Recommendations for teaching problem solving stem from a discussion of the differences in the functioning of the left and right hemispheres of a person's brain. (JT)

This study sought to identify prerequiste concepts for a child to perform length measurement meaningfully. Conservation of length and use of transitive reasoning were major areas identified. Implications for teaching are given, especially concerning the use of a number line as a model for presenting arithmetic operations. (LS)

Described is a strategy that shows students how one mathematical concept can be connected to another. The emphasis is on both process and product and can lead to creating a learning environment where students do mathematics as mathematicians do. (KR)

Described is an activity where base-10 blocks are used to develop students' skills in reading, writing, and visualizing large numbers. An activity sheet that helps students with decimal points is included. (KR)

Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (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…

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

Describes the Agam program, a 36-unit curriculum program to introduce students to basic visual concepts and that applies visual abilities and visual thinking to learning tasks. Describes two units at the third grade level, "Ratio and Proportion" and "Numerical Intuition," and makes observations of the students' learning. (MDH)

Describes seven problems designed to enhance the development of four types of student communication in mathematics: (1) describing observations; (2) justifying solutions and solution processes; (3) documenting thinking; and (4) completing or creating mathematical problems. (MDH)

Describes the use and rationale of "Silent Teaching," a teaching technique in which the teacher remains silent as students generate and evaluate hypotheses while trying to understand an as-yet undiscovered concept. (MDH)

Presents a study of 87 second graders to demonstrate that achievement tests in primary mathematics emphasize pupil's lower-order thinking by comparing answers to interview questions from constructivist and traditionally instructed groups. Results indicated that constructivist instructed students demonstrated superior higher-order thinking on tasks…

Presents a 6-day unit for grades 2-4 to enable students to understand the concept of time and how the analog clock works. Using concrete materials and cooperative learning, the unit presents cognitive, affective, and psychomotor objectives and activities for each lesson. (MDH)