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Math-A-Draw: Level I, Addition and Subtraction; Level II, Addition and Subtraction; Level III, Subtraction; Level IV, Multiplication with One-Digit Multipliers; Level V, Division with One- Digit Divisors; Level VI, Two-Digit Multiplication and Division by Judith N. Parsons Review by: Adele Neuberg The Arithmetic Teacher, Vol. 32, No. 7 (March 1985), pp. 55-56 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41192606 . Accessed: 09/06/2014 18:46 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 185.44.79.13 on Mon, 9 Jun 2014 18:46:47 PM All use subject to JSTOR Terms and Conditions

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Math-A-Draw: Level I, Addition and Subtraction; Level II, Addition and Subtraction; Level III,Subtraction; Level IV, Multiplication with One-Digit Multipliers; Level V, Division with One-Digit Divisors; Level VI, Two-Digit Multiplication and Division by Judith N. ParsonsReview by: Adele NeubergThe Arithmetic Teacher, Vol. 32, No. 7 (March 1985), pp. 55-56Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192606 .

Accessed: 09/06/2014 18:46

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

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National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

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Space Math. Apple II+, He, 48 К , one disk drive. 1983, $49.95. Learning Well, 200 S. Ser- vice Rd., Roslyn Heights, NY 11577.

Space Math is a drill-and-practice game cover- ing addition, subtraction, multiplication, and division of whole numbers. From one to six students take turns in a team effort to stop alien forces from destroying Earth. Students who correctly answer a problem are given the oppor- tunity to shoot down an alien spaceship and score points. If a student answers a problem incorrectly or misses the spaceship while trying to shoot it down, the aliens score points.

The teacher-utilities portion of the program allows teachers to change the number and type of problems that will be presented to the stu- dent, change the level of difficulty in shooting a target, and view or print the percentage of correct answers given by each student. In se- lecting the type of problem for each round, the teacher can choose the operation (addition, subtraction, multiplication, or division), the number of digits in each part of the problem, whether the problem involves renaming, and whether the problem is displayed in a horizontal or vertical format. Students choose whether to shoot the alien spaceship from the keyboard or with a joystick or paddles. Sound can be con- trolled.

Space Math is easy to use and technically well done. It is designed to encourage cooper- ation rather than competition among students. Students who tried the program found the game's format motivating and fun, especially when played with a joystick. (The nonrepeating keys of the Apple II + made the keyboard option difficult to use.)

Unfortunately, however, the program is more fun than it is educational. For all but the easiest problems, students will need to compute with pencil and paper and then type their final an- swer at the keyboard. The need for pencil and paper could be eliminated if students could enter their answers from right to left and if the intermediate steps in the computational algo- rithm were displayed on the screen. - Sandra V. Turner, National College of Education, Ev- ans ton, IL 60201.

The Whatsit Corporation: Survival Math Skills. Apple II, 48K, Applesoft, DOS 3.3 (also available for TRS-80 Model III or 4, 48K.) 1983, $55. Sunburst Communications, 39 Washington Ave., Pleasantville, NY 10570.

The Whatsit Corporation is an exciting simula- tion that gives students the experience of run- ning a simulated small franchise business for a period of six months. It was developed for consumer mathematics classes in grades 6-12 but could also be used in business and econom- ics classes.

Before buying the franchise, students can conduct a market survey, consult an economist, and borrow money. Once open for business, they face regular decisions to order inventory, hire or lay off salespeople, set prices, advertise, borrow more money, pay state sales tax, hire outside consultants, or pay on existing loans. Unexpected problems, such as late shipments or supply shortages, provide an additional chal- lenge.

March 1985

Students can use the simulation individually, or they can be divided into small groups to run the simulation cooperatively as a team project. From one to five hours are required for the entire simulation. Each group can save on the disk the results of a partially completed simula- tion and continue it another day. All the varia- bles interact in a realistic way. However, if teams of students compete with each other, the decisions of one group do not in any way affect the success of the others.

This business simulation differs from others on the market because students must keep their own records of income, expenses, sales, inven- tory, and cash on hand. Forms provided in the teacher's guide help the students to organize this information. By keeping records, students gain practice in calculating with whole numbers and decimals, estimating, evaluating formulas, computing simple interest, and creating and using graphs. Mathematics becomes a tool for making business decisions and analyzing the results of those decisions.

Besides a complete description of the pro- gram and forms for keeping records, the teach- er's guide includes classroom activities to pre- pare students for using the simulation, masters for overhead transparencies, student work- sheets with answer keys, a glossary of econom- ic terms, and a follow-up evaluation. Sunburst not only includes a backup disk in the package but will replace at no charge any disk that is accidentally damaged.

This courseware gets high marks in all cate- gories: educational value, ease of use, technical quality, and support materials. Tenth-grade stu- dents who used it with me were anxious to play again to see if they could improve the closing balance sheet the second time around. Their only complaint was that the ms and ws of the uppercase and lowercase typeface lacked clar- ity, but this minor problem was soon forgot- ten. - Sandra V. Turner.

