Abstract
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.
A portion of this paper was given at the PESGB Gregynog Conference, ‘Orientations Towards Wittgenstein ‘ (Wales 2015), hosted by Paul Standish and Naomi Hodgson.
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Notes
- 1.
Following convention, titles for Wittgenstein’s works are abbreviated (RFM = Remarks on the Foundation of Mathematics, BB = The Blue and Brown Books (Preliminary Notebooks), LC = Lectures and Conversations on Aesthetics, Psychology and Religious Belief, Z = Zettel, PI = Philosophical Investigations , OC = On Certainty, LFM = Lectures on the Foundations of Mathematics, WL = Wittgenstein’s Lectures, CV = Culture and Value, LW1 = Last Writings on the Philosophy of Psychology , PO = Philosophical Occasions), with section (§) or page number (p.), with full citation and initials (e.g., RFM) in the References.
- 2.
When a teacher instructs a pupil to add 2 to 100, 200, 300, ….why is it ‘wrong’, he wonders, for a pupil to add 4 instead, when reaching 1000, 2000 …—frustrating teachers expecting 1000 + 2 (PI §185)?
We say to him ‘Look what you’ve done!’—He doesn’t understand. We say: ‘You were meant to add two: look how you began the series!’ (PI §185)
I do it, he does it after me; and I influence him by expression of agreement, rejection, expectation, encouragement. I let him go his way, or hold him back; and so on.
Imagine witnessing such teaching. None of the words would be explained by means of itself; there would be no logical circle. (PI §208)
- 3.
- 4.
Wittgenstein was aware of the brilliant, inspired mathematician Srinvasa Ramanujan working with Cambridge Professor G.H. Hardy in 1914 (see PI §144 and Z §461 re: Indian mathematicians). Coincidentally, this book was produced in Ramanujan City, India.
- 5.
Mighton was a consultant on, and even made a guest appearance in, the movie ‘Good Will Hunting’ (1997) in which Matt Damon played a custodian at MIT who turns out to be a math prodigy (also starring Ben Affleck and Robin Williams).
- 6.
Taking up this theme, Michael Luntley , Paul Smeyers , Paul Standish , Nicholas Burbules, Richard Smith , and I addressed these topics in both a PES panel and PESGB symposium in 2016.
- 7.
Bill Daggett, International Center for Leadership in Education . See http://premierespeakers.com/bill_daggett.
- 8.
Andy Hargreaves, Quest conference (York Region, 2005).
- 9.
Wittgenstein notes that members of religious forms of life reason differently in response to assertions about the final judgment (LC, pp. 53–55).
But what men consider reasonable or unreasonable alters. At certain periods men find reasonable what at other periods they found unreasonable. And vice versa.
But is there no objective character here?
Very intelligent and well-educated people believe in the story of creation in the Bible, while others hold it is proven false, and the grounds of the latter are well known to the former. (OC §336)
- 10.
Not that Rorty or Dewey first noticed this contradiction ; Kant’s Pedagogy turned apposition between methods and goals in child rearing into a philosophical antinomy.
One of the greatest problems in education is, How can subjection to lawful constraint be combined with the ability to make use of one’s freedom? For constraint is necessary . How shall I cultivate freedom under conditions of compulsion? I ought to accustom my pupil to tolerate a restraint upon his freedom, and at the same time lead him to make good use of his freedom. (Kant 1904, §29, p. 131)
- 11.
Referring to liberal-analytic distinctions between indoctrination and teaching as the giving or weighing of evidence, McClellan (1976: 53–4) refers to ‘counterfeits of teaching.’
- 12.
Beginning: ‘One must start out with error and convert it to truth. That is, one must reveal the source of error, otherwise hearing the truth won’t do any good.’
- 13.
Working together on a high school philosophy text (Stickney 2011), Andrew Wilson wrote the logic unit.
- 14.
Wilson notes: Musicians (savants, prodigies) not needing scales often practice and improvise so much they are immersed in the activity all the time; to some extent, scales are embedded in the repertoire constantly rehearsed.
- 15.
The propositions describing this world-picture might be part of a kind of mythology. And their rule is like that of rules of a game; and the game can be learned purely practically, without learning any explicit rules (OC §95).
- 16.
One of the most important methods I use is to imagine a historical development for our ideas different from what actually occurred. If we do this, we see the problem from a completely new angle (CV, p.37e).
- 17.
Instead of the unanalysable, specific, indefinable: the fact that we act in such-and-such ways, e.g., punish certain actions, establish the state of affairs thus and so, give orders, render accounts, describe colors, take an interest in others’ feelings. What has to be accepted, the given—it might be said—are facts of living // forms of life (PI §630; cf. PI, p. 226).
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Stickney, J. (2017). Wittgenstein and Judging the Soundness of Curriculum Reforms: Investigating the Math Wars. In: Peters, M., Stickney, J. (eds) A Companion to Wittgenstein on Education. Springer, Singapore. https://doi.org/10.1007/978-981-10-3136-6_32
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