An example is used to illustrate the four levels: rote, observational, insightful, and formal. (MP)

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

Children between the ages of 10 and 13 were asked to write stories to accompany five computational problems. Stories were scored for suitability and it was found that students were most successful on subtraction and least successful on multiplication stories. Scores on this test correlated with mathematics achievement scores. (SD)

A view is presented that there are people with inborn mathematical talent, and that people with such talent need to receive the best instruction possible. (MP)

This discussion centers around the dangers in making too precise a particular concept in educational psychology that distinguishes between two types of understanding, instrumental and relational. (MP)

Richard Skemp, author of The Psychology of Learning Mathematics, briefly outlines his theory of schematic learning and comments on motivation, contributions by psychologists to the learning of mathematics, British Curriculum Projects, "Modern Mathematics," and provisions for slow learners and for gifted children. (DT)

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)