New Books for Pupils Edited by Judith E. Jacobs George Mason University Fairfax, VA 22030

1, 2, 3, My Computer and Me! Donna Bearden. 1983, 99 pp., $10.95. ISBN 0-8359- 5228-2. Reston Publishing Co., 11480 Sunset Hills Rd., Reston, VA 22090.

This book is a workbook on Logo for elemen- tary school children. It includes activities and ideas for learning the commands; writing, edit- ing, and saving procedures; variables; recur- sion; and color. Commands and information for TI, Apple, and MIT Logo are incorporated throughout the text.

The illustrations are cleverly done, and the teaching ideas are superb. The book requires a

significant amount of reading, so it would be difficult for a child in early elementary school to use it as a workbook. The commands for the different versions of Logo are distributed throughout the book and could be distracting and confusing for children (and teachers!).

This book could be an excellent resource for a teacher, although it would be difficult for children to use independently. - Adele Neu- berg, George Mason University, Fairfax, VA 22030.

M at h -A- D raw: Level I, Addition and Subtraction; Level II, Addition and Subtraction; Level III, Subtraction; Level IV, Multiplication with One- Digit Multipliers; Level V, Division with One-Digit Divisors; Level VI, Two-Digit Multiplication and Divi- sion. Judith N. Parsons. 1983, 64 pp. ea., $5.95 ea. Pitman Learning, 19 Davis Dr., Bel- mont, С А 94002.

This series of learning games provides a unique approach to drill and practice. Each book con- tains twenty-seven reproducible problem sets. Each problem set consists of A and В work- sheets. Worksheet A contains basic computa- tional problems. Worksheet В presents a dot- to-dot activity in which students create a picture by using their answers from worksheet A to connect the dots. An answer key is includ- ed with each book.

Level I provides problems in addition and subtraction for kindergartners through low sec- ond-grade students, including addition with sums up to and including 20, missing addends, missing subtrahends, sequences of numbers to 20, comparisons of the size of two numbers, and three-addend addition.

Level II gives problems in addition and sub- traction for first-, second-, and less able third- grade students, including addition and subtrac- tion with one, two, and three digits (primarily with no regrouping). Eight sets do include some regrouping in addition.

Level HI offers practice in subtraction for high second, third, and low fourth graders. Included are problems involving subtraction from 10 to 18, with regrouping in either the units or tens places or both. The majority (twenty sets) include mixed regrouping. Checking is included for every problem and is necessary to do the dot-to-dot picture.

Level IV provides practice in multiplication with one-digit multipliers for third-, fourth-, and low fifth-grade students. Two problem sets are given for each individual multiplier 2 through 9. In addition, review pages with a combination of multipliers are included, as well as some exer- cises with dollars and cents.

Level V provides practice with one-digit divi- sors for high third, fourth, and low fifth graders. Pages include both division by each specific divisor as well as a review with a combination of divisors. Remainders are introduced in the second half of the problem set. Checking is a necessity for each problem and is part of the dot-to-dot activity.

Level VI includes practice with two-digit multiplication and division for high fourth, fifth, and low sixth graders. Nine of the problem sets

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deal with multiplication. Division by multiples of 10 constitutes the first half of the problems. The other problems have the divisor with a constant number (2 through 9) in the units place (e.g., 12, 22, 32, 42, 52, . . .). Again, checking is an integral part of each division problem.

The table of contents identifies the specific skill area for each problem set. This specificity would make it easy for the classroom teacher to work on individual computational skills.

The introduction to each book has tips for teachers. The author recommends that students do the computation, have it checked for accura- cy, and then do the dot-to-dot activity. It might be more beneficial as a checking device for the students if the problems are not checked prior to the dot-to-dot activity.

It is so difficult to get children to practice computation; these problems and the dot-to-dot activities supply some motivation and an ele- ment of "fun" with the mathematics. - Adele Neuberg.

New Books for Teachers Edited by Randall I. Charles Illinois State University Normal IL 6I761

Concerns over the quality of mathematics education in England and Wales led the British government to establish the Committee of In- quiry into the Teaching of Mathematics in Schools under the direction of W. H. Cock- croft. The committee's charge was to study the state of mathematics education and to make recommendations for improvement. The com- mittee met for the first time on 25 September 1978 for a total of sixty-four days. The final report of the committee is entitled Mathematics Counts: Report of the Committee of Inquiry into the Teaching of Mathematics in Schools under the Chairmanship of Dr. W. H. Cock- croft.

To help the committee with its charge, Great Britain's Department of Education and Science commissioned a review of existing research on the teaching and learning of mathematics under the direction of A. Bell and A. Bishop. The review of research was published in three vol- umes. Each volume is reviewed here. - Randall I. Charles.

A Review of Research in Mathemat- ical Education, Part A: Research on Learning and Teaching, a. w. Bell, j. Costello, and D. Kuchemann. 1984, 336 pp., $19. ISBN 0-7005-0612-8. Distributed in the U.S. by Humanities Press, Atlantic Highlands, NJ 07716.

