The foreknowledge that a given school mathematics problem might have no specific solution or no solution at all affords students the challenge of investing careful consideration in the explicit problem conditions, as well as in the problem's unstated assumptions. Hence, the implication is that mathematics teachers, rather than speaking to their…

This teacher's guide is the ninth in a set of 20 activity booklets for teaching mathematics to children in grades 1-8. The 20-level curriculum embodies carefully delineated areas of learning arranged in progressive stages, eliminating grade restrictions and permitting continuous growth according to the individual's ability and rate of learning.…

The processes and strategies used by Finnish second graders in solving verbal multiplication and division tasks were investigated, and the relationship of these processes and strategies to Piagetian abilities, memory capacity skills, and rational number concepts was charted. Three categories of strategies were classified: operations based on…

In this practicum students' (n=27) learning styles were used to develop teaching lessons and strategies that would improve mathematics learning in a second grade classroom. Each child's learning style was determined through the Swassing-Barbe Modality Index (SBMI). Pretests for mathematics concepts were given. Each concept was then taught…

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…

A study explored the effectiveness of an instructional approach designed to help students establish connections between their understanding of the decimal system and the stardard symbols and procedural rules used to solve decimal problems. Ten children each in grades 4 through 6 participated. They were individually interviewed prior to and six…

This document analyzes one chapter of a textbook for college remedial mathematics. This analysis is done by one of the textbook authors. The chapter under discussion deals with fractions. The text authors, writing from a constructivist perspective, attempted to write problems which not only developed specific conceptual and heuristic objectives…

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics program. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…

Reports on a study designed to investigate aspects of young children's knowledge of fractions and partitions of quantities. Findings suggest that although children did not have a deep understanding of the concept of one half, a significant number demonstrated a powerful systematic procedure leading to the creation of accurate equal fractional…

Presents a set of activities, in reproducible format, emphasizing geometry. The activities offer experiences in area measure, whole number and fractional computation, and problem solving in spatial relationships. (PK)

Described is a way to incorporate mathematics into such disciplines as social studies, English, science, and library skills. Emphasized is that connections must be made among various topics so that students can see how mathematical ideas are related and how one mathematical idea can help them understand others. (KR)

Examines what prospective elementary and secondary mathematics teachers understand about mathematics when they enter formal teacher education. Results reveal that the mathematics understanding of elementary and secondary teacher candidates tends to be rule-bound and inadequate. (BB)

Presents guidelines for designing and using extensions, which are exercises that follow or extend the basic presentation of an idea, in the mathematics area of the Montessori program to give children more experience and depth as they explore key mathematical concepts. Describes extensions that address counting, sorting, and working with decimals.…

A teaching experiment with six third graders to analyze their ways of operating while solving fraction tasks. Children's quantitative reasoning with fractions was based on their quantitative reasoning with natural numbers. Presents the constructive itinerary of one of the most advanced children in the group. (Contains 44 references.) (Author/MDH)