We first distinguish between the school mathematics tradition typically established in textbook-based classrooms and the inquiry mathematics tradition established in classrooms where instruction is compatible with constructivism. We then focus on the inquiry mathematics tradition and consider the theoretical and pragmatic tensions inherent in the view that mathematical learning is both a process of active individual construction and a process of acculturation. Particular attention is given to the ways in which both constructivist and sociocultural theorists address this issue. Finally, we discuss the development of instructional activities for inquiry mathematics classrooms.

Radical constructivism is argued to differ from many other interpretations of constructivism in North America due to its emphasis on the epistemological impact of student inventions. It recognizes that students’ views are not simply inadequate or incomplete adult views, and it allows for the reconceptualization of the mathematical content of the expert in light of student invention. Two examples of student work are examined for their epistemological content. One example is drawn from a fourth grade class learning about least common denominators. The other is from a teaching experiment with a college freshman about exponential functions. A distinction between “voice” and “perspective” is introduced to differentiate between the epistemological content attributed to the student (voice) and its impact on the knowledge of the expert (perspective).

Within the large number of works that are considered to be within a radical constructivist perspective and following the research done by our group over the last several years, an experiment was developed which required 35 college students to reflect on the production of scientific knowledge, and specifically on how this knowledge is constructed and negotiated. One of the most remarkable findings of this research is without doubt, that these students showed themselves to be brilliant epistemologists and were able, in a reflective way, to develop a better informed idea of science.

Radical constructivism is argued to differ from many other interpretations of constructivism in North America due to its emphasis on the epistemological impact of student inventions. It recognizes that students’ views are not simply inadequate or incomplete adult views, and it allows for the reconceptualization of the mathematical content of the expert in light of student invention. Two examples of student work are examined for their epistemological content. One example is drawn from a fourth grade class learning about least common denominators. The other is from a teaching experiment with a college freshman about exponential functions. A distinction between “voice” and “perspective” is introduced to differentiate between the epistemological content attributed to the student (voice) and its impact on the knowledge of the expert (perspective).

Abstract: The term “constructivism” has become fashionable in recent years, but many who use it seem to be unaware that it was launched by Piaget more than half a century ago to characterize his revolutionary theory of knowing. This paper briefly outlines some of the breaks the constructivist orientation makes with conventional epistemology. I focus on the mechanism of communication and suggest that one prerequisite of successful teaching is insight into the students conceptual world.

Key words: philosophy, radical constructivism, education

It has been difficult to integrate constructivism within the paradigms of didactic theory. In this paper, the author attempts to explain this situation: constructivism is asymetrical. Although constructivism eliminated recourse to an external object, it has continued to recognize “the subject in itself”. This article suggests an epistemologic change that would allow constructivist paradigms within didactic theory. In conclusion, the author presents some examples which illustrate how “didactic epistemology” can structure practical and theoretical research.

According to the theory of constructivism, development and transformation of practical knowledge are a vital process that is unavoidable and that occurs without there being necessarily an intention to educate or to learn. A human being can effectively consider the circumstances of his or her existence when he or she produces this kind of knowledge: one always knows something that is relatively viable for oneself! Contrary to traditional writings that evaluate practical knowledge according to their degree of conformity to “established” school knowledge, the analysis proposed here considers that it is formal school learning that should be subjected to the constraints of pratical informal learning.

This article illustrates the process of constructing answers to impossible problems. The authors describe a conceptual frame, related to issues at the intersection of psychology and didactics, which is used to develop a model to analyse the various reasoning strategies used in students’ elaboration of responses. The choice of impossible problems of various complexities is in itself a research process that is particularly useful in demonstrating the effects of contracts (experimental and didactic) on students’ responses and the interactions between “public” and “private” aspects of answer formulation. The authors provide examples of response productions of 10 and 11 year old students; these illustrate the elaboration strategies described above.