Leslie P. Steffe earned his Ph.D. in mathematics education in 1966 from the University of Wisconsin working under the direction of Henry Van Engen. He joined the faculty of mathematics education at the University of Georgia in 1967, where he was appointed Distinguished Research Professor in 1985. Along with Ernst von Glasersfeld and John Richards, a philosopher of mathematics, he established the research program, Interdisciplinary Research on Number (IRON), circa 1976, which continues on through the present time. The book, Children’s Fractional Knowledge, published by Springer in 2010, is one of the latest publications of this research program.

Cobb P. & Steffe L. P. (1983) The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education 14(2): 83–94. Fulltext at http://cepa.info/2096

The constructivist teaching experiment is used in formulating explanations of children’s mathematical behavior. Essentially, a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time – anywhere from 6 weeks to 2 years. The explanations we formulate consist of models – constellations of theoretical constructs – that represent our understanding of children’s mathematical realities. However, the models must be distinguished from what might go on in children’s heads. They are formulated in the context of intensive interactions with children. Our emphasis on the researcher as teacher stems from our view that children’s construction of mathematical knowledge is greatly influenced by the experience they gain through interaction with their teacher. Although some of the researchers might not teach, all must act as model builders to ensure that the models reflect the teacher’s understanding of the children. Relevance: Constructivist teaching experiment, Model building, Clinical interview. Teaching episode, Counting scheme, Teacher as researcher

Glasersfeld E. von & Steffe L. P. (1986) Composite units and the operations that constitute them. In: Burton L. (ed.) Proceedings of the 10th International Meeting on Psychology in Mathematics Education. University of London Institute of Education, London: 212–216.

Glasersfeld E. von & Steffe L. P. (1991) Conceptual models in educational research and practice. Journal of Educational Thought 25(2): 91–103. Fulltext at http://cepa.info/1419

Traditionally, there has been a certain amount of detachment between teachers of mathematics and cognitively oriented educational scientists who endeavored to develop theories about the learning of mathematics. At present, however, there are signs of a rapprochement, at least on the part of some of the scientists, who have come to realize that their theories must ultimately be evaluated according to how much they can contribute to the improvement of educational practice. Healthy though this realization is, it at once raises problems of its own. At the outset there is the research scientists” inherent fear of getting bogged down in so many practical considerations that it will no longer be possible to come up with a theory that may satisfy their minimum requirements of generality and elegance. Then, when scientists do come up with a tentative theory, there is the difficulty of applying it in such a way that its practical usefulness is demonstrated. This would require either scientists” direct involvement in teaching or the professional teachers” willingness and freedom to become familiar with the theory and to incorporate it into actual teaching practice for a certain length of time. In both cases, it will help if scientists and teachers can establish a consensual domain. In other words, they must come to share some basic ideas on the process of education and the teaching of mathematics in particular.

Glasersfeld E. von, Steffe L. P. & Richards J. (1983) An analysis of counting and what is counted. In: Steffe L. P., Glasersfeld E. von, Richards J. & Cobb P. (eds.) Children’s counting types: Philosophy, theory, and application. Praeger, New York: 21–44.

Richards J., Steffe L. P. & Glasersfeld E. von (1981) Reflections on interdisciplinary research teams. In: Wagner S. & Geeslin W. E. (eds.) Modeling mathematical cognitive development. Clearinghouse for Science, Mathematics and Environmental Education, Columbus OH: 135–143. Fulltext at http://cepa.info/1354

Richards J., Steffe L. P. & Glasersfeld E. von (1983) Perspectives and summary. In: Steffe L. P., Glasersfeld E. von, Richards J. & Cobb P. (eds.) Children’s counting types: Philosophy, theory, and application. Praeger, New York: 112–123.

Riegler A. & Steffe L. P. (2014) “What Is the Teacher Trying to Teach Students if They Are All Busy Constructing Their Own Private Worlds?”: Introduction to the Special Issue. Constructivist Foundations 9(3): 297–301. Fulltext at http://cepa.info/1076

Context: Ernst von Glasersfeld introduced radical constructivism in 1974 as a new interpretation of Jean Piaget’s constructivism to give new meanings to the notions of knowledge, communication, and reality. He also claimed that RC would affect traditional theories of education. Problem: After 40 years it has become necessary to review and evaluate von Glasersfeld’s claim. Also, has RC been successful in taking the “social turn” in educational research, or is it unable to go beyond “private worlds? Method: We provide an overview of contributed articles that were written with the aim of showing whether RC has an impact on educational research, and we discuss three core issues: Can RC account for inter-individual aspects? Is RC a theory of learning? And should Piaget be regarded as a radical constructivist? Results: We argue that the contributed papers demonstrate the efficiency of the application of RC to educational research and practice. Our argumentation also shows that in RC it would be misleading to claim a dichotomy between cognition and social interaction (rather, social constructivism is a radical constructivism), that RC does not contain a theory of mathematics learning any more or less than it contains a theory of mathematics teaching, and that Piaget should not be considered a mere trivial constructivist. Implications: Still one of the most challenging influences on educational research and practice, RC is ready to embark on many further questions, including its relationship with other constructivist paradigms, and to make progress in the social dimension.

Steffe L. P. (1991) The constructivist teaching experiment: Illustrations and implications. In: Glasersfeld E. von (ed.) Radical constructivism in mathematics education. Kluwer, Dordrecht: 177–194. Fulltext at http://cepa.info/2098

In an epistemology where mathematics teaching is viewed as goal-directed interactive communication in a consensual domain of experience, mathematics learning is viewed as reflective abstraction in the context of scheme theory. In this view, mathematical knowledge is understood as coordinated schemes of action and operation. Consequently, research methodology has to be designed as a flexible, investigative tool. The constructivist teaching experiment is a technique that was designed to investigate children’s mathematical knowledge and how it might be learned in the context of mathematics teaching (Cobb & Steffe, 1983; Hunting, 1983; Steffe, 1984). In a teaching experiment, the role of the researcher changes from an observer who intends to establish objective scientific facts to an actor who intends to construct models that are relative to his or her own actions.

Steffe L. P. (1991) The learning paradox: A plausible counterexample. In: Steffe L. P. (ed.) Epistemological foundations of mathematical experience. Springer, New York: 26–44.

In the summer of 1985, Carl Bereiter published an article in the Review of Educational Research titled Toward a Solution of the Learning Paradox. Ever since, it has been my intention to provide a counterexample to the paradox. Fodor (1980b), who is credited by Bereiter as clearly stating the learning paradox, views learning as being necessarily inductive. “Let’s assume, once again, that learning is a matter of inductive inference, that is, a process of hypothesis formation1 and confirmation” (p. 148). Given his view of learning, Fodor states the learning paradox in the following way.

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