Wittgenstein and Judging the Soundness of Curriculum Reforms: Investigating the Math Wars



Wittgenstein’s rule-following argument draws considerable attention: its policy significance for education , very little. Confronted with rule deviation, what justifies claims to ‘sound’/‘unsound’ implementation of curricular reforms, or reasonable adaptation? Playing on John Mighton’s Possible Worlds scenario, I probe these questions on different planes of inquiry through similar vignettes, focused on his ethically aimed math training program (JUMP). Surveying the topic space, I first touch on fervent debate between Rorty and his critics, Putnam and McDowell , over ‘solidarity’ grounding judgment. Must ‘soundness’ claims be ‘answerable to the world,’ and if so, how do we justify our educational practices ? Is sharing a ‘sense’/‘sensibility’ (a fact/value) of ‘pedagogic soundness’ sufficient to uphold its veracity? I then explore the controversy between contending paradigms of discovery learning and Mighton’s guided training in math fundamentals, illustrating opposition between liberal-analytic definitions of teaching with training . In terms of student diversity, which possible worlds beckon account? Finally, drawing on Medina , we see the problem of encountering alien practices through the lens of ‘logical insanity.’ Faced with seemingly ‘unsound’ reforms, teacher resistance acts as healthy, conservative brakes; alternately, recalcitrance can normatively blind teachers to innovation, effectively stalling improvement in learning . Not an either/or in terms of grounding, balance is advocated between the need for (a) faithful immersion in demonstrative practices in order to understand (immanently) their sense within the flow of classroom life; and, (b) the professional need for reasons or warrants—liberal-analytic , rational justification motivating the exertion of energy needed to sustain change initiatives.


Wittgenstein Mighton Mathematics training Discovery learning Liberal-analytic philosophy Rorty Putnam Mcdowell 


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Authors and Affiliations

  1. 1.University of TorontoTorontoCanada

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