, written in 1963. In this representative example of his views and style, he discusses teaching, learn- ing, and the preparation of teachers and illus- trates with examples.
Following this sample of Plya's work, G. L. Alexanderson chronicles a brief overview of the life and contributions of Plya. This article is followed by an entertaining, thought-provoking history of problem solving itself, written by Alan Schoenfeld.
The book then proceeds to two papers, one written by Peter Hilton and Jean Pedersen and one by Lester Lange, which outline specific mathematical situations and sequences that ex- emplify problem solving. It seems that these two papers are generally more intended for secondary teachers than for elementary teach- ers.
The book then addresses teaching consider- ations directly. Jeremy Kirkpatrick discusses both philosophical and practical pedagogical considerations, and Marilyn Suydam outlines in clear language the current state of research regarding the teaching of problem solving.
Finally G. L. Alexanderson provides a help- ful time line of Plya's works.
The book is virtually a "must read" for anyone interested in problem solving. The topics are profound but are dealt with in clear and engaging writing styles. It both informs and raises substantial questions. Its intended audi- ence seems to be the person with a prior interest in the basics of problem solving, but the novice could also profit from it. It seems some- what more directed to the secondary level than to the elementary, but teachers at all levels can read it and be challenged and informed by it. - David R. Duncan, University of Northern Iowa, Cedar Falls, IA 50614.
From Other Publishers Creative Graphing, M. Freeman. 1986, 64 pp., $5.95 paper. ISBN 0-914040-47-2. Cuisen- aire Company of America, 12 Church St., Box D, New Rochelle, NY 10802. "Do you have a pet? How do you get to school? Where were you born? Do you wear a seat belt
when riding in a car?" These are some of the questions explored in this book's graphing ac- tivities. The activities deal with the collecting, organizing, interpreting, and summarizing of data in tables, charts, and Venn diagrams. Motivating elementary- and middle-level stu- dents becomes easy when the task is interesting and relevant to their own lives. Since the stu- dents provide the data for the graphs, they will become involved in the graphing. Through dis- cussions concerning the graphs, students will learn about each other as well as mathematics.
The first section of the book deals with details of why, when, and how to use graphs. The second section describes processing: the examining, analyzing, and interpreting of the graphs. The focus in processing is on asking three types of questions: (1) basic number skill and estimation; (2) analytical and extension; and (3) personal and opinion. The third section contains twenty-four examples of graphs. Sam- ple questions to be used for processing are given in the teacher notes for each of the graphs. The fourth section contains an addition- al sixty-two ideas for graphs.
I was surprised by the title of this book that the focus was not on bar, line, and circle graphs; rather it deals only with tables, charts, and diagrams. The strong points of the book are the well-designed graphs, the variety of formats used for the graphs, and the emphasis on ques- tioning. This book would serve as an excellent source of graphing ideas and teaching sugges- tions to help develop students' critical thinking skills. - De Ann Huinker, University of North- ern Iowa, Cedar Falls, IA 50614.
Houghton Mifflin Mathematics, K-8, 1987 ed., Lehn R. Capps, W. G. Quast, Mary Ann Haubner, William L. Cole, Leland Webb, and Charles E. Allen. 1987, K-$5.10; Grades 1-2- $8.10; Grade 3- $13.86 cloth, $10.74 paper; Grades 4-6- $13.86; Grades 7- 8 - $16.14. Also available teacher's edition, teacher's resource book, workbooks, tests, ma-
nipulative aids kits, daily review booklet, lan- guage and vocabulary activities manual, pro- gram record card, instructional courseware, computer management system, Spanish edi- tion, and overhead visuals. Houghton Mifflin Co., One Beacon St., Boston, MA 02108. This K-8 series has incorporated several impor- tant strands into the usual mathematics curricu- lum. The problem-solving component provides somewhat limited initial instruction on each of twenty-three problem-solving strategies devel- oped over the first nine years but gives plenty of opportunity for practice, nearly daily, on good, varied problems. Materials and suggestions for cooperative group problem solving are also supplied.
Strategies for mental mathematics and esti- mation are presented. Again, although teachers may need to supplement and illustrate initial presentations of each strategy, provision is made for continued reinforcement, both during the year it is introduced and in succeeding years.
Calculator use is suggested in many lessons, and a page per chapter is devoted to computer literacy from grade 3 on.
Daily, cumulative, and vocabulary reviews are provided in the text and by supplementary materials. Assignment guides, including home- work where appropriate, appear in each lesson of the teacher's edition. Much separate supple- mentary material is available - reteaching, practice, enrichment activities, manipulative aids, tests, management systems, transparen- cies, and so on.
Most lessons follow a somewhat similar for- mat of developmental instruction, guided prac- tice, and seatwork (including problem solving). The teacher's edition gives some suggestions for developing the lesson, often employing the use of manipulative materials. This would ap- pear to be a key component, since the lesson in the student's text usually gives only one illus- trated example followed by many practice exer- cises. Conscientious teachers will want to pro- vide the meaningful development needed.
REFEREES! flu An Invitation from the v^inHlu
Editorial Panel ^fuvY The Editorial Panel invites members interested in serv- uff I 111 ing as a referee of manuscripts to request guidelines ||'1 I If/ and a personal data sheet from NCTM. I I 'jt Each of the articles that appears in the Arithmetic 111 I
Teacher is judged for content and style by at least three Jill I IV referees. The success of the Arithmetic Teacher is very v^wm^rjaaL much dependent on these volunteer efforts. / '
December 1987 41
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Article Contentsp. 41
Issue Table of ContentsThe Arithmetic Teacher, Vol. 35, No. 4 (December 1987), pp. 1-44Front MatterOne Point of View: Children's Right to Be Wrong [pp. 2, 20]Readers' Dialogue [pp. 4-5, 25]Divide and Conquer: Unit Strips to the Rescue [pp. 6-12]From the File [pp. 12-12]Using Historical Materials in the Mathematics Classroom [pp. 13-16]Assessing For Learning: Tests-a Tool for Improving Instruction [pp. 17-18, 44]Ideas [pp. 19-24]Problem Solving: Tips For Teachers [pp. 26-27]Two-sided Pies: Help for Improper Fractions and Mixed Numbers [pp. 28-32]Research into PracticeMicrocomputer Use in the Elementary School [pp. 33-34]
Teaching Mathematics with Technology: Common Multiples: Activities on and off the Computer [pp. 35-37]Reviewing and ViewingComputer MaterialsReview: untitled [pp. 38-38]Review: untitled [pp. 38-38]
New BooksFor TeachersFrom NCTMReview: untitled [pp. 38, 40]Review: untitled [pp. 40-40]
From the File [pp. 40-40]Reviewing and ViewingNew BooksFor TeachersFrom NCTMReview: untitled [pp. 41-41]
From Other PublishersReview: untitled [pp. 41-41]Review: untitled [pp. 41-42]Review: untitled [pp. 42-42]Review: untitled [pp. 42-42]Review: untitled [pp. 42-42]Review: untitled [pp. 42-42]
EtceteraReview: untitled [pp. 43-43]Review: untitled [pp. 44-44]Review: untitled [pp. 44-44]