Calculators are seen to shift the student focus in problem-solving situations from "how to do it" to "what to do," by keeping computation from standing in the way when pupils write or solve problems. (MP)

Teaching by learning activities is contrasted with teaching by objectives. Four types of learning activities are identified. (JT)

A series of activities that focus on the process of measuring are presented. The material is designed to help children develop a concept of measurement by leading them through the processes used in establishing formal measurement systems over the centuries. (MP)

Activities that allow students to represent patterns concretely before showing the patterns in color on paper are presented. Three basic activities are described, with suggestions made for extensions that allow further pupil exploration of multiples. Student discovery of relationships not found by the teacher is expected. (MP)

Presents seven scenes showing everyday classroom situations that give students the options of applying their own problem-solving strategies to solve everyday problems of life and enable them to experience mathematical power coming from self-initiated insights into mathematical concepts. (MDH)

The role of language in learning mathematics is discussed. A variety of philosophical essays and research findings are cited as the author argues for the importance of language as a tool for understanding and creativity in mathematics. (SD)

Six different methods were used by students to solve the problem of finding the area of a given trapezoid. A seventh method used by textbooks is also discussed. (MP)

Having students find and cut out of graph paper the 12 pentominoes can provide an enjoyable exercise in perception, discovery, and double checking. The pentominoes can then be used to illustrate informally several geometric concepts. (SD)

A number of paper-folding activities are described. The activities illustrate geometric concepts, theorems, and construction techniques. (SD)

Discovering 3 by 3 magic squares, using numbers 1 through 9, is presented as a learning activity on three different levels. (MP)

Alternative identification and instructional procedures are discussed. Instructors are warned against assuming an equivalence between the quantity of mathematical work a child demonstrates and the quality of that child's thinking. A need to integrate qualitative information is seen. Two types of activities for gifted pupils are detailed. (MP)

Presents three features of "Good" questions: requires students to do more than simply remember a strategy to answer; promotes student learning while answering the question; and have several acceptable answers. Considers how questions can be used to cater to the range of student abilities. (MDH)