Original Research

Making mathematical meaning: From preconcepts to pseudoconcepts to concepts

Margot Berger
Pythagoras | Issue 63 | a104 | DOI: https://doi.org/10.4102/pythagoras.v0i63.104 | © 2006 Margot Berger | This work is licensed under CC Attribution 4.0
Submitted: 20 October 2006 | Published: 20 October 2006

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I argue that Vygotsky’s theory of concept formation (1934/1986) is a powerful framework within which to explore how an individual at university level constructs a new mathematical concept. In particular I argue that this theory can be used to explain how idiosyncratic usages of  mathematical signs by students (particularly when just introduced to a new mathematical object) get transformed into mathematically acceptable and personally meaningful usages. Related to this, I argue that this theory is able to bridge the divide between an individual’s mathematical knowledge and the body of socially sanctioned mathematical knowledge. I also demonstrate an application of the theory to an analysis of a student’s activities with a ‘new’ mathematical object.


tertiary mathematics;


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