Calculator Problem Solving: Using Calculators to Teach Mathematics and Problem Solving byAlfred Capoferi; Terrence CoburnReview by: Paula FillimanThe Arithmetic Teacher, Vol. 32, No. 8 (April 1985), pp. 48-49Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192645 .

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the year (again, particularly at levels A and B) because some material has not yet been taught. The topics in the quizzes may not follow the sequence in your mathematics series. The di- rections and wording of some questions are unclear.

The level-A tests include a translation of mathematics vocabulary words into four lan- guages: Spanish, Hmong, Laotian, and Viet- namese. Its usefulness is not readily apparent. If it is designed for the teacher, a pronunciation guide is needed. If it is for the more literate upper-grade-level students, it could be orga- nized better from the other language into En- glish, rather than the other way around.

Math Capsules is an attractive idea with some merits, but it is limited by weakness in the wording of questions, errors in editing, and a limited use in the time span of the school year. Would half as many quizzes do the job? -

Nancy Imhof, Arlington County Public Schools, Arlington, VA 22207.

Primary Math: Book B, Preschool and Kindergarten. Deborah Buchanan. 1984, 168 pp., $10.95. ISBN 0-8665 1-189-X. Dale Seymour Publications, P.O. Box 10888, Palo Alto, CA 94303-0879.

In Primary Math 168 perforated pages are di- vided into six skill units, record-keeping pages for the teacher, and award pages for students. Each unit provides patterns for the bulletin board, pictures supporting a central theme, materials for students, and testing activities. A short story introduces each sequence of activi- ties and provides the central motivational theme of that unit. For example, the skill of identifying coins (penny, nickel, and dime) re- volves around the "lunch bunch" needing to purchase food items. A bulletin board and story introduce the unit, followed by twenty-three activities and a mastery check. Coins are en- larged so that the teacher can make coin stick puppets for the students. The enlarged coins are not clear. The items seem unrealistically priced, such as a dime for a hot dog and a penny for a cookie.

Each sequence of activities begins with a list of prerequisite skills. Then a sequence of activi- ties is presented, with a mastery test at the end of the set. Many of the activities require the manipulation of concrete items. Although mod- els of the items are included in the book, the teacher needs to duplicate and assemble them. Making sixty drumsticks, "coin match" wheels, or wristwatches for each unit can take a lot of time. Students would have difficulty mak- ing the items, so the teacher duplicates, en- larges, staples, and manipulates the items.

In preschool and kindergarten workbooks, the quality of the artwor-k and the values it expresses are important factors to consider when deciding whether to use them in a class- room. This workbook stars two stereotypical children whose names and costumes change but whose features remain insipidly similar. They appear on progress reports, award forms, and other student materials. Other illustrations in the workbook suffer from similar faults. Illus- trations of some objects, such as cars and planes, are quite outdated, whereas others are

so simplified as to be difficult to identify. - Sandra S. Watson, Alexandria City Public Schools, Alexandria, VA 22206.

New Books for Teachers Edited by Randall I. Charles Illinois State University Normal, IL 61761

Capitol-izing on Computers in Edu- cation: Proceedings of the 1984 As- sociation of Educational Data Sys- tems Annual Convention. Edited by c. Dianne Martin and Rachelle S. Heller. 1984, 496 pp., $35.95. ISBN 0-88175-019-0. Computer Science Press, 11 Taft Ct., Rockville, MD 20850.

The editors of Capitol-izing on Computer Edu- cation undertook the ambitious task of organiz- ing over 100 papers presented at the 1984 annu- al convention of the Association of Educational Data Systems in Washington, D.C. In most such reports of conference proceedings, the reader is confronted with a wide range of mate- rial, with perhaps only a few articles of particu- lar interest. This book is no exception.

The editors followed the lead of the confer- ence's organizers by dividing the book into five major tracks: Computers in Elementary Educa- tion, Computers in Special Education, Comput- ers in Secondary and Higher Education, Com- puter Science and Research, and Computers in School Administration. Each track contains ar- ticles that more or less relate to a particular category of interest, though many articles are applicable to more than one track. For exam- ple, "Computer Literacy - a Word of Caution" by Koehler and Ossler should be of interest to educators and administrators at all levels, though it appears as a component of the third track. Also, the report by Feibel et al. on "Teachers' Courseware Recommendations ..." should be of considerable use to district software-evaluation committees and teachers of all levels. The book's organization makes it somewhat difficult for readers to identify which articles might be of interest to them. The persis- tent will find the search fruitful, however, since several articles are timely and interesting.

