101 Ways to Learn Mathematics Using BASIC (K-8) by Richard J. ShumwayReview by: Mary Kim PrichardThe Arithmetic Teacher, Vol. 36, No. 2 (October 1988), pp. 58-59Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193483 .

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help explain achievement patterns in junior high school mathematics and how these patterns may affect language minority students and their opportunity to learn.

The editors of this book state that the rela- tionship between language skills and mathemat- ics is not well understood. Yet it is one funda- mental issue to be understood if we are to improve the access to education for all our students. Therefore, while drawing on the work and research of a "wide array of experts from diverse fields," they have tried to identify the important research questions on the topic of the language-mathematics relationship. They also hoped to "identify and document existing data banks appropriate for conducting secondary analyses/' In doing so, much exchange be- tween the contributors resulted in revisions and rethinking, along with a recommendation for further study of these issues. The book may be used by researchers in this area, as well as by those interested in a compilation of the wide range of variables to be considered in a study of the language-mathematics relationship.

The presentation of this wide range of varia- bles constitutes the strength and purpose of this book. The emphasis given by different re- searchers is interesting for the reader relatively new to the field and yet specific enough to be truly informative. Relevant statistical analyses are included in the chapters. The book ends with a touching account of a Cochiti Indian's experience with schooling away from the com- forting, loving home environment of his reser- vation. The preceding impersonal, large-group data was "brought to life" for me and reminds us that our goal is to improve education and learning for "real people" when analyzing the language-mathematics connection. - Nancy M. Wilson, Valley View Elementary School, Oxon Hill, M D 20745.

Mental Math in the Middle Grades, Jack A. Hope, Barbara J. Reys, and Robert E. Reys. 1986, 121 pp., $8.95 paper. ISBN 086651-312-4. Dale Seymour Publications, P.O. Box 10888, Palo Alto, CA 94303. Mental Math is a book of blackline masters designed to aid the teacher in incorporating mental calculations into the daily mathematics practice of middle grade students. This book is part of a three-part series that addresses the need for more organized instruction in helping students learn the techniques of "figuring in your head." The first book is designed for students in grades 2-4, and the third book is written for grades 6-8. This second book in the series is designed for grades 4-6.

This program improves students' ability to do mental mathematics by presenting approxi- mately one lesson a week throughout the school year. The book consists of four units, each beginning with a special interest page about experts in mental calculation. The format of these pages lends itself to use on the overhead projector or bulletin board.

Each unit contains nine lessons, and each of the lessons consists of two pages: a teaching page for introducing the new strategy and a

"power builder" page designed for practicing the given strategy using two different sets of problems.

The introduction to the book offers informa- tion on how to schedule, plan, and present the lessons and gives guidance on practicing the strategies in addition to offering information on related practice. Tests are included to monitor students' progress throughout the program on a unit-by-unit basis. Two forms of a cumulative test are included, which can be used as a pretest and posttest.

Since all the pages are perforated, the teacher can arrange corresponding lesson information in individual packets by week or unit to orga- nize for teaching the strategies.

In a world filled with calculators and comput- ers, mental computation often lacks attention in the regular mathematics curriculum. Mental Math offers a planned program of instruction in mental calculation that complements the regu- lar classroom curriculum and addresses an im- portant aspect of mathematics ability as high- lighted in the third National Assessment of Educational Progress in mathematics. - Dana S. Adams, New Hanover County Schools, Wilmington, NC 28403.

One Hand at a Time, Patricia e. Smith. ¡987, 90 pp., $9.95 paper. ISBN 0-86651-347-7. Dale Seymour Publications, P.O. Box 10888, Palo Alto, CA 94303. This book addresses a difficult concept for the primary school student and offers a sequential approach to the teaching of time that is refresh- ing in its simplicity. With the young learner's need to visualize and manipulate his or her environment concretely, the author has pre- sented a method "for isolating specific time- telling concepts and for bringing the abstract concepts to a concrete framework." The focus of the book is on teaching time through a one-hand-at-a-time approach that spends a great deal of instruction on the hour hand and its placement at the hour, half hour, and quarter hour. The minute hand is addressed and studied in isolation only after a thorough investigation and sequential practice of the hour hand is complete.

The material is in the form of blackline mas- ters for those items that require written work following the completion of the activities listed for each chapter. Also, a set of open-ended blackline masters is included to be used by the teacher as necessary for the specific needs of the students. Many of the chapters contain information on interesting topics to whet the students' curiosity, such as clocks of the past, why clocks are round, and why two hands are better than one. Several bulletin-board ideas are presented to complement the concepts be- ing studied. Matching games, simple board games, and riddle games are included to give the necessary practice in developing the con- cepts.

The chapter addressing the "before and af- ter" concepts is particularly well presented. Using only the hour hand, students are asked to determine whether the time shown is before or

after the given time through several activities and worksheets.

The author recommends using the one- handed-clock approach exclusively rather than pulling lessons from this book and combining them with lessons dealing with two-handed clocks. To enable students to make the transi- tion from telling time on one-handed clocks to using two-handed clocks, the author includes a chapter on combining the hour and minute hands so that students can deal with a two- handed clock with accuracy.

This book can be used by the teacher as the core of a developmental time-telling unit for primary school students or as a remedial tool for those students in the upper elementary school levels who have not mastered the con- cept of time. The special education student would also benefit from this instructional aid.

Given the pervasive use of digital time in today's society, it is refreshing to see a treat- ment that deals with the concept of time specif- ically, logically, and sequentially and at the same time addresses the developmental apti- tude of the learner. - Dana S. Adams.

