Teaching Mathematics with Semiotic Representations by Raymond DuvalMy rating: 2 of 5 stars
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Literary theorist Kenneth Burke famously defined man by stating that "Man is the symbol-using (symbol-making, symbol-misusing) animal…” Philosopher Susanne K. Langer observed in Philosophy in a New Key that “The assignment of meanings is a shifting, kaleidoscopic play, probably below the threshold of consciousness, certainly outside the pale of discursive thinking….” There may be no more economical way to illustrate a circle than the image of the closed curve and an indicated center. Yet, I have encountered many students competent to, say, go between graph and equation, yet unaware of any connection to a set of coplanar points equidistant from a fixed point of the same plane no matter how many images they have produced or interpreted. Duval challenges us to make the transmission of the base concept as the measure of success, not superficial figurative problem-solving. As Duval sums up,
“Contrary to what has been always postulated in mathematics education, discrimination of the relevant units of meaning in different representations does not result from the acquisition of concepts, but it is the prerequisite for this acquisition.”
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