The authors discuss the evaluation of mathematics learning at four levels: associative learning, concept learning, principle learning and problem solving. (MM)

Preschoolers were given instruction in the three set relations: (E) equivalence, (G) greater than, and (L) less than. Instructional sequence of the relations was the only independent variable. Posttest scores of the EGL sequence group were significantly better than those of the control groups. (RS)

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)

Discusses: (1) different types of learning (concepts, properties, facts, procedures, algorithms, skills, and problem solving); (2) types of learning behaviors; and (3) types of representational models, considering concreteness, meaningfulness, and manipulation (active manipulation, passive manipulation, and nonmanipulation). (JN)

Some students can perform operations on fractions when using physical materials, but are unable to transfer this ability to operations with symbolic expressions. They seem to view the manipulative and paper-and-pencil problems as different and are not surprised to get different answers. (SD)

Multiple embodiment is explained and discussed, with activities described that might be used to develop concepts in geometry and in arithmetic. A series of questions is raised about the choice, use, and organization of embodiments; suggestions for action research are made. (DT)

A description is given of several theories of learning styles. The implications for mathematics education are discussed; special attention is given to corrective teaching. (MK)