Logo Works: Lessons in Logo by S. Cory; M. WalkerReview by: Cheryl A. RossThe Arithmetic Teacher, Vol. 35, No. 3 (November 1987), pp. 58-59Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194272 .

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1. Reorganization of chapter 1 (on problem solving). Puzzle-type problems that cannot be solved by the usual Polya strategies are not part of the problem set but are presented alone in a "Time Out" section. A section on using the calculator as a problem-solving tool has been moved from the appendix to chapter 1 .

2. Chapters 10 and 11 include Logo instruc- tion, and problems involving the writing of Logo procedures are added to the problem sets in the geometry sections.

3. Probability and statistics are separated into two chapters, with stem-and-leaf plots and mis- uses of statistics included in the statistics chap- ter.

I have used the second edition of this text with preservice elementary school teachers. Sufficient material is included to cover two three-hour semester courses in mathematics content, supplementing with more work on problem solving, estimation and mental- computation skills, and laboratory activities. -

Mary T. Whalen.

Learning Math with Logo, Rudy v. Neufeld. 1986, 1 student text (232 pp.) and 1 teacher resource (136 pp.), $29.95; 5-14 stu- dents texts, $24.95 ea., 1 teacher resource; 15 or more student texts, $19.95 ea., 1 teacher resource; + $2.00 shipping, paper. Logo Pub- lications, 7 Conifer Crescent, London, ON N6K2V3.

The student text is a series of Logo activities and investigations designed to be an introduc- tion to computer literacy and an aid in imple- menting the mathematics curriculum for grades 4-7. The texts can be used with Apple Logo, Terrapin Logo (Apple), and Commodore 64 Logo; prior computer or Logo knowledge is not necessary. The activities are designed to help students learn mathematics using a guided- discovery approach. Concepts treated in the activities include number lines, estimation, op- erations, integers, parallel lines, polygons, de- grees, pi, circles, variables, recursion, slides, flips, turns, tessellations, and area. The stu- dents also learn how to format disks, save procedures, and read from disks.

The student text can be used by individuals or for group instruction. Each lesson includes an introduction, a precomputer lesson, a guid- ed-discovery activity, and an extended-learning activity. Students are encouraged to solve prob- lems by thinking with the turtle and by walking through the commands before using screen commands. The teacher resource book states clear objectives for chapters and sections. Each section includes grade-level identification, mathematics concepts covered, the Logo com- mands required, the Logo commands learned, materials needed, and necessary editing in- structions. A precomputer lesson, a guided- discovery activity, and an extended-learning activity are then detailed. Often follow-up sug- gestions are included. Suggested answers to

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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.

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questions in the student text are given. Blackline masters that correspond to certain activities in the student text are also found throughout the teacher resource book.

The activities emphasize the user being a problem solver and the controller of the turtle. The teacher resource book states that many of the activities are not precisely described and are meant to be open-ended to encourage the students to "play turtle" in investigating ideas. The activities also include good ideas for using many concrete materials. Not having access to many computers would not prohibit teachers from using these materials.

In summary, these books offer upper elemen- tary school teachers ideas for introducing math- ematical concepts using Logo while not teach- ing many Logo commands. They offer students the chance to learn about learning. - Cheryl A. Ross, Hudson Community Schools, Hudson, I A 50643.

Logo Works: Lessons in Logo, 5. Cory andM. Walker. 1985, 262 pp. + 141 pp. in teacher's manual + reproducible worksheets + disk; student book (paper) + disk, $29.95; teacher's manual (paper), $12.95. ISBN 0-927510-04-9 and 0-927510-05-7. Terrapin, 222 Third St., Cambridge, MA 02142.

The student book is a series of forty-six lessons for developing the Logo language and extending students' knowledge of geometry, arithmetic, computer programming, computer literacy, and problem solving. It is designed for use with Terrapin, Apple, or Commodore Logo. The lessons provide a balance of classroom struc- ture with Piagetian learning for those teachers who wish a quality Logo program for their students. The student text seems to be written for upper elementary and junior high school students new to Logo, although it could be used in senior high school. The activity disk that accompanies the student book contains sample files to which the students are directed in the lessons.

The activities include Logo primitives, writ- ing procedures, editing, managing workspace and files, variables, recursion, and problem solving. Concepts of polygons and of circles are treated in separate chapters. Each student les- son contains a narrative presenting new ideas, activities to practice those ideas, and explora- tions to challenge students further. The book is easy to read with numerous Logo diagrams appearing as they would on a screen and with important words and sections highlighted or in boldface type. The questions in the lessons encourage students to use higher-level thinking skills.

The separate teacher's manual is very useful for teachers who may not themselves be totally at ease with teaching Logo. Each lesson corre- sponds to one in the student text and includes lesson objectives, vocabulary, additional infor- mation, ideas for expanding students' thinking, points to emphasize, ways to guide computer activities, and potential problem areas. The manual also includes some reproducible pages for record keeping, chapter covers for a student

58 Arithmetic Teacher

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tube for reading decimals by covering the comma with a dot to represent a decimal point. The students could then form numbers from 0 to 9999.999.

