Analyzed was the mental activity required to answer Profile Test questions. This was then related to the results of pupils with differing profiles. Most of the mental activity could be reduced to three categories of knowledge: data, short operations, and paths. These categories are then discussed and applied. (MNS)

Five steps described by Dienes by which mathematics is learned are illustrated through the use of the topic of direct proportion. (MP)

Investigated was the learning of the mathematical uses of "more,""fewer," and "less" at a very early stage in the development of ideas. (CW)

Space and shape, estimating and measuring, and number are viewed as the three strands of mathematics that come together as a child develops mathematically. Five cognitive/mathematical levels of development, labeled discrimination, order, application, operation, and estimation, are identified and discussed. (MP)

Student comments about having time in class to think and solve problems are presented. Stressed are teaching methods which allow students to familiarize themselves with the problem, think about solution processes, work through the solution process, and reflect while solving a problem. (CW)

Provided is an example of the use of the Pythagorean Theorem to give learners experience in applying mathematical rules. A proof for the theorem is included. Precautions and alternatives are discussed. (CW)

The contrast between the teaching of reading and mathematics is drawn. A new set of learning conditions for mathematics is presented based on a model of reading instruction. Immersion, demonstration, engagement, expectations, responsibility, use approximation, response, refinement, and outcomes are discussed. (CW)