Abstract
There are two types of conceptual metaphor, that is, grounding metaphors and linking metaphors. Grounding metaphors allow you to project from everyday experiences (like putting things into piles) onto abstract concepts (like addition). Linking metaphors link two different branches of mathematical concepts, for instance linking geometry to arithmetic, as when you conceive of numbers as points on a line.
The purpose of this paper is to analyze mathematics learning from the view of conceptual metaphor. Two types of conceptual metaphor yield two types of mathematics learning, that is, mathematics learning by grounding metaphors and mathematics learning by linking metaphors.
The following figure and table show some differences between mathematics learning by grounding metaphors and mathematics learning by linking metaphors.
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[table]
Through several specific topics of mathematic learning, the author shows some features of the two types of mathematics learning. The results are as given below.
- In the mathematics learning by grounding metaphors
[G-1] Concrete experiences give a meaning to mathematical concepts.
[G-2] The proficiency of mathematical concepts yields the reification of symbolic representations of mathematical concepts.
- In the mathematics learning by linking metaphors
[L-1] Meaning of a mathematical concept will come from the other mathematical concept by linking metaphor.
[L-2] Mathematical problems can be solved by linking metaphors in which original problems are metaphorically replaced by other problems.
[L-3] The linking metaphor may encourage the emergence of new mathematical ideas.
