by Nancy L. Markus
Many adult education and workplace education teachers in Ohio are aligning their instruction with the National Council of Teachers of Mathematics (NCTM) standards in order to provide more effective, beneficial instruction. The following are additional recommended readings and activities that will help you implement an effective, successful mathematics program, using many of these strategies. These suggested materials are of high quality, have practical use, are readily available, and are not typical GED® or pre-GED® textbooks. Current adult mathematics teachers throughout the United States have recommended the resources.
If you wish to purchase books and manipulatives, you can call or write the publisher directly (see information accompanying each annotation) or contact one of the these companies. Many of the books are available from:
The Math Learning Center
P.O. Box 3226
Salem, Oregon 97302
Fax: (503) 370-7961
Note: The Math Learning Center has no shipping charges for delivery within the United States.
2150 Enterprise Drive
Mt. Pleasant, Michigan 48858
Fax: (517) 773-5894
Please note that the quoted prices are approximate and may vary slightly from publisher to publisher. Dale Seymour publications are often available from other resources, such as those listed above, and often at a lower cost.
Many resources can be borrowed from your ABLE Regional Resource Centers. If you have trouble locating an item, please contact the Ohio Literacy Resource Center.
ELEMENTARY SCHOOL MATHEMATICS: Teaching Developmentally (second edition)
Author: John A. Van De Walle
Publisher: Longman (1994)
10 Bank Street
White Plains, New York 10606
While an expensive text, this book is the "gold standard" for teaching mathematics. The book covers the following: reflections and directions of teaching mathematics, learning in a mathematics environment, developing understanding in mathematics, developing problem-solving processes, assessment, the development of number concepts and number sense, developing meanings for operations, mastering the basic facts, whole number place-value development, pencil-and-paper computation with whole numbers, mental computation and estimation, developing fractions concepts, computing with fractions, decimal and percent concepts and decimal computing, developing the concepts of ratio and proportion, developing measurement concepts, geometric thinking and concepts, logical reasoning, exploring beginning concepts of probability and statistics, preparing for algebra, technology and mathematics, planning for developing instruction, and mathematics and students with special needs.
This 500+ page book gives concrete activities and teaching suggestions as well as information on how concepts are learned in order to maximize the benefits of instruction. This reference book includes black line masters that can be used in a variety of ways. The mathematics presented is geared from beginning concepts to early high school math. It provides a sound foundation for more advanced concepts. It is highly recommended and appropriate for pre-GED, GED, ESL, and college developmental classes.
About Teaching Mathematics: A K-8 Resource
Author: Marilyn Burns
Publisher: Math Solutions Publications
Distributed by: Cuisinaire Company of America (1992)
P.O. Box 5026
White Plains, NY 10602-5026
This book reflects current ideas about mathematics education. The first part of the book looks at the issues of mathematics reform, including using word problems to develop arithmetic understanding, going beyond word problems, and managing the classroom for problem solving. The second part looks at problem solving in each of the strands of measurement, probability and statistics, geometry, logic, patterns and functions, and number sense. Finally, the third part looks at specific topics such as number concepts, place value, addition and subtraction, multiplication, division, fractions, decimals, and percents.
This book includes rationale and activities that are appropriate for both pre-GED® and GED® students. It includes blackline masters and an extensive bibliography.
Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Volume II
Authors: Luetta Reimer and Wilbert Reimer
Publisher: Dale Seymour Publications (1995)
P.O. Box 10888
Palo Alto, CA 94303
Fax: (415) 324-3424
This book contains another fifteen stories about the lives of the people behind great mathematical discoveries and ideas. These stories, which include some about women and minorities, can be used as background information for teachers or for students to read and discuss. The reading level is pre-GED, but the information would be appropriate for all levels.
PROBLEM SOLVING...a basic mathematics goal. Becoming a better problem solver - Volume 1
PROBLEM SOLVING...a basic mathematics goal. A resource for problem solving - Volume 2
Prepared by: Steven P. Meiring
Published by: Ohio Department of Education (1982)
Division of Inservice Education
65 South Front Street
Columbus, Ohio 43266
Cost: $1.00 each in the state of Ohio/$10.00 each elsewhere
While seemingly an older resource, these publications are excellent for teachers hoping to make their students better problem solvers. An overview of problem solving, strategies and approaches to problem solving are included in Volume 1. Volume 2 includes an introduction to teaching problem solving, research and psychological summaries, problem solving strategies, and teaching considerations. Ideas for getting started by using textbooks, acquiring, adapting, and generating good problems, as well as creating a problem solving environment and including calculators are part of this second volume. Both volumes include problems readily usable in the ABLE classroom.
