Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students' learning in experimental classrooms. However, these sequences involve…

This case study discusses an activity that makes up one of five lessons in an ongoing classroom teaching experiment. The goal of the teaching experiment is (a) to gain insight into kindergartners' spatial structuring abilities, and (b) to design an educational setting that can support kindergartners in becoming aware of spatial structures and in…

This article considers two small groups of students in the same Grade 8 mathematics classroom whose approaches to the same mathematical problem result in very different experiences. Using videotapes and written transcripts, an analysis of the groups' working processes was undertaken using Sawyer's pre-existing structures required for the presence…

This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of…

This study is part of a large research and development project aimed at observing, describing and analyzing the learning processes of two seventh grade classes during a yearlong beginning algebra course in a computer intensive environment (CIE). The environment includes carefully designed algebra learning materials with a functional approach, and…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

The aim of this study is to describe and analyze students' levels of understanding of exponents within the context of procedural and conceptual learning via the conceptual change and prototypes' theory. The study was conducted with 202 secondary school students with the use of a questionnaire and semi-structured interviews. The results suggest…

Investigates procedural and conceptual aspects in preservice elementary school teachers' understanding of the Fundamental Theorem of Arithmetic. Participants' responses indicated that a possibility of alternative prime decompositions was often not overruled, and this influenced students' ability to make inferences regarding factors and divisors of…

Describes the habits of mind that would be most desirable for students to develop. In high school for example, content-specific habits would include geometric habits of mind that support the mathematical approaches, and algebraic ways of thinking that complement the geometric approaches. (AIM)

The second in a series of three articles, some themes of an undercurrent of educational objectives that move beyond the evident content goals are outlined. The themes relate the computer software materials analyzed in Part I to the cognitive experiences that students should have in learning about subject matter. (MDH)

This study explored how one eighth grade girl learned about the structure of recursive programs in BOXER programing language. The method of impasse resolution was presented in detail and used both to understand how she constructed her understanding and as an empirical method to analyze her learning. (MDH)

This study examined the representations that a 16-year-old student made using the flexible computer system, "Boxer," in learning the genetic code. Results indicated that programing made it easier to build and explore flexible and useful representations and encouraged interdisciplinary collaboration between mathematics and biology…

Presents anecdotes, discussion, and definitions of the terms natural, conflicting, and alien as they relate to the teaching and learning of mathematics. (MKR)

Shows fragility of knowledge in connection with a false application of mathematical induction, as observed in a problem-solving course for prospective teachers. The attempt to explain the observations is based upon an analysis of the logic underlying proof by mathematical induction and a concept formation theory. (MKR)

A longitudinal study followed Brian from grade five through grade seven to examine his representation and development of mathematical knowledge. Some observations over the four years were that Brian liked to figure things out, responded poorly to suggestions not fitting the representation he constructed, and changed attitudes from purposeful and…