Columbus Returns! Math Activities for the Middle Grades. Monograph 1 Montana Council ofTeachers of MathematicsReview by: David J. TschiggfrieThe Arithmetic Teacher, Vol. 35, No. 2 (October 1987), p. 58Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193251 .

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facts appropriate for students needing this prac- tice beginning with the third grade. The pro- gram does not have a management option.

Vanilla Facts presents a wide selection of problem types. The user can choose the type of operation, the highest number fact, the speed at which the evaluation comes, and the number of problems offered, as well as the option of a printed worksheet. Unfortunately, the number of choices could very easily overwhelm a young student who is unsure of what options to pick. The program does not use graphics or sound to motivate students and does not offer hints if a student is stuck or even allow more than one attempt at an answer.

Vanilla Facts is a very dry, bare-bones pro- gram. Its one advantage, its range of choices, can be a disadvantage for young students. Too many basic-fact drill-and-practice programs are on the market that provide motivation and instruction for me to recommend this one. -

Jacqueline Gorman, Indiana University, Bloomington, IN 47405.

New Books

For Teachers From NCTM

20-percent discount on all NCTM publications for individual NCTM members

Mathematics Curriculum Outline and Sample Activities for Gifted Students- Grades 2 through 8. Alexander Tobin, project coordinator, Alan Barson, Robert Murphey , and Donald Scheuer, contributing authors. (Funded by the NCTM Mathematics Education Trust.) 36 pp., $3. Na- tional Council of Teachers of Mathematics, Dept. E, 1906 Association Dr., Reston, VA 22091.

The authors of these mathematics activities for the mentally gifted believe that "doing mathe- matics provides the proper environment for learning mathematics." The activities were de- veloped to be used in conjunction with an existing mathematics program used in the Phil- adelphia School District in grades 2-8. The function of this segmentof the program "is to develop the intellectual abilities of the students, not necessarily to develop new content."

Logic; combinatorics, probability, and statis- tics; geometry and topology; functions; and computer strands are included, with two to five activities in each strand. Objectives, materials, and samples are listed for each activity.

Edited by Diane Thiessen University of Northern Iowa Cedar Falls, IA 50614

Teachers of mathematically gifted students may find some ideas here that they could incor- porate into their own programs. - Mary T. Whalen, University of Northern Iowa, Cedar Falls, IA 50614.

From Other Publishers

Columbus Returns! Math Activities for the Middle Grades. Monograph ι by the Montana Council of Teachers of Mathemat- ics. 74 pp., $5. Mary Buck, C. R. Anderson Middle School, 1200 Knight Ave., Helena, MT 59601.

This monograph is a collection of favorite ac- tivities and games selected from nearly 1000 pages of resource materials. These activities were originally written in 1974 by thirteen jun- ior high school teachers from Columbus, Mon- tana. Included in the thirty-six selections are class experiments, computational games that serve as alternatives to drill and practice, cal- culator activities, and problem-solving materi- als. Although originally designed for grades 7-8, teachers using these materials reported positive results and increased motivation with students from grades 5 through high school (presumably general mathematics classes).

The book consists of thirty-one activities covering whole numbers and place value; frac- tions; palindromic, prime, composite, and square numbers; measurement and estimation with ruler and. protractor; decimals; ratio and proportion; indirect measurement; percent; in- tegers; powers of two; scientific notation; geo- metric constructions; geometric vocabulary; statistics; probability; graphing rational and ir- rational numbers; and problem solving. Also included are five classroom games about order of operations with whole numbers, operations with integers, operations with decimals, and metric measurement.

In addition to some well-known activities (the three-digit reversal or 1089 puzzle, palindromic numbers, pentominoes, Contig), some interest- ing extensions and applications of typical junior high school content also appear. For example, "Experiments with Fractions" offers a series of valuable hands-on work with the meaning of fractions. In one of the experiments, from among five pieces of paper students are asked to select the one that is- as large as the sample sheet provided. Another activity asks students to explain why extending a proportion to a new situation is not always appropriate: "Jim Jumper can jump 5 m with a 15 m running start. How far can he jump with a 75 m running start?"

Two classroom experiments among the many included demonstrate the extension of typical junior high school topics. The "Ratty Problem" is a simulation using dice or a spinner to deter- mine the probability of catching rats at various openings in a maze. "The Mod Squad" is an experiment in generating student measurement data to determine Mr. and Ms. Mod. In the process, students focus on the selection of mean, median, or mode as the best indicator of the concept of average.

Perhaps the most interesting and novel activ- ity, "Rational Pictures," focuses on the repre- sentation of rational and irrational numbers. Students graph each digit in the decimal expan- sion of the number on a grid. The graph of each successive digit is rotated 90° clockwise. At the conclusion of the graphing activities, students are asked to generate questions that search for patterns and generalizations, such as How can you categorize the picture of a rational number? and How does the picture of an irrational num- ber differ from the picture of a rational number?

In summary this monograph is a valuable source of extension, practice, and application activities for the traditional junior high or mid- dle school mathematics curriculum. In addition, the activities that have been selected were written, used, and tested in the classroom by teachers and students, and they have been proved useful and successful. - David J. Tschiggfrie, Dubuque Community School Dis- trict, Dubuque, I A 52001.

Digging into Logic, Beverly Post and Sandra Eads. 1987, 48 pp., $5.95 paper. ISBN 0-8224-4458-5. David S. Lake Publishers, 19 Davis Dr., Belmont, С А 94002.

Digging into Logic is an excellent source for activities to develop middle and junior high school students' critical thinking skills. The book is a collection of thirty reproducible ma- trix problems of the following type: "Mark, Meg, Melissa, and Mareie are all artists. One child uses only colored felt pens; one child uses only black pencils; one child uses only water- colors; and one child uses only crayons. Find out what each child uses." This problem is followed by four numbered clues, such as, "Melissa loves bright colors, but she doesn't use felt pens."

The problems are arranged from simple to complex. A matrix grid is provided on each page. Students must fill in the names and other pertinent information and then proceed to solve the problem with the aid of the clues provided. Three pages at the back of the book allow students to make their own logic problems and share them with their classmates.

The authors encourage teachers to work through the sample problem (the one previously quoted) with their students. Step-by-step direc- tions are included for this introduction. The authors then suggest that the problems be used in one of three ways: independent activities at learning centers; extra or supplementary work for those finished with assigned work; or a minicourse for the entire class.

I agree with Post and Eads in their contention that critical thinking can be taught, and I think that these logic problems would be an entertain- ing way to start your students on the road to being critical thinkers. - Mary T. Whalen.

MathsCope 1 : Essential Maths Skills, Barrie Fenby, Paul Pogue, Allen Gorlick, Lorna Strobel, and Lorna Wiggan. 1983, 279 pp. ISBN 0 85896-818 5. MathS- Cope 2: Essential Maths Skills, Bar- rie Fenby, Peter Cribb, Greg Gibs, Allan Gray,

58 Arithmetic Teacher

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