Tobbs Learns Algebra: Puzzles and Problem Solving by Thomas C. O'BrienReview by: Richard MorrowThe Mathematics Teacher, Vol. 77, No. 5 (May 1984), pp. 390-391Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27964085 .

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chance to solve the problem even if it is difficult.

A number of options are present throughout the program. The ESC

key may be used to exit the session and start again, continue, or enter the instruction mode. The instruc tion mode allows the user to repeat specific problems or scan the com

plete problem set. This flexibility is a big plus.

The best use of PSST is with students who need extra guidance in analyzing problems, but it can also be used to give better students a deeper understanding of problem solving. The program has a wide

range of problems and allows for user control. This program is a

teaching, not a testing, program. ?Leon H. Roland, Billings Public

Schools, Billings, MT 59102.

Read and Solve Math Problems #2, Ann Edson and Allan A. Schwartz. Apple II, 48K, 2 disks and 14 re producible activity masters, $98 (also available, 4 cassettes and 14 reproducible masters, $89). Edu cational Activities, P.O. Box 392, Freeport, NY 11 520.

Read and Solve Math Problems #2 is a handsomely packaged tutorial

and-learning system that may be used for teaching students in

grades 4-6 or for remedial work in

grades 9-12. In this program, the student is taught the strategies needed to solve two-step problems of the type "Kim played 18 minutes in the first half and 20 minutes in the second half of the game. If Bob

played only 22 minutes in the entire game, how many minutes fewer did Bob play than Kim?" The student is trained to read carefully to detect key words or phrases that are vital clues. In the example above, the word "fewer" indicates subtraction. In step 1 of the two

step process, the student must decide which operation to use in

setting up the initial equation, " 18 + 20 = N." To complete this

step, the student performs the mathematical operation and types in the answer with the appropriate label. In the previous example, the student must type in the phrase "38 points" to receive credit for a correct response. The information in step 1 is used to calculate the final answer in step 2. Again, the student must decide which oper ation to use and which label to

apply. The final acceptable answer is "16 points."

The instructional model used in

the program emphasizes the impor tance of reading before doing.

Mathematics teachers know that verbal problems are not just mys terious jumbles of words and num bers requiring some special type of

sorcery or wizardry to decipher. Only a few problems are! In these

seemingly confused assemblages of words and numbers are road maps, complete with road signs and destination clues. The trick is to

spot the clues and signs; finding them can be done by reading the

problem carefully. This program at

tempts to teach mathematics stu dents to be smart readers.

The complete package consists of two disks containing eight les sons and a set of supplementary ac

tivity masters. The documentation is comprehensive and highly in formative. The rationale of the in structional model is carefully ex

plained. The content of each of the

eight lessons is clearly outlined, and the authors make a special effort to suggest different ways in which the components of the

system can be used. An excellent

management system is provided in which the computer not only takes

charge of record keeping but also decides when a student is ready to

progress to the next lesson. In

itially, the students enter the pro gram by typing in their full names. Then the computer sets up a

progress file under each name. Per formance on each lesson is evalu ated by a scoring system in which

acceptable performance is the 70

percent level. If performance is below this level, the student is not allowed to go forward. Since the

program is not menu-driven, the student cannot bypass a trouble some lesson. The teacher can use the management system to check the progress of an individual stu dent or of a whole class. The screen

displays are written in bold upper case and lowercase letters and are

very easy to read. The student re

ceives lots of help and encourage ment if a mistake is made. On the first error, the program branches to a tutorial in which the student is given additional help in under

standing the problem. On the second error, the correct answer is

displayed along with a detailed ex

planation of the solution process. All prompts are positive and en

couraging. Errors of input are so

effectively trapped that it is vir

tually impossible to "bomb" the

program. All routines and com

mands needed to run the program are taught in the first lesson, which, incidentally, everybody must complete. The program can be used as a teaching tool in the class room, or it can be stationed in a

media center for drill or remedia tion. The publisher has a 30-60-day preview policy. ?Laurence John son, South Pasadena High School, South Pasadena, CA 91030.

Sets, Probability and Statistics: The Mathematics of Insurance, James M. King. 1983, Apple Pilot

(SuperPILOT also available), 4 disks, manual, teacher's key to an swers, $50. American Council of Life Insurance, 1850 St., N.W.,

Washington, DC 20006.

Many mathematics teachers are familiar with the thirty-five-page red-cover booklet of the same title distributed by the Institute of Life Insurance since 1972. The booklet

was prepared in cooperation with Paul Clifford, Mildred Keiffer, and Max Sobel.

James M. King of the Univer

sity of Georgia produced the com

puter program in cooperation with the American Council of Life In surance. His adaptation closely fol lows the content of the booklet.

The four disks contain ten les sons: Introduction, Sets, Sample Spaces, Probability, Statistics, Mortality Tables, Interest, Figur ing Premiums, Annual Premiums, and Pilot Calculator (a special pro gram to do the related arithmetic).