In addition to the two articles already men- tioned, an article by Cain and Semmes on the use of Logo as a medium of instruction for transformation geometry is particularly infor- mative in that it describes an attempt to inte- grate the use of the microcomputer into the teaching of mathematics rather than make the computer the object of instruction. "Software Evaluation Procedure . . ." by Johnson and Van Dusseldorp provides a detailed software- evaluation procedure for teachers of students with learning disabilities. Lodish, Meister, and Tannhauser discuss the introduction of comput-

ers in elementary schools through the media center. Leaderer and Golden summarize efforts to use computers in a resource setting with learning disabled students and include several interesting mini-case studies of such students' involvement with computers. Other topics in- clude computer camps, the development of software-authoring systems, electronic commu- nication, writing on the computer, instruction in programming, and implementation of computer science courses. Abstracts of the two keynote addresses are also included.

The book seems to suffer from a few design problems: the type font changes with each article, and many are presented in a dot-matrix font that, in some cases, is poorly duplicated. In an attempt to publish the proceedings quickly and inexpensively, only the main headings have been reset by the publisher. A second com- plaint involves the uneven lengths of articles. Many are one-page abstracts or summaries of the presentations. I found these to be of only slightly more use than the descriptive titles. It would have been helpful to include a mailing address and telephone number for each of these authors to assist the interested reader with future correspondence.

I would recommend this book to planners of computing curricula at all levels and, somewhat hesitantly, to teachers implementing computers into their instruction. Though many useful arti- cles are included, the organization of these proceedings makes it difficult to select topics of interest and relate articles to each other. No attempt has been made to synthesize or summa- rize the vast amount of information presented in each track. Similar information is also available in popular journals and magazines. - Randall Souviney, University of California - San Diego, La Jolla, CA 92093.

Calculator Problem Solving: Using Calculators to Teach Mathematics and Problem Solving. Alfred CapofeH and Terrence Coburn, eds. 1984, $5 + postage. Terrence Coburn, Oakland Schools, 2100 Pon- tiac Lake Rd., Pontiac, MI 48095.

This monograph contains a wide range of re- sources addressing the issue of calculator use in the mathematics classroom. The various re- sources are organized into subtopics including rationale, research, in-service training, teaching strategies and activities, potential impact, and recommendations for administrators.

As the editors state, the major purposes of the monograph are to develop an awareness of the benefits of using calculators to teach mathe- matics, to promote in-service opportunities, and to provide recommendations for adminis- trators in support of decisions that need to be made about the use of calculators in the schools.

The recommendations in NCTM's An Agen- da for Action "to take full advantage of the power of calculators" and additional NCTM statements on the use of minicalculators in schools are the bases of the rationale. The editors include a list of reasons for using calcu- lators, along with examples of applications for each.

48 Arithmetic Teacher

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A short section on research is followed by an in-service model consisting of four two-and- one-half-hour sessions. Each session features material and activities on the following topics: teaching mathematics content, using a calcula- tor, problem solving, and curricular and admin- istrative issues.

The outlines refer to statements and activities found throughout the monograph. This practice causes some problem in the flow, as it requires page flipping.

The section on teaching strategies and activi- ties has sample pages from many well-known calculator activity resources. In the section entitled "Resources," the authors present re- views of many books and articles about calcula- tors. In most cases they are the same publica- tions referred to, or printed throughout, the monograph.

The last section of the book is directed to- ward administrators and includes information on the philosophy supporting the use of calcula- tors, their selection and instructional uses, and in-service training.

Although the monograph contains many ex- cellent individual articles and excerpts, the in- formation in some sections appears disjointed. The problem in combining the writing of many people is that of maintaining continuity. How- ever, good information can be abstracted from this monograph, and an extensive collection of supplemental resources on calculators is sug- gested. - Paula Filliman, Glenview Public Schools, Glenview, IL 60025.

Learning Mathematics: The Cogni- tive Science Approach to Mathe- matics Education. Robert B. Davis. 1984, 401 pp., $34.50. ISBN 0-8939 1-124-X. Ablex Publishing, 355 Chestnut St., Norwood, NJ 07648.

Bob Davis has long been influential as a creator of, and commentator on, curricular and instruc- tional innovations. His Madison Project, for example, was one of the finest of the many exciting programs of the late fifties and sixties. Fans of Bob Davis who are not familiar with his Journal of Mathematical Behavior may wonder what he has been up to lately. This volume gives an ample answer.

Intended as a report of his long-term study (started in the seventies), the book evolved into an exposition of a cognitive science approach, particularly as it applies to mathematics educa- tion. This approach is perhaps earmarked by its view of humans as information processors, with the aim of describing what goes on inside learn- ers' heads when they are carrying out educa- tional tasks (and other cognitive tasks as well - the theory is quite comprehensive).

Thus, the early chapters set the framework for the information-processing approach and include, for those unfamiliar with the terms used, a chapter on basic concepts. Later chap- ters focus on particular concepts, such as pro- cedures, frames, memory and memory organi- zation, representations and their construction, retrieval, and problem solving. Subsequent chapters give Davis's views of the weaknesses

in most school curricula. The final chapter gives an overview of the cognitive-science approach to mathematics education and Davis's cautious- ly optimistic view of the near future.

