The title of this paper is evidence of my long-standing concern for the third aspect of the Hegelian triad—thesis, antithesis, and synthesis—as it applies to mathematics education. Hegel, we recall, interpreted societal change as a reconciliation of opposites, a thesis and its antithesis, into a higher union or integration which he called synthesis. In a very real sense, we can use this conceptual model to interpret the changes that have taken place in school mathematics programs in recent years (and even over the past several thousand years) as man has attempted to select and transmit this segment of the culture.
