language aspects of algebra – from a semiotic/linguistic perspective language aspects of algebra
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Language aspects of algebra – from a semiotic/linguistic perspective
Language aspects of algebra
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 How you say
(symbolic) Process
Capability How you do
Understanding Concept
concepts what you do
Example
a) 2(x + 1) = 3xb) 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.
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