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MIT Logo for the Apple (Terrapin/Krell) by Rick Billstein; Shlomo Libeskind; Johnny W. Lott Review by: Beverly Rich The Arithmetic Teacher, Vol. 33, No. 5 (January 1986), pp. 58-59 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41194156 . Accessed: 15/06/2014 04:45 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 195.34.79.54 on Sun, 15 Jun 2014 04:45:27 AM All use subject to JSTOR Terms and Conditions

MIT Logo for the Apple (Terrapin/Krell)by Rick Billstein; Shlomo Libeskind; Johnny W. Lott

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MIT Logo for the Apple (Terrapin/Krell) by Rick Billstein; Shlomo Libeskind; Johnny W. LottReview by: Beverly RichThe Arithmetic Teacher, Vol. 33, No. 5 (January 1986), pp. 58-59Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194156 .

Accessed: 15/06/2014 04:45

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].

.

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

http://www.jstor.org

This content downloaded from 195.34.79.54 on Sun, 15 Jun 2014 04:45:27 AMAll use subject to JSTOR Terms and Conditions

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

Mathematics and Logo: A Turtle Trip through Geometry. Kathleen Mar- tin and Donna Bearden. 1985, 164 pp., $19.95. ISBN 0-8359-4279-1 . Prentice-Hall, Englewood Cliffs, NJ 07632.

This teacher's guide is designed for middle school teachers who are experienced in Logo and are looking for meaningful mathematical activities appropriate for students literate in Logo. Mathematics and Logo explores the world of geometry by using questioning in con- junction with manipulatives, experiments, and computing projects.

Chapters 1 and 2 explore the relationships of the angles in triangles, polygons, and stars

through a variety of off-computer activities us- ing hinged mirrors and paper folding. Chapter 3 examines right triangles (isosceles and 30-60-90) in experiments on the lengths of the sides.

Chapter 4 deals with construction of tan- grams from squares and triangles, and chapter 5 explores regular, semiregular, and kaleidoscop- ic tessellations. Chapter 6 develops a variety of optical illusions that can be challenging to the eye as well as the mind. Chapters 7-9 explore the geometry of spirals. The final chapter ties Logo into the geometry of string art. The ap- pendixes contain blackline masters of diagrams and activity sheets, as well as listings of possi- ble solution procedures in both LCSI and MIT Logo. A disk containing these procedures can be purchased from the publisher for approxi- mately $10.

Mathematics and Logo is an excellent teach- er's guide. The questions presented in the de- velopment of the topics parallel questioning techniques that should be used when exploring Logo and are superb for the study of geometry. The topics are explored on a concrete level with a variety of activities and experiments. The conclusions from these explorations are fo- cused on computer activities for further devel-

opment, which can extend into a variety of new areas of exploration. Teachers are encouraged to have students expand on their findings to predict outcomes in tangential areas.

This book is one of the few on the market that does not spend time on teaching the Logo language but attempts to apply the power of Logo to the exploration and development of the creative world of mathematics. If both the students and teachers are proficient in Logo to the point of understanding the use of variables and recursion, then this book is an excellent resource. - David Barnes, Illinois State Univer- sity, Normal, IL 61761.

MIT Logo for the Apple (Terrapin/ Krell). Rick Billstein, Shlomo Libeskind, and Johnny W. Lott. 1985, 350 pp., $26.95. ISBN 0- 8053-0860-1 . Benjamin! Cummings Publishing Co., 2727 Sand Hill Rd., Menlo Park, С А 94025.

Logo has been receiving a great deal of atten- tion because of its ease of use and because it is a powerful language for introducing program- ming. This book is an introduction to the MIT version of Logo for the Apple II series of

From tha File

( Computation | * DIVINGO (any number of players) д

Object: To drill and to reinforce basic division facts I I I IT"

Materials needed л'ШЗ 7ГЁШ з(СШ 1 . A set of expendable game sheets. See the illus-

tration. Enough game sheets will be needed for □ D □ each player to have one for each game played. A i i i number of different game-sheet forms should be 6l[j □ 10|LI U 9|UG made by varying the location of the problems on the sheets. D_ D D_

2. A set of forty cards, four each of the digits 0-9 5 (□"□"

q IQ

□ 2 !□

D Directions 1 . The cards are shuffled and stacked with numerals facing down. A leader picks the top

card and reads its numeral aloud. 2. Each player chooses a square on his or her game sheet and places the numeral

called in that square. Once placed, a numeral cannot be moved to another square. 3. The first player who completes three division problems in any row, column, or

diagonal is the winner.

Variation/extension D To drill and practice more difficult division, problems of the form D | D D D can be used. Only problems with remainders of zero should be allowed.

From the file of Ruth A. Meyer and James E. Riley, Western Michigan University, Kalamazoo, Ml 49008

-Readers are encouraged to send in two copies of their classroom-tested ideas for "From the File" to the Arithmetic Teacher for review -

58 Arithmetic Teacher

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Computers. The nine chapters in the book begin with the history and philosophy of the language. The first chapter introduces the primitive com- mands in Logo, the turtle, and the basic arith- metic operations, and chapter 2 shows how to define new words in the form of procedures. The third chapter expands the use of proce- dures and introduces variables. Chapter 4 deals with recursion (the calling of a copy of the procedure itself); both tail-end and embedded recursion are addressed. The fifth chapter intro- duces coordinates and discusses procedures for constructions and tessellations. Chapter 6 intro- duces more arithmetic commands and uses them in all types of problems. Chapter 7 shows how Logo can be used for simulations and game applications. The Logo Shape Editor on the utilities disk is also discussed. The last chapter shows how Logo can manipulate words and sentences. This list processing is applied to a variety of problems.

