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. https://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. https://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. https://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. https://constructivist.info/9/3/297

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. (1983) The teaching experiment in a constructivist research program. In: Zweng M. G. T. K. J. H. P. S. M. (ed.) Proceedings of the fourth International Congress on Mathematical Education. Birkhauser, Boston MA: 469–471.

Steffe L. P. (1988) Possibilities for the construction of a sense of number by animals. Behavioral and Brain Sciences 11(4): 598–599. https://cepa.info/8159

The target article by Davis & Perusse provides an occasion to isolate theoretical concepts that explain how certain nonhuman animals might construct a sense of number. The authors implicitly challenge the conventional belief that the mind of a nonhuman animal is incapable of performing the operations underpinning the construction of number. It would surprise me if that conventional belief is not altered in the future. In fact, I attribute a unitizing operation to any organism that is capable of constructing concepts of objects as externalized, permanent objects with an existence independent of the organism experiencing them.