Transcript Linguistics
Language aspects of algebra Language aspects of algebra – from a semiotic/linguistic perspective The symbolic language of algebra has evolved over time to become an efficient describe medium to powerful generate Mathematical ideas Aspects of Symbolic Language • Language relies on – Economy of symbol use – Limited set of linguistic patterns • These features make it possible to express powerful mathematical ideas squeezed into manageable “chunks” of symbol strings Power of Symbolic Language Precision Economy Efficiency Ambiguity in Language • Power and efficiency – ambiguity • Problem for learners • Instead of removing the ambiguity, for example, by introducing new symbols, remove the ambiguity by focusing instruction on the linguistic form of a given symbol string Linguistic Aspects There are a limited number of modes of algebraic expression, which, once mastered enable an individual to read, write, speak mathematics – undertake transformations – develop conceptual understanding – Linguistic Aspects • Notion of representation – Different forms of variables • Abstraction of methods – formulas, identities, theorems • Truth of sentences • Patterns of mathematical reasoning • Teachers and students underestimate the importance of the explicit study of these linguistic elements • What is opaque to the student may be transparent to the teacher 2x + 3 double the number and add 3 opaque transparent • Focus on physical signs and placement order • Look through the symbols to underlying mathematical meaning Multiple Aspects of Symbolic Competence Understanding of linguistic categories Form Practical (symbolic) Process Capability How you do How you say Understanding Concept concepts what you do Example a) 2(x + 1) = 3x b) 2(x + 1) = 2x + 2 What is each equation about? a) numbers, unknown, equality of number b) Operations, equivalence of operations As students grasp the nature of symbolic algebra’s linguistic aspects, they gain power to use mathematical contexts to remove ambiguity from any given symbol string. Explicit instruction within this focus helps students gain autonomy and fully master algebraic thinking.