101 Ways to Learn Mathematics Us- ing BASIC (K-8), Richard J. Shumway. 1987, vii + 245 pp. Prentice-Hall, Englewood Cliffs, NJ 07632. While reviewing this book I did not actually count the suggested activities; however, I am certain that 101 is a modest estimate of the number of "ways to learn mathematics" pre- sented by the author. The topics are well- chosen to span the K-8 curriculum: arith- metic - whole numbers, decimals, and fractions; geometry - measurement, graphing, and geometric shapes; probability - random numbers, permutations, and combinations; and concepts from beginning algebra - functions and solving equations.

Each chapter is made up of a series of activ- ities related to a common mathematical topic. For example, some of the topics in the chapter "Decimals and Fractions" involve solving equations, scientific notation, random deci- mals, and the INT function. Each activity in- cludes a BASIC program and exercises related to understanding and modifying the program. Most of the programs in the book can be used on any computer. Programs that involve graph- ics are written for Apple computers; however, they are easily adapted to other computers.

This book is different from most of the books on BASIC programming because of its focus on applications for the mathematics classroom. One of its strengths is that it can be used in a variety of ways. According to Shumway, its audience includes prospective teachers enrolled in college mathematics courses, mathematics students with access to computers, and current teachers interested in using computers to teach mathematics.

It should be noted that this book is not a programming manual and that if it is used in a course for teachers, it might be appropriately supplemented with a BASIC handbook. Shumway's approach to using BASIC is to learn by doing. Commands and instructions are

58 Arithmetic Teacher

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used as they are needed to explore mathemati- cal topics and problems.

Finally, the major strength of this book is the fact that "all the activities are based on real experiences with teachers and children." As a mathematics educator, I particularly like this book because it helps prospective and current teachers to see how programming activities can enhance mathematics teaching and learning. I recommend this book for use with both teach- ers and students. - Mary Kim Prichard, Univer- sity of North Carolina at Charlotte, Charlotte, NC 28223.

Teaching and Learning Mathemat- ics Part 1 and Teaching and Learn- ing Mathematics Part 2, edited by Paul Ernest. 1987, part 1-75 pp., part 2-77 pp., $3.46 ea. paper. ISBN 85068-0948. Curriculum Resources Centre, University of Exeter, St. Luke's, Heavitree Rd., Exeter, EX1 2LU, En- gland. i nese two snort volumes are part or a series ot occasional publications on current educational topics. Published by the School of Education at the University of Exeter, they reflect the changes that are transpiring in mathematics education in Great Britain. The editor of this series, Paul Ernest, cites three factors that are contributing to the increased fervor in mathe- matics education: (1) within the last five years several government documents have been pub- lished recommending changes in the teaching of mathematics; (2) an increased use of calculators and computers in the schools has been noted and continues; (3) continued research has be- gun to elucidate even further the teaching and learning of mathematics. Many articles in this series address these recent influences: David Burghes looks at the current government initi- atives and recommends some changes of his own in "Mathematics Education for the 21st Century: It's Time for a Revolution!"; Dudley Kennett addresses the technological advance- ments in "Using Interactive Video in Second- ary Mathematics"; and Charles Desforges shares research on the importance of discussion in the mathematics classroom in "Classroom Processes and Mathematical Discussions: A Cautionary Note."

Although this series addresses the unique concerns of British educators, the ideas dis- cussed would be of value to American mathe- matics educators, particularly those at the uni- versity level. Many of the same problems plague the classrooms of both continents: the persistence of recitation; the lack of meaningful classroom dialogue; and the divorce of mathe- matics from the lives of children. Several arti- cles address these concerns. In his article "Mathematics - an Alternative Approach" David Hobles outlines the need to return the context to mathematical learning. He briefly describes an innovative curriculum develop- ment project entitled "Alternative Mathemat- ics," which organizes mathematical experi- ences around five contexts: business and

commerce, environment, design, science and technology, and leisure and recreation. In an- other article entitled "Investigations: Where to Now?" Stephen Lerman argues for shifting the focus from problem solving to problem posing. He claims that students need increasing oppor- tunities to investigate and extend a given set of data in numerous ways. By enabling students to examine situations and pose their own prob- lems, teachers empower children with a way of thinking that helps them to examine their own lives more critically. In another timely article, "Mathematics Teaching - Belief and Practice," Barbara Jaworski calls for teachers to be re- searchers. She acknowledges the importance of an investigative approach to mathematics and encourages teachers to give students various opportunities to express and explore ideas for themselves. She reiterates the importance of discussion in the mathematics classroom.

This series of articles highlights some impor- tant directions for mathematics education. Al- though the reader is somewhat hampered by not having a complete understanding of current government initiatives and curriculum develop- ment projects, nevertheless, the concerns raised are important ones for all mathematics educators to consider. - David J. Whitin, Uni- versity of South Carolina, Columbia, SC 29208.

ondPiocDing

Etcetera

Developing Computational Skills, Carole E. Greenes, George E. Immerzeel, Linda A. Schul man, and Rika C. S pun g in. Set of 26 teaching cards, 154 exercise cards divided into 12 sections (a total of 154 problems) with answers, and 50 award certificates, $46.50. DLM Teaching Resources, One DLM Park, Allen, TX 75002. Developing Computational Skills is a sequen- tially developmental program, boxed and orga- nized on 5-inch-by-8-inch cards, that leads stu- dents through step-by-step algorithms for adding, subtracting, multiplying, and dividing

Edited by Ann Neaves Boling Jackson Public Schools Jackson, MS 39225-2338 Patricia Wilson University of Georgia Athens, GA 30602

October 1988 59

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