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Algebraic symbolism as a conceptual barrier in learning mathematics

Book Contribution - Book Chapter Conference Contribution

The use of symbolism in mathematics is probably the mostly quoted reason people use for explaining their lack of understanding and difficulties in learning mathematics. We will consider symbolism as a conceptual barrier drawing on some recent findings in historical epistemology and cognitive psychology. Instead of relying on the narrow psychological interpretation of epistemic obstacles we use the barrier for situating symbolism in the ‘ontogeny recapitulates phylogeny’-debate. Drawing on a recent study within historical epistemology we show how early symbolism functioned in a way similar to concrete operational schemes. Furthermore we will discuss several studies from cognitive psychology which come to the conclusion that symbolism is not as abstract and arbitrary as one considers but often relies on perceptually organized grouping and concrete spatial relations. We will use operations on fractions to show that the reliance on concrete spatial operations also provides opportunities for teaching. We will conclude arguing that a better conceptual understanding of symbolism by teachers will prepare them for possible difficulties that students will be confronted with in the classroom.
Book: 6th East Asia Regional Conference on Mathematics Education, Proceedings
Volume: 3
Pages: 2 - 10
ISBN:9786162232589
Publication year:2013
Accessibility:Open