King's adaptation is a very neat

package, well suited to show users how "abstract math" is used in real-life (or death) situations. The lessons are user friendly, with just enough humor, and should further

popularize the original text. Your

Apple system should have an Auto start ROM to use the disks.

A twelve-page booklet is includ

ed, which contains helpful infor mation written in uncomplicated terms, on how to use the disks.

Directions are given for dupli cating the program disks so that

many students can use them. This feature by itself is one of the big gest selling points of the package. Every secondary mathematics de

partment should have this software for use by both students and teachers.?John Izzi, Toll Gate Ed ucational Complex, Warwick, RI

02886.

Tobbs Learns Algebra: Puzzles and Problem Solving, Thomas C. O'Brien. Apple II, 48K, DOS 3.3

390 ?--Mathematics Teacher

This content downloaded from 132.203.227.62 on Wed, 16 Jul 2014 08:49:41 AMAll use subject to JSTOR Terms and Conditions

(also available for TRS-80, 32K), includes backup disk and teach er's guide. $49. Sunburst Com munications. 39 Washington Ave.. Pleasantville. NY 10570.

The author claims that these pro grams allow students to practice five skills involving formulas. This statement is true?without the

help of a teacher, students can

learn and practice skills, although guidelines for use are mentioned

subsequently. The five skills that can be prac

ticed are the following: (1) coordi nating addition and multiplication in a formula; (2) working backward

from given numbers to find a for

mula; (3) determining an entry point when dealing with formulae; (4) distinguishing between possible and impossible values in a formula

when information to determine the exact values is missing; and (5) finding a mathematical formula to fit given data, using sums, prod ucts, square roots, and transforma tions of digits.

I have tried the programs with students and elementary school teachers. My prealgebra students had fun with the first three skills and were able to function on their own. The format allows up to four

players (or teams) to work on each

computer. I found it best to have the students work as teams to lend

support to each other in getting over the tough spots.

When the students got to the fourth skill, none of them were able to continue. They needed the teacher's help to know that they were to place an acceptable

answer, not the correct one. The

group of adults had the same diffi culty. The skill practiced is valu

able, but adult help is required. The fifth skill also requires the

teacher's assistance. Without such

guidance, even gifted students may have trouble determining what kinds of answers are acceptable.

The manual is adequate for any teacher to use, since it contains

background information and in structions on how to use Apple, Atari, and TRS-80 computers.

I can easily recommend Tobbs Learns Algebra for use, within the

guidelines mentioned earlier, be cause it provides problem-solving practice, a rare feature in program of the type.?Richard Morrow,

Mirman School, Los Angeles, CA 90049.

I

a

L- I

NEW PRODUCTS Edited by Margaret Holland 1712 Forestdale Boulevard

Birmingham,AL 35214

Games Tha Billion Mark. $7.50 (+$1.50

for shipping). WLW Enterprises. P.O. Box 43325. La Tijera Station. Los Angeles. CA 90043.

Called by its developers a "game oriented learning medium," Billion

Mark uses a game board similar to that for Monopoly. Instead of deal

ing in property, players deal in de

posits and withdrawals of money

(represented by cards) in positive and negative powers of ten. A roll of one, two, or three dice deter mines the forward moves of play ers' tokens and places on the board direct "exponential" or other oper ations that involve laws of ex

ponents, inequalities, large num

bers, factors, multiples, scientific

notation, and number patterns. Other concepts that are reinforced or made more comprehensible in clude place value, numeration, and, above all, large numbers up to trillions. Such a concept is cer

tainly in keeping with the nature

of our computerized and inflation

ary age. The tokens provided for six

players are plastic thimbles! Their

significance eludes me, but it is

easy to make them stay on their

proper places. Some of the direc tions for the game require the play ers to name values in the thou sands or of certain powers. The ob

jective of the game is to collect the

greatest number of billion mark

chips, to stay in the black and out of the red (represented by positive and negative powers of ten, respec

tively). Risk cards and numeration charts are included; these charts,

however, must be facedown during play.

Teachers and students should be able to follow the rules and learn the basic game in a reason able length of time. As they pursue the game further, they can learn the fine points and run their hold

ings into astronomical figures?or into bankruptcy?both standard outcomes today. Although not

specifically designed to promote the metric system, this game should facilitate practice in using it. If this game catches on, it should furnish both fun and learn

ing.

NEW PROJECTS Edited by Margie Hobbs State Technical Institute

at Memphis Memphis, TN 38134

In-Service Videotapes on Demand in Spokane Have you, as a teacher, talked with someone else (fellow teacher, su

pervisor, or college instructor)

about how to teach a particular mathematical topic? Or, as a cur riculum supervisor or professor, have you searched for ways to in crease your productivity? If only you could minimize repeating dem onstrations and explanations, time would be saved. In an effort to sat

isfy these needs, the Spokane Public Schools (with funding from ROLM South Central) is devel oping a series of K-12 mathematics

videotapes. The tapes enable teach ers to observe and listen to other

May 1984 391

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