Intersubjectivity in mathematics teaching: meaning-making from constructivist and/or sociocultural perspectives?

In 1996, Stephen Lerman wrote a paper entitled Intersubjectivity in Mathematics Learning: A Challenge to the Radical Constructivist Paradigm? In this paper he presented two views of “intersubjectivity”, one a sociocultural view, rooted in the work of Vygotsky and the other a radical constructivist view, with particular reference to the work of Ernst von Glasersfeld and Les Steffe. He was very critical of the latter view. I found this paper and subsequent papers and arguments from Steffe and from Steve, hugely interesting and influential on my own work. In this chapter, I take up the two perspectives of intersubjectivity and, through a number of examples, try to show how interactions and associated meanings could be addressed using each perspective as a lens. For me it is important that the perspectives do not point to what “is” but rather offer a way of interpreting what is seen; offering a conjecture relating to the social factors and cultures that influence what we observe. One conclusion is that, though the theories are not interchangeable and their approaches to conceptualising knowledge construction are incommensurable, they say nothing about what is right or wrong. As researchers we have to be extremely transparent in our use of theory, justifying arguments and interpretations rigorously in relation to the perspective we take.