Intersubjectivity In Mathematics
Learning:
A Challenge To The Radical
Constructivist Paradigm?
Radical Constructivism + Intersubjectivity = Social Constructivism?
What is Radical Constructivism?
• Inspired by the work of Jean Piaget (1896–1980), the pioneer of the
study of cognitive development in children.
• Based on the idea that the individual is the central element in
meaning-making.
• Individual focuses on their own experiences; the child is the creator
of their own knowledge.
• Development is a natural human process which is primary to learning.
• Individual students actively construct their own mathematical
realities.
What is Intersubjectivity?
• Refers to shared meanings constructed by people in their
interactions with each other.
• Places communication at the centre of meaning-making.
• Gives more attention to social aspects of mathematics learning.
• In mathematics we are concerned with students acquiring the
language and concepts of the community of mathematicians.
What is Social Constructivism?
• Based on ideas of Lev Vygotsky (1896–1934) who believed that
learning and social interactions are what form consciousness, and
learning leads development.
• Collaborative experience where groups interact to develop their
learning.
• It takes greater account of social interactions and language as a
mechanism for an individual to construct thoughts and concepts.
• Grown out of the attempt to incorporate an explanation for
intersubjectivity into an overall constructivist position.
Why does Social Constructivism fail?
• Integration of notions of social construction of knowledge into a
constructivist view of learning is problematic.
• The difference is where each theory places the source of meaning;
one the cognizing individual, the other cultural practices.
• Addresses neither the insights nor the drawbacks of either
constructivism or intersubjectivity.
• Incorporates social interactions and collaborations but this in itself
does not explain what intersubjectivity is fully therefore does an
injustice to both theories.
Relevance to mathematics education
• We are concerned with students acquiring the language and concepts
of the community of mathematicians.
• Constructivist pedagogy is centred on individual problem-solving
which encourages rich constructions of the part of the students.
• However there must come a stage when those ideas are extended
and compared with other interpretations and meanings from other
discourses.
• Intersubjectivity suggests materials, tools, peers and teachers are
constitutive of learning.
Why should we abandon constructivism?
• “Otherwise we might lose the strength of the insights of cultural
studies over the last few decades by subsuming them into mentalistic
psychology.” (p138)
Quotes
• “For Piaget, the individual is a self-regulating autonomous organism, making
sense and meaning from sensorimotor, social and textual experiences… For
Vygotsky, consciousness comes about through communication, through
mediation, and through language in particular.” (p147)
• “I suggest that the extension of radical constructivism toward a social
constructivism, in an attempt to incorporate intersubjectivity, leads to an
incoherent theory of learning.” (p133)
• “The unsatisfactory outcome of adding on the latter to the former, because that
latter is more than a greater emphasis on social interactions.” (p147)
• “A fully cultural psychology is a different world view and a challenge to the
mentalism that lies at the heart of Piagetian psychology and therefore
constructivism in all its forms.” (Harre & Gillet in Lerman, p136)
• “There is only a problem concerning the enculturation of children into
mathematical signifiers and into the discourse of mathematicians if we insist that
somehow people construct their own private languages and meanings.” (p147)