Functional Thinking with Graphs

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  • 1 Institut für Didaktik der Mathematik (IDM)

The representation of functions by curves and areas, however, has opened a new world of notions and taught one of the most fruitful methods by which the human mind has enhanced its own powers, … Between two arbitrary quantities, one of which may be conceived of as being dependent on the other, no relationship, not even the most complicated one, is conceivable which would not be representable by a curve, a fact instructively documented by Quetelelt's representation of the penchant towards crime, literary talent, etc., by curves as a function of the individual's age. This way of imagin ing the connection between things thus is just as useful for the administrator, the national economist, the physicist and the meteorologist. (Emil du Bois-Reymond, my translation. R. B.)

Journal for Research in Mathematics Education

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