Each chapter begins with a list of the new vocabulary to be discussed. Page references for each term, primitive, and special key combina- tion are given. A preliminary problem is also given so the reader has some idea of the type of problem that can be solved using the ideas in the chapter. The preliminary problem is solved in a systematic manner at the end of the chap- ter. A summary of special keys is highlighted in each chapter and a summary of commands appears at the end of sections and chapters. A problem set is given at the end of each section and each chapter. These sets include a variety of problems for exploration and practice of new

concepts. Answers to most of the odd-num- bered exercises are on the disk that is included with the book. An instructor's guide can be ordered that includes all answers. Boxed math- ematical asides give derivations or explana- tions. These can be used or skipped, depending on the level of expertise of the user. The book also includes a glossary and a bibliography.

The diskette also includes six games that can be used by students with no previous experi- ence in Logo. All the student has to do is read the appropriate game and type "start" for the instructions to be displayed and the game to begin. The appendix tells about the games and how to use them. It also gives modifications that the user can make to the games. The diskette can be copied, so programs are safer.

This book can be used by students and teach- ers who have little or no experience with Logo or computers and by experienced program- mers. Teachers of third grade through high school can get ideas to use with their classes. The amount of mathematical background will determine the depth of exploration.

The book has several strengths. The authors take great care in showing that recursion is the process of a procedure calling a copy of itself. They show the telescoping model to illustrate how recursion works. They show that recursion is not simple looping and detail ways to stop recursive processes. This is one of the best chapters on recursion that I have seen. The list processing is also well handled. This topic is another that often gets lost in the graphics capabilities of Logo. Interesting and sometimes

wvni ORDER FORM- . Educational Materials • Sack* • Quantity • Unit Price • Total Price

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20% Discount: Individual members, bookstores, or quantity orders for 10 or more SUBTOTAL $ copies of a single title shipped to one address. Prices subject to change without . notice. Virginia residents add 4% sales tax. Billed orders will include shipping Less 20% $ and handling charges.

MEMBERSHIP dues support the development, coordination and delivery of NCTM services, including $13 for each ARITHMETIC TEACHER and MATHEMATICS TEACHER subscription and $2 for five issues of the NCTM News Bulletin.

D Arithmetic Teacher (AT) • 9 issues, September-May, for elementary school teachers, parents, and teacher educators. Individuals $35; Institutions $40.* $ ф * Additional AT copies for institutions mailed to the same address $13/0RDER/YEAR. ф $

G Mathematics Teacher (MT) • 9 issues, September-May, for secondary school and two-year college mathematics teachers, and teacher educators. Individuals $35; Institutions $40. *

D Both Arithmetic Teecher and Mathematics Teacher for individuals only $48. $ Full-time student dues are V2 regular membership dues. For mailing outside the U.S., add $5 for the

first AT or MT per membership and $2.50 for each additional AT or MT

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January 1986

familiar problems are explored in terms of list processing.

Another strength of the book is its emphasis on problem solving. The authors use the four steps that are based on Polya's work in mathe- matical problem solving: (1) understanding the problem; (2) devising a plan; (3) carrying out the plan; and (4) looking back. The preliminary problem is solved showing each of these steps explicitly. Other problems are solved using this method, but the individual steps are not stated.

Finally, the diskette for use with the book is very good. The games are easily accessible to novice Logo users and can be modified by more experienced programmers. The games include "Dartgame," "Sketch," "Chase," "Chame- leon," "Golf," and "Lander." They range from a game to practice turtle distances and angles to one that simulates physical phenome- na as the student tries to land a rocket on a rocky planet. The games are fun and show the many and varied problems that can be done using Logo. - Beverly Mich, Illinois ótate uni- versity, Normal, IL 61761 .

Etcetera Edited by Carol Novi 1 1 is Larson University of Arizona Tucson, AZ 85721

The Children's Mathematics Calen- dar 1986. Theoni Pappas and Irish Margah. 1985. $6.95. Math Aids, P.O. Box 64, San Carlos, С А 94070.

This calendar contains a different mathematical problem for each day of the year. The solution to each problem is the date on which it appears. The problems involve whole numbers, frac- tions, decimals, and percentages, as well as some geometry and measurement. Each month the top half of the calendar presents information and illustrations about a different mathematical topic. Some of the topics included are hexagons in nature, infinity and large numbers, optical illusions, and mathematical logic games.

This calendar could help arouse interest in mathematics in grades 3-8. Most of the mathe- matical problems and topics are too difficult for grades K-2. Third and fourth graders might need help in reading about the monthly topic and following directions for the activities.

This attractive, inexpensive calendar could be used as a springboard to having students read trade books with mathematical content. The problem of the day could be used for review and to encourage students to explore the many ways that any given number can be expressed.

A longer review of the 1985 calendar is in- cluded in the September issue. - Carol Novillis Larson. W

59

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