It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that…