GROUP SOLUTIONS: Cooperative Logic Activities for Grades K-4
Author: Jan M. Goodman
Publisher: GEMS (1992)
Great Explorations in Math and Science
Lawrence Hall of Science
University of California at Berkeley
Berkeley, CA 94720
This is a companion book to Get It Together: Math Problems for Groups, which was highly recommended in the original OLRC annotated bibliography. This is a collection of cooperative learning activities more appropriate for the pre-GED® student. The information the group needs to solve a problem has been put on clue cards. Each member of the group has a different bit of information, so everyone has to cooperate to solve the problem. This is an exceptionally easy format for the teachers who want to begin using cooperative activities in mathematics with their lower level readers.
The first part of the book discusses Cooperative Logic in the Classroom, what it is, and how teachers make it work successfully. Trouble-shooting deals with common problems that may be faced in the beginning stages of cooperative logic and how to deal with them. Cooperative Logic in Multilingual Classrooms gives tips for teaching cooperative logic in an ESL setting. Finally, cooperative logic activities are presen-ted, including an overview, material preparation, classroom management tips, introductory activities, assessment and extensions.
There are advantages to using cooperative learning activities both for the teacher and the students. The teacher has fewer units to supervise, and thus can spend more time observing the students and their progress as they begin to "own" their problem solving skills. Groups work appeals to more modalities and easily accommodates other disciplines in the math classroom. Success in problem solving is a morale booster. All students, in the ABLE classroom and in family or workplace literacy, benefit from learning to explain themselves more clearly and can work together on these activities. Learning to work together is an important life-skill in today's world.
USING MANIPULATIVES IN THE ADULT EDUCATION CLASSROOM
In order to help adult students with concept development and "mathematical sense making" it is suggested that manipulatives be incorporated into all classrooms. Manipulatives are not merely necessary for low level students; they facilitate learning and sense making for all students. Manipulatives must be used carefully, or they, too, will become another layer of misunderstanding. Not all manipulatives are necessary for every classroom. There are quality activities and strategies that can be used with many different manipulatives. The following books are recommended for use with the different manipulatives, which are often available inexpensively. It is hoped that adult education teachers will begin to see the benefits of using manipulatives in all levels of adult mathematics instruction.
LET'S PATTERN BLOCK IT
Authors: Peggy McLean, Lee Jenkins, and Jack McLaughlin
Publisher: Activity Resources Company, Inc. (1973)
P.O. Box 4875
Haywood, California 94540
This book is designed for use with pattern blocks, which are standard sets of colored geometric shapes. A pattern block set includes a white rhombus, yellow hexagon, red trapezoid, orange square, blue rhombus, and green triangle. Activities included in this book include very basic identification, patterns, symmetry, geometry, games, and strategy puzzles. While the book may at first appear juvenile, it actually contains much material and many activities appropriate to the pre-GED® and GED® classroom.
FRACTIONS with Pattern Blocks
Author: Mathew E. Zullie
Publisher: Creative Publications (1988)
1300 Villa Street
Mountain View, CA 94941
This book of activities is intended to help teachers and students understand concepts concerning fraction relationships and operations with fractions. The activities are to be used with a standard set of pattern blocks. Pages are perforated so they can be easily removed from the book and used as duplicating masters. Teachers are allowed to duplicate the materials for their own classes. Most of the activities are appropriate for adult students with a wide range of abilities. These manipulatives and activities help in introducing new concepts, reinforcing and clarifying concepts, and providing drill and practice in both the pre-GED® and GED® classroom.
Problem Solving with Pentominoes: Grades 1-4 Activity Book
Author: Alison Abrohms
Publisher: Learning Resources, Inc. (1992)
Lincolnshire, Illinois 60069
Pentominoes are manipulatives formed from five squares. This book provides puzzle activities for students using these manipulatives. The book is geared to all levels of adult students and covers concepts needed for the GED. Activities focus on the mathematical concepts of transformations such as slides, turns, and flips and tessellations such as tiling, symmetry, area, perimeter, congruence, and similarity. Extensions for more challenging activities are included. Activities also promote cooperative learning.
SQUARE TILE: EXPLORATIONS AND PROBLEMS: Grades 4-9
Authors: Don Miller and Bishne Naraine
Publisher: Tricon Publishing (1995)
Mt. Pleasant, Michigan 48858
This book is a wonderful resource that shows teachers how numbered or colored square tiles can be used to reinforce a variety of mathematical ideas via non-routine problem situations. Activities are designed to help students improve their mental and estimation skills, to challenge students via equations or familiar computational algorithms, to introduce geometric ideas, and to develop problem solving strategies using games. The main goal of all the activities is to provide students with experiences designed to improve their mathematical skills while helping them to become better problem solvers.
The mathematical content covered spans a wide ability range. It is particularly useful for students in pre-GED® and GED® level classes.
Note: While colored square tiles may be purchased, actual ceramic tiles may be obtained inexpensively through retail tile stores.