Cobb P., Perlwitz M. & Underwood D. (1996) Constructivism and activity theory: A consideration of their similarities and differences as they relate to mathematics education. In: Mansfield H., Patemen N. & Bednarz N. (eds.) Mathematics for tomorrow’s young children: International perspectives on curriculum. Kluwer, Dordrecht: 10–56. https://cepa.info/6868

The primary purpose of this chapter is to clarify the basic tenets of activity theory and constructivism, and to compare and contras instructional approaches developed within these global theoretical perspectives. This issue is worthy of discussion in that research and development programs derived from these two perspectives are both vigorous. For example, the work of sociocultural theorists conducted within the activity theory tradition has become increasingly influential in the United States in recent years. One paradigmatic group of studies conducted by Lave (1988), Newman, Griffin, and Cole (1089). and Scribner (1984) has related arithmetical computation to more encompassing social activities such as shopping in a supermarket, packing crates in a dairy, and completing worksheets in school. Taken together, these analyses demonstrate powerfully the need to consider broader social and cultural processes when accounting for children’s development of mathematic cal competeuce.

Francovich C. (2010) An interpretation of the continuous adaptation of the self/environment process. International Journal of Interdisciplinary Social Sciences 5: 307–322. https://cepa.info/1129

Insights into the nondual relationship of organism and environment and their processual nature have resulted in numerous efforts at understanding human behavior and motivation from a holistic and contextual perspective. Meadian social theory, cultural historical activity theory (CHAT), ecological psychology, and some interpretations of complexity theory persist in relating human activity to the wider and more scientifically valid view that a process metaphysics suggests. I would like to articulate a concept from ecological psychology – that of affordance – and relate it to aspects of phenomenology and neuroscience such that interpretations of the self, cognition, and the brain are understood as similar to interpretations of molar behaviors exhibited in social processes. Experience with meditation as a method of joining normal reflective consciousness with “awareness” is described and suggested as a useful tool in coming to better understand the nondual nature of the body. Relevance: The article directly addresses problems and strategies for conceptualizing and working with nondual phenomena and the paradoxes therein.

Keiding T. B. (2007) Learning in context: But what is a learning context? Nordic Studies of Education 2: 138–148. https://cepa.info/887

This article offers a re-description of the concept of learning context. Drawing on Niklas Luhmann and Gregory Bateson, it suggests an alternative to situated, social learning and activity theory. The conclusion is that the learning context designates an individual’s reconstruction of the environment through contingent handling of differences and that the individual emerges as a learner through the actual construction. The selection of differences is influenced by the learner’s actual knowledge, the nature of the environment and the current horizon of meaning in which the current adaptive perspective becomes a significant factor. The re-description contributes to didactics through renewed understanding of the participants’ backgrounds in teaching and learning. Relevance: The paper focuses on learning context as individuals’ mental construction, on the distinction between teaching as context for learning and learning contexts, and on re-description of participants’ backgrounds as temporary horizons of meaning.

Steffe L. P. (1996) Social-cultural approaches in early childhood mathematics education: A discussion. In: Mansfield H., Pateman N. A. & Bednarz N. (eds.) Mathematics for tomorrow’s young children. Kluwer, Dordrecht: 79–99.

The caption that I have chosen for my discussion of the papers by Peter Renshaw and Paul Cobb is particularly relevant because it encapsulates much of what I want to say. Both authors emphasize that socio-cultural theory, whatever its form, has come to the fore in early childhood mathematics education. Renshaw provides an excellent overview of Vygotsky’s socio-cultural theory and how it has influenced mathematics education at the Academy of Pedagogical Sciences in Moscow, and Cobb provides an equally insightful comparison and contrast of Soviet Activity Theory and social constructivism. Rather than attempt to carry on with comparing and contrasting the two theories, my goal is to bring Piaget’s genetic epistemology squarely into sociocultural theory and to explore the consequences of doing so. Piaget based his genetic epistemology on interaction as a hard core principle, so in my view it is unnecessary to keep genetic epistemology and sociocultural theory separate as we create our visions of what early childhood mathematics might be like. In fact, I believe that including Piaget’s genetic epistemology in sociocultural theory is especially important in the context of early childhood mathematics education.

Steffe L. P. & Tzur R. (1994) Interaction and children’s mathematics. In: Ernest P. (ed.) Constructing mathematical knowledge: Epistemology and mathematics education. Falmer Press, London: 8–32. https://cepa.info/2103

In recent years, the social interaction involved in the construction of the mathematics of children has been brought into the foreground in order to sptcify its constructive aspects (Bauersfeld, 1988; Yackel, etc., 1990). One of the basic goals in our current teaching experiment is to analyse such social interaction in the context of children working on fractions in computer microworlds. In our analyses, however, we have found that social interaction does not provide a full account of children’s mathematical interaction. Children’s mathematical interaction also includes enactment or potential enactment of their operative mathematical schc:mes. Therefore, we conduct our analyses of children’s social interaction in the context of their mathematical interaction in our computer microworlds. We interpret and contrast the children’s mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. We challenge what we believe is a common interpretation of learning in radical constructivism by those who approach learning from a social-cultural point of view. Renshaw (1992), for example, states that ‘In promulgating an active. constructive and creative view of learning,… the constructivists painted the learner in close-up as a solo-pia yer, a lone scientist, a solitary observer, a me:ming maker in a vacuum.’ In Renshaw’s interpretation, learning is viewed as being synonymous with construction in the absence of social interaction with other human beings. To those in mathematics education who use the teaching experiment methodology, this view of learning has always seemed strange because we emphasize social interaction as a primary means of engendering learning and of building models of children’s mathematical knowledge (Cobb and Steffe, 1983; Steffe, 1993).