This is the sixth in a series of ten self-contained units designed for use by students in ninth grade general mathematics classes. This unit is divided into eight sections dealing with different types of mathematical thinking. Some topics presented include functions, permutations and combinations, symmetry, inductive thinking, and logic. Though…

An elementary school mathematics program can be structured to allow students to practice computational skills and also become familiar with concepts that need to be mastered in algebra. The activities described begin with students' life experiences, continue through concrete and pictorial experiences, and conclude with abstract activities and…

Using four activity sheets, students learn to identify fractions that are easy to use in estimation situations. (MNS)

How students are convinced that they have the correct solution to a problem, free of contradiction, is discussed. The role of counterexamples and the need for a situational analysis of problem-solving behaviors are each included. (MNS)

Use of compatible numbers resulting in easy mental computations is described, along with related teaching and testing tips. (MNS)

Discussed is an approach in which algebra and geometry are interwoven in a series of problems that develop one from another. The two main concepts are the algebraic concept of function and the geometric concept of the "family of quadrilaterals." (MNS)

Children's solutions to simple word problems requiring addition or subtraction skills develop through four stages: (1) modeling with objects; (2) utilization of both modeling and counting strategies; (3) reliance on counting strategies; and (4) reliance on number facts. The current primary mathematics curriculum fails to capitilize on rich…

A set of references on problem solving is provided, coded by age level and types of content. Background information and instructional activities are both included. (MNS)

This report on mathematics education in Soviet elementary schools was prepared by a writer for the Novosti Press Agency in Moscow. It notes that mathematics is taught by subject specialists beginning in grade 4 and provides details on both curriculum and instructional practices. (MNS)

The various roles and uses of mathematics in developing global awareness in students are considered. Mathematics as a unifier of human experience and problem solving with a global emphasis are discussed with many illustrative examples. (MNS)

Methods of finding algebraic expressions to fit number patterns are explored. (DT)

This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

This paper presents the design and some results of a series of teaching experiments. The design was created to develop a model for everyday math lessons, that describes the conditions which foster or hinder the construction of new mathematical meanings. The development process includes the students' epistemic processes, their social interactions,…

We deal with the study of the senses and the meanings generated in the representation of the unknowns in the resolution of word problems involving two unknown quantities. The discussed cases show the difficulties that the students beginning the algebra learning have to deal with when using the equality between "unknown things". For them,…

This paper describes how one group of students developed personally meaningful ways to reason mathematically within the context of measurement. Episodes taken from a first grade classroom in which a 4-month teaching experiment was conducted are presented. One of the goals of the teaching experiment was to develop instructional sequences designed…