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Vygotsky's theory of scientific concepts and connectionist teaching in mathematics

Swanson, David

[Thesis]. Manchester, UK: The University of Manchester; 2016.

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Abstract

This thesis can be described in various terms. It is a translation of Vygotsky's theory of scientific concepts, in reality a theory of development, into a theory of mathematics teaching and learning. It is a theorisation, and development, of connectionist pedagogy in mathematics (a relatively underdeveloped, yet exemplary, amalgam of various reform/progressive /meaningful approaches to teaching). And, it is an investigation of the elements and processes involved in mathematical concept development, and the mediating role which classroom tasks can play. Alongside this, these understandings are embedded within a wider understanding of society, schooling, mathematics and mathematics teaching which help explain the current dominant practice in the classroom, and in doing so add to the understandings already described. In sum, the thesis therefore represents the beginnings of a systematic Marxist perspective of mathematics education which can cohere analysis at the multiple levels of society, schooling, classroom teaching and learning, and individual concept development. As such it is also, as should always be the case with Marxist perspectives, a guide to action for critical mathematics educators.The thesis begins with context, motivation and strategy, an overview of relevant literature, and an explanation of the methodology and methods used within. The relationship between Vygotsky's theory of concept development and connectionist teaching is then outlined and developed. The wider societal perspective follows, with an emphasis on generalised commodity production as the key shaper of schools and classrooms. Both of these themes are then developed in relation to the example of vocational mathematics, both providing evidence of the existence and nature of scientific activity and concepts, and connecting their absence to the obstacles related in the previous section. The thesis continues by exploring a pedagogical development based on Vygotsky's theory, looking at the explicit problematising of generalisation, and analysing classroom dialogue in relation to this. In the other direction, a theoretical development is then made, following an illustration of the pedagogical and theoretical framework through the development of a particular concept. Finally, conclusions are drawn and future work outlined.