This paper describes how the notion of the strongly didactic contract can serve to characterize the teaching adopted to implement a task in probability. It is particularly focused on the reality of mathematical work performed by students and teachers. For this research, classroom sessions were developed in an in-service teacher training course…

This paper substantiates the notion of inclusive materialism by illustrating the role of signs and micro-perception in the learning process of multiplication. Inclusive materialism, offered by de Freitas and Sinclair, considers mathematical learning a process of becoming a learning assemblage, which embodies various materials in a Deleuzian sense.…

Constructivist learning theories have become the dominant ideology in educational circles, in part, because there is a primacy on the agential individual with its definite identity. However, precisely because "to construct" is a "transitive" verb, it occludes the fact that in learning and development, we come to know something…

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through…

It is argued that the view of mathematics as an activity emphasizing intuitive thinking is compatible with an axiomatic-deductive approach. (MP)

Reports on important learning processes that emerged during adult mathematics classes that used a teaching approach compatible with a social constructivist theory of knowing. Concludes that affective processes precipitated students' responsiveness, modifying the immediate learning context which influenced student thinking, creating a snowball…

Typical classroom conversation of teachers and pupils during examples of mathematics instruction are analyzed. The importance of references as essential parts of speech acts in conversation is emphasized. (MP)

Experiments by Russian educators on teaching algebra in elementary grades are summarized by the author. The algebra taught consisted of generalized solutions to concrete problems that are usually presented with fixed numerical values. (JP)

Ideas on a teaching-learning theory of ratio are presented. Views of children and of members of an international panel are presented, and five questions and their responses are compared with real classroom experience. (MNS)

This report describes several student investigations in an undergraduate mathematics degree course. (MP)

The theoretical and reference frameworks developed in a 1982 study proved effective for developing a constructivist approach leading children to build a meaningful and efficient symbolism of number. Results of a three-year longitudinal study are described. (MNS)

Described is the Educational Leaders in Mathematics (ELM) Project, a four-stage inservice teacher program designed to stimulate teachers' development of a constructivist view of learning. The impact of the intervention was studied, and results indicated that teachers' beliefs were affected, producing changes in teaching strategies. (MDH)

Proposes that although the past 30 years have seen increasing efforts to make mathematics more relevant and useful, schools continue to fail. Argues that forced rote learning is the direct cause of this failure and that improved teaching methods must be developed. Urges that shifts in methodology be phased in gradually. (TW)

An analysis of a 10-minute episode in which 7-year-old students (n=3) engage in collaborative small group activity is presented to explore the relationship between individual learning and group development. Students learned as they interactively constituted situations for justification or validation, yielding an institutionalized solution method.…