This book's stated aim is "to display the main outcomes of research relevant to the teaching and learning of mathematics, . . . not to formu- late recommendations for action but to provide background information."

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After an overview and a brief discussion of the mathematics curriculum, the next sixty pages deal with memory, logical thinking, and Piagetian stages of intellectual development. Chapter 4 discusses the distinctions among skills, concepts, strategies, and attitudes. Chap- ter 5 deals with the teaching of facts and skills. Subsequent chapters discuss children's under- standing of concepts in specific topic areas, aspects of teaching, processes (including prob- lem solving and proof), attitudes, individual differences, the role of language, evaluation and assessment, and calculators and computers. The concluding chapter, "Using Research," is simply a listing and brief discussion of the sources of research reports in the United States and Great Britain. A ten-page supplement is included, which is described as "an attempt to update, where necessary, the comments and conclusions of the review in light of recent work."

One of the major strengths of this book is the degree to which the authors have documented and emphasized the idea stated on pp. 5-6, that is, "The recognition that these three elements, Skills and Facts, Conceptual Structures, and General Strategies and Appreciation involve distinct aspects of teaching and require separate attention pervades the research on teaching." Another strength is the inclusion of more mate- rial than usual on the role of memory and language in the teaching and learning of mathe- matics. Some readers will welcome an update on research on Piagetian developmental stages and the references to Piaget in various parts of the report.

My major concerns about the book are those of currentness, depth, and completeness of some of the topics. For example, the section on the teaching of facts and skills is quite brief and lacks thoroughness and organization. Useful studies, such as the one by Carol A. Thornton, "Emphasizing Thinking Strategies in Basic Fact Instruction" (Journal for Research in Mathematics Education 9 [May 1978]: 2 14-27), were omitted.

After an eight-page discussion of problem solving, the general implications mentioned in the summary (last paragraph, p. 234) are essen- tially that "awareness of problem types and categorization of methods of solution should be features of learning. Also, the amount of real problem solving being performed should be increased."

Although other specifics are mentioned earli- er, readers might desire a more in-depth look at current research on problem solving. This ex- ample is characteristic of the "implication" sections that appear somewhat infrequently in other sections of the book. Note, however, that this book is the first of a set of three volumes, so an evaluation of their depth of coverage might change depending on the nature of the other books.

Readers may also want to be careful to sepa- rate some of the authors' conclusions from those more specifically supported by research. For example, the statement, "Combined with what we know of the difficulty of performing algorithms such as those for multiplication and division with speed and accuracy, we are forced to conclude that this is not a mode of function-

ing for which the human brain is well designed; in this respect it is unlike the calculator or the computer" (p. 93) seemed to go well beyond the reported research.

Even with these limitations, this book pro- vides a perspective on research in several areas of the learning and teaching of mathematics. In most places it is readable, and it includes sever- al examples of children's reactions to mathe- matics. The book certainly causes one to think about a lot of issues associated with the mean- ingful teaching of mathematics and can augment other sources of research information. - Phares G. O'Dajfer, Illinois State University, Normal, IL 61761.

A Review of Research in Mathemat- ical Education, Part B: Research on the Social Context of Mathematics Education. A. J. Bishop and Marilyn Nick- erson. 1984, 84 pp., $9.25. ISBN 0-7005-0613-6. Distributed in the U.S. by Humanities Press, Atlantic Highlands, NJ 07716.

This book is an intelligent and integrated pre- sentation of literature dealing with institutional and social constraints affecting the teaching of mathematics. Constraints external to the teach- er form the basis for chapters on institutional factors, pupils as a constraint, societal con- straints, and the structure of the teaching pro- fession. The second half of the book, on inter- nal constraints, covers the effects of initial training, in-service training, professional devel- opment, and characteristics of teachers.

One valuable feature of this book is its careful consideration of research from both sides of the Atlantic. Although this point may also be true of the other two volumes in this series, this feature is particularly valuable here because many of the sources are probably unfamiliar to most mathematics educators. For this reason, a mathematics educator curious about this field would have difficulty surveying this literature without such a resource as this. Many of the sources are not specific to mathematics teach- ing, and in fact, some are from different disci- plines altogether. In such cases, however, con- clusions are relevant to mathematics education and, therefore, are considered in this book.

A second outstanding feature of the book is the manner in which it is written. Important ideas are related to mathematics teaching and learning rather than presented as a mere list of conclusions of studies related to the topic being discussed. This style of presentation leads natu- rally to the last chapter, which summarizes these ideas and their implications for mathemat- ics teaching. In this chapter the discussions of leadership and support roles and of teacher stress are particularly well done. Perhaps the most interesting conclusion is that further re- search on how social factors influence the quali- ty of mathematical learning would be more profitable than a continuation of research on learning by individual children. In fact, the insight gained from research on societal factors might lead to a better understanding of the learning of mathematics by the individual child.

Obviously, this book would be of interest to researchers. The topics covered, the ideas put forth, and the conclusions drawn would also

Arithmetic Teacher

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