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 (nonradical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

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,…

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…

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,…

This article communicates findings from a year-long constructivist teaching experiment about the relationship between four sixth-grade students' multiplicative structures and their construction of improper fractions. Students' multiplicative structures are the units coordinations that they can take as given prior to activity--i.e., the units…

Analysis of episodes from a mathematics course for prospective elementary teachers run as a whole-class constructivist teaching experiment provides a detailed look at how classroom norms for mathematical justification were established given the prospective teachers' traditional expectations of school mathematics and the teacher's reform-oriented…

Describes five college and two high school students' understandings of function and limit in a graphics calculator-based environment and identifies instances where students' understanding seems to have been influenced by the availability of a graphing calculator. (27 references) (MKR)

Describes the development of the ability to identify a ratio as the appropriate measure of a given attribute by (n=26) prospective elementary teachers. It was concluded that traditional procedural approaches to teaching ratios do not challenge students to develop their own mathematical models of the world. (21 references) (MKR)

Discusses dilemmas teachers may face when shifting their concept of teaching or tutoring from explaining or telling to a constructivist perspective of facilitating the development of students' knowledge structures. Examines teachers' decisions during a 20-minute segment of dialogue between a student and teacher while studying linear functions. (14…

Attempts to distinguish between the lecture method and the constructivist approach, in general, and by citing classroom scenarios. The author cautions those whose writing seems to unintentionally endorse traditional lecture and drill and practice methods. (MKR)

Addresses the challenges, risks, and rewards of teaching about linear functions in a technology-rich environment from a constructivist perspective. Describes an algebra class designed for junior high school students that focuses of the representations and real-world applications of linear functions. (MDH)

Describes the structure and content of SummerMath for Teachers, an experimental mathematics course designed to help inservice teachers become mathematical thinkers. The course was organized around mathematical explorations and focused on mathematical processes. Includes excerpts from teachers' journals. (Contains 17 references.) (MKR)