Abstract
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.
Highlights
The issue of how an individual makes personal meaning of a ‘new’ mathematical object is a fundamental issue in mathematics education
Understanding the extreme case of a mathematical object introduced through a definition provides a window into what is happening when a learner encounters a new mathematical object, no matter the academic level and no matter that it may be introduced through exemplars and/or with diagrams
I have argued that the notion of the functional usage of a sign together with the construct of the pseudoconcept, can be used to explain how the divide between an individual’s initial mathematical activities and a socially sanctioned mathematical definition is bridged
Summary
The issue of how an individual makes personal meaning of a ‘new’ mathematical object is a fundamental issue in mathematics education. At many universities the student is frequently introduced to a new mathematical object through a definition1 From this definition, the learner is expected to construct the properties of the object (Tall, 1995). Notion, and as I argue later, the learner’s use of the mathematical signs in activity and communication is a necessary first step in the appropriation of mathematical meaning. This usage precedes an understanding of the mathematical object signified by the mathematical sign. My focus is on how a student at university level makes meaning of a new mathematical object presented in the form of a definition, my arguments relate to school level mathematics. Understanding the extreme case of a mathematical object introduced through a definition provides a window into what is happening when a learner encounters a new mathematical object, no matter the academic level and no matter that it may be introduced through exemplars and/or with diagrams (as is common practice in many South African high schools)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