Davis intended the book for researchers in cognition and for both in-service and preservice teachers. Be assured that the writing is vintage Davis, full of examples and, in general, just fun to read. This praise should not be interpreted to mean the reading is trivial; the theory has deep, but accessible, ideas, and a few of the examples involve calculus. The anecdotes are drawn from incidents involving preschoolers, learners in K- 12, and adults, so nearly every teacher can find something of almost immediate pertinence.

Teachers will also be particularly attracted to the explanations given by the theory for some common errors made by students and the use of everyday or familiar experiences as the basis for building mathematical knowledge (e.g., in- struction "must build on things that the stu- dents already understand"). Some may learn for the first time of what Davis calls "disaster studies," in which researchers have revealed the shallow and even erroneous understandings of students who, under conventional measures, were doing all right in school. And, it is always instructive when someone of Davis's stature lists his criticisms of most mathematics curricu- la: teaching bits without a larger view, relying too much on words alone to communicate, allowing (forcing?) students to learn by rote imitation, and pacing material too slowly.

This book should indeed be of value to those interested in examining an information-process- ing approach as a means either of explaining students' (cognitive) behavior or of guiding instruction. - Larry Sowder, Northern Illinois University, De Kalb, IL 601 15.

Micro Info Package: Microcomput- ers in Education: An Introduction, by Adeline Naiman ($5), The Software Finder: A Guide to Educational Mi- crocomputer Software ($16), and Mi- crocomputers in Education: Re- source Handbook, edited by Sharon E. Woodruff ($10). 1983, $28 complete set. TERC Publications, Dept. M, 44 Brattle St., Cam- bridge, MA 02138.

Microcomputers in Education: An Introduction would be a good resource for a school district that is in the beginning stages of developing a computer-literacy, computer-mathematics, or any other computer-based curriculum. Naiman suggests the need for planning before setting up any kind of computer-education program. Some important considerations include curricular needs, availability of software, expansibility of hardware, support of the community and busi- ness, teacher education, and financial re- sources. She lists possible sources of aid avail- able to districts, suggests and discusses areas to be considered when deciding on the content of computer education, provides information sources for hardware and software, and makes suggestions concerning training of teachers and for evaluating the success of the program.

In the appendixes are models for decisions about purchasing microcomputers; lists of peri-

odicals, reviews of software, books, and profes- sional organizations; examples of software evaluation forms; and a partial list of users' groups and software suppliers in the northeast. This book would be a good resource up to a point - it was printed in January 1982, and therefore its currency is limited. To a district in the beginning stages of developing a computer program, it could provide helpful hints and serve as a model in making decisions.

Microcomputers in Education: Resource Handbook is what its title suggests. In the beginning, Woodruff states that one of the pur- poses of the book is to provide a reference tool for teachers and administrators. She begins with a list of major manufacturers of hardware. She also provides a selected list of manufactur- ers of peripherals and their compatibility with particular computers.

An annotated listing of commercial sources of software is next. This partial list contains only major sources, since over 700 commercial sources of educational software exist. This list does provide the educational disciplines for which the company produces software and the hardware for which it is produced. The author also has an annotated listing of major directo- ries of educational software and sources of reviews of software. Still another primary source of information about communication in education is that of professional associations. Woodruff lists those with national constituen- cies that have been responsible for the primary support of educational computing, as well as users' groups and clearinghouses. The book ends with lists of colleges and universities offer- ing master's or doctoral programs in computer education and of organizations devoted to re- search and development.

The Software Finder, formerly entitled School Microware Directory, begins with an introduction stating how it is organized and how to use it and a page showing how to interpret the information given in each software listing. The software described could be used in most, if not all, disciplines in modern curriculums. Areas such as business, career education, En- glish, guidance, health, industrial arts, mathe- matics, science, and social science are includ- ed, just to name a few.

These software are listed according to hard- ware systems and subject areas. The descrip- tions include the type of software, such as game, tutorial, or drill and practice; the subject for which it might be used; the grade level; a description of what it does; the hardware for which it is compatible; the source of written reviews; the price; and the name and address of the publisher.

Other indexes in this book include the con- tents of program packages, software for admin- istrative applications, and software suppliers; indexes by title are also included. The book appears to be a fairly comprehensive list of software and its vendors, but it cannot be very up to date, since it was copyrighted in 1983. However, at the rate software is being pro- duced, any such book cannot be completely up to date. Overall it appears to be a good resource for locating available software by content, com- puter, and publisher. - Mary Wiesner, Katy ISD, Katy, TX 77450.

April 1985 49

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