What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…

An instrumental technique is presented to help students create a symbolic representation that may aid the process of choosing an appropriate operation to solve a problem. Current research and practice are discussed; then the part-part-whole model is presented. (MNS)

This manual is used with MATHBOXES, a computer program written for Apple II microcomputers to help children relate formal mathematical symbols for representing simple word problems to the informal strategies using physical objects that they naturally use to solve them. There is a substantial body of research that documents that young children are…

Thinking Approach to Problem Solving (TAPS) is a decision-making model that will assist students, kindergarten through grade eight, to decide on the choice of operation in routine mathematical word problems. The TAPS algorithm, or plan, suggests that students read a word problem, determine the question to be answered in the problem, use concrete…

The purpose of this manual is to present a series of lessons on solving word problems, each focusing on a specific concept. The solving of story problems should be incorporated into the daily mathematics lesson so that children can maintain and increase their skills. The lessons are sequenced according to their complexity. Lessons one through…

Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)

Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

Learning the techniques of critical thinking and problem solving can be easy for children when presented problems involving fun topics. Problem sets which range from easy to hard written by elementary school students and educational consultants are included. Topics include addition, subtraction, multiplication, division, and fractions. Each topic…

Presents the teaching strategy of having first grade students write their own word problems. Suggests the use of calculators to permit students to create problems with larger, more realistic numbers. Gives examples of student-generated problems and discusses students' attempts to solve the problems. (MDH)

The purpose of this curriculum guide is to assist Training Specialists in teaching Adult Basic Education/General Educational Development (ABE/GED) students basic skills in language arts and mathematics. The guide begins with an introduction (purpose, overview, adult learner characteristics, teacher type), curriculum policies, curriculum structure,…

The purpose of this curriculum guide is to assist Training Specialists to teach Adult Basic Education/General Education Development (ABE/GED) students intermediate skills in reading, English, and mathematics. The guide begins with an introduction (purpose, overview, adult learner characteristics, teacher type), curriculum policies, curriculum…

Recent research suggests that many middle school students approach mathematical story problems with strategies that are not based on possible meanings for the operations, yielding success for one-step problems, but providing a weak background for approaching algebra story problems. This document reports the findings and the materials developed by…