1. Radical Constructivism + Intersubjectivity = Social Constructivism?
Intersubjectivity In Mathematics Learning: A Challenge To The Radical Constructivist Paradigm?
Radical Constructivism + Intersubjectivity = Social Constructivism?

2. 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.
All constructivists draw their inspiration from Piaget’s work

3. 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.

4. 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.
All constructivists draw their inspiration from Piaget’s work

5. 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.
All constructivists draw their inspiration from Piaget’s work

6. 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.
All constructivists draw their inspiration from Piaget’s work

7. 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)
All constructivists draw their inspiration from Piaget’s work

8. 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)