Pairing Logical and Pedagogical Foundations for the Theory of Positive Rational Numbers—Henkin’s Unfinished Work

Abstract

Five different ways of “founding” the mathematical theory of positive rational numbers for further logical development are presented as Leon Henkin outlined in 1979 in the form of notes for a future paper, suggesting that pairing them up with five representation models could possibly yield further pedagogical development. In turn, he thought that this would indicate a large variety of ways in which this number system, as any other, can be introduced in a classroom setting—many of them quite different from traditional ways. His wish was to explore how varying modes of deductive development can be mirrored in varying classroom treatments rooted in children’s experience and activities. This dream never came to full fruition. Preliminary ideas about corresponding pedagogical embodiments for each logical development are briefly presented here for the next generation of researchers in mathematics-education and curriculum developers to contemplate with, bearing in mind that Henkin’s work itself may need additional polishing.