Recent research suggests that knowledge is stored in the learner's head as a network of concepts or constructs. Children's mathematical problem-solving strategies become increasingly abstract as they are able to engage in more abstract thinking. An experimental study using an alternative Cognitively Guided Instruction approach is described.…

Views of (n=70) 16- and 17-year olds on mathematical knowledge, activity, and learning were analyzed using factorial techniques. Findings suggest there was no simple systematic relationship between beliefs about the nature of mathematical knowledge and the teaching and learning of mathematics. (19 references) (Author/MKR)

A mathematician who has been teaching for 58 years discusses 3 types of knowledge that are subjects for teaching or learning (what, how, and why) and why teaching must include problem solving or the use of the Socratic, Moore, or discovery method. (MKR)

Outlines a model of mathematical understanding as a whole, dynamic, nonlinear, recursive growing process, entailing "folding back" for the reconstruction of inner level knowing. Presents examples from seventh graders' work. Discusses teacher awareness of student level of understanding, and implications for development of mathematics…

Didactic transposition theory asserts that bodies of knowledge are designed not to be taught but to be used. Discusses didactic transposition, the transposition of knowledge regarded as a tool to be used to knowledge as something to be learned in mathematics textbooks. (14 references) (MDH)

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

Explains the constructivist theory of knowledge and discusses the theory's implications for teaching remedial college students. Analyzes student performance on a college placement test to highlight the differences between how novices and experts process scientific or mathematical materials. Suggests a radical change in introductory algebra…

Focuses on the language used by elementary mathematics teachers and its relationship to students' understanding of mathematical concepts, as well as their misconceptions. Describes eight situations in which the use of precise, formal mathematical terms could be replaced by informal language, particularly when introducing new concepts. (TW)

Used are test and interview data to extract evidence as to what level tenth graders have coordinated the worlds of arithmetic and algebra and can move freely between them. More dissociation is shown than was expected. (Author/MVL)

Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)

Reports misconceptions identified in students with respect to the topic of parallel lines and the teaching strategies found to be useful in challenging those misconceptions. (11 references) (MDH)

This paper presents a framework utilized in two research projects for mathematics teacher learning based on what is understood about students' mathematics learning. The framework is grounded in a social constuctivist perspective and builds on Karplus' Learning Cycle. A framework for mathematics education identifies a learning cycle that progresses…

Videotaped interviews of 29 Australian students from grades 1-3 were analyzed to assess and compare the processing loads of mathematical representations and strategies used by teachers and children to learn the concept of place value. Results indicated that some representations and strategies impose an unnecessary processing load that can…