Although the Place Value Tube is a conve- nient manipulative for each student to have in order to learn how to read numbers, it is not designed to teach place value. The tube teaches the representation of numbers. The idea of place value needs to be addressed with such manipulatives as chips, sticks, and bundles or Dienes blocks. The workbook includes practice activities for representing numbers but does not give sufficient instruction to help students un- derstand place value. The Place Value Tube is a good aid to supplement other materials. - Patricia S. Wilson, University of Georgia, Ath- ens, GA 30602.

Zombookee: A Challenging Num- ber Game. Set contains three decks of cards, one crocodile, and player's manual. 1986, $11.00. The Teachers' Laboratory, 214 Main St., P.O. Box 6480, Brattleboro, VT 05301.

Zombookee is a card game for two to eight players in which a player tries to collect sets of three cards forming an arithmetic fact. Three sets consist of different colored cards, with each card containing one whole number less than or equal to twenty. Players must make an

Authors Sought for NCTM Yearbook on Teaching and Learning in the '90s

Potential authors are invited to submit manu- scripts for the 1990 Yearbook, Mathematics Teaching and Learning in the 1 990s. The thrust of the yearbook will be to provide a thought- provoking analysis of forces that potentially alter the teaching and learning of mathematics in grades K-12 during the next decade.

The teaching and learning of mathematics will be subjected to a number of different forces dur- ing the 1 990s, including developing theoretical or philosophical and research-based perspectives on how mathematics is learned, changes in demo- graphics and economics of our society, emerging models for effective instruction, and accelerating technological advances in calculators, computers, and telecommunications. Analyses of these forces and their implications for mathematics in- struction in the elementary, middle school, and high school grades will be the focus of the year- book.

The yearbook editor is Thomas J. Cooney, University of Georgia, Athens, Georgia.

Guidelines for authors, which include a more complete description of the topics to be ad- dressed and instructions for preparing manu- scripts, can be obtained from

Christian R. Hirsch ueneral Yearbook Editor Department of Mathematics Western Michigan University Kalamazoo, MI 49008.

The deadline for submission of manuscripts is 1 March 1988.

addition, subtraction, multiplication, or divi- sion fact using three cards of different colors. Players control the action by selecting the color of cards to be passed to the left or right and by drawings. Wild cards and penalty cards intro- duce an element of chance.

This game can provide a practice setting for groups of two to eight students. Students can monitor the game. Students can play the game after development of only the addition facts and could benefit from the game as long as they need to practice arithmetic facts. When groups of only two or three play, students can plan and implement strategic moves to get winning sets of cards. My better students quickly took to planning strategies, and slower students picked up on this advantage. Looking at your oppo- nents' cards is encouraged, as all cards are kept faceup during play. Less strategy is possible as the size of the group increases.

My third graders like Zombookee. I recom- mend it as one of a variety of practice materials. Practice on multiplication and division facts is limited to those facts whose product or quotient is less than or equal to twenty (unless additional cards are constructed). The instruction book contains some superfluous material but does give information on variations and advanced versions of the game. - Darlene D. Davis, Clarke County School District, Athens, G A 30605. ψ

JauM?? t° b^ ^dxNzrtiyzo

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November 1987 59

notebook, and screen protractors for working with degrees and the turtle. Answers to student activities are given in the teacher's manual. An especially nice feature is an appendix that dis- cusses the use of color, differences among the various versions of Logo, the coordinate plane, and the printing of both text and graphics on various printers.

The lessons do not include any work with words and lists. Only graphics ideas are pre- sented. Teachers wanting advanced Logo con- cepts will not find them in these materials.

In summary, these are excellent activities for teaching and learning Logo. The concepts of Piagetian learning are also nicely balanced with provisions of structure for the teacher. - Cheryl A. Ross.

Etcetera Place Value Tube, Carolyn G. Zimmer- man. 1986, tube with seven movable bands, each numbered 0-9, + 32-pp. workbook. CeeZee Enterprises, Box 293, Mechanicsburg, PA 17055.

The Place Value Tube, a large-number and place- value teaching aid, consists of a nine-inch tube with seven movable bands around the tube. Each band contains the numerals 0-9. By sliding the seven individual bands around the tube, the learner can create numerals ranging from 0 000 000 to 9 999 999. Commas are printed on the tube to separate millions, thousands, and hundreds. The tubes are available assembled or unassembled and may have oaktag bands or pressed-cardboard bands. A class set of 30 ranges from $72 to $132. Although the assembly appeared to be easy, the oaktag bands did not work as well as the pressed-cardboard bands. A workbook designed for third and fourth grade is available to supplement the place-value tubes.

The tube gives students in upper elementary school the opportunity to create a variety of numerals easily. It helps the students organize the digits into hundreds, thousands, and mil- lions by furnishing commas to separate the sets of digits. The Place Value Tube gives the stu- dent a chance to explore such ideas as increas- ing the tens place by one or decreasing the thousands-place digit by two. All this can be done without paper and pencil and the mess of erasing or comparing the old number and new number. The aid will help students learn to read numbers between 0 and 10 million. It will also help them learn how to represent ideas such as one thousand, two tens, and three ones. It would be possible to remove some of the bands and address smaller numbers. For example, remove three bands and work with numbers from 0 to 9999. Also teachers could adapt the

Edited by Carol Novillis Larson University oj Arizona Tucson, AZ 85721

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