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Metacognition seems pretty universally positive. I'm wary of viewing it as such. Aside from the obvious criticisms like "you can't learn to ride a bicycle by thinking about and writing a 200 page treatise on riding bicycles" I'd like to know some concrete places where metacognition should be discouraged in mathematics education. Wittgenstein, for example, may have argued that we acquire the ability to do mathematics by implicitly learning what not to think about or reach for in a very unconscious way akin to natural language use. Even if one views Wittgenstein's views on mathematical practice as fringe, one might note that the typical (or perhaps I should say "ideal" in the sense of Reuben and Hersh) mathematician's aversion to philosophizing about mathematics reflects a general attitude against metacognition in mathematical practice…perhaps fearing one's never getting down to business because of being lured by the sirens of philosophy. Here, though I would like more concrete criticisms in the everyday practice of teaching.

Being an odd mathematician in terms of my attitude toward philosophy, I would love it if metacognition were universally good for students, as then we could just have them write in order to build in some continuity of concepts. I pause, though, when presented with a formalist critique akin to a Wittgenstein-like position above.

Jon Bannon
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    Metacognition can be faux-destructive when it inhibits movement toward goals... by seeing/declaring those goals as silly or stupid. (Teenagers routinely do this by implicity imposing the criterion of whether a given thing is connected to sex, drugs, or rock-'n'-roll, for example.) This can indeed create awkwardnesses in routine, cookbook math courses, for the obvious reasons... similarly in some of the "requirements" in the beginning of grad school. But, in fact, I claim "metacognition" is (eventually) mathematical methodology... self-management? Very mundane, after all? – paul garrett Apr 29 '16 at 22:19
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    I perform metacognition all the time, and I see many piers getting some intuitive/philosophical advice on how to "think". I think metacognition is fine for higher-level math students (students above their grade level) but possibly a bad thing for students at or below their grade level. Those students I will often find more doubtful of their abilities. – Simply Beautiful Art May 03 '16 at 00:42
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    It is certainly difficult to find counter-examples in literature. However, meta-cognitive strategies are well-known to have an effect size of 0.5 or higher (0.72 for "reciprocal teaching" according to John Hattie). This is well within the threshold of "must-do" teaching methods - i.e. you will see more positive outcomes if you look for ways to apply meta-cognition strategies rather than looking for places that it shouldn't be applied. – Marian Minar Jun 22 '16 at 14:58
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    Perhaps related or at least interesting: https://flavorsandseasons.wordpress.com/about/, the Flavors and Seasons project about the experential aspects of doing mathematics. – J W Aug 11 '16 at 19:27
  • Possibly relevant post: https://matheducators.stackexchange.com/questions/7745/books-on-meta-cognition-that-would-be-relevant-for-those-involved-in-mathematics – kcrisman Mar 11 '19 at 13:57
  • Two remarks: (1) in this Britsh mega study, metacognition is in the second place as an effective strategy of effective learning: https://educationendowmentfoundation.org.uk/evidence-summaries/teaching-learning-toolkit/; (2) Singapore that excels in PISA Math Tests includes metacognition as one of its core ideas. – Humberto José Bortolossi May 13 '20 at 10:57
  • Your link is no longer always going to the essay. Free GoogleBooks doesn't always show the same snippet. I did try Wiki, but it was pretty long and I wasn't clear what the specific ed buzz slanted meaning was supposed to be. – guest philosopher Apr 01 '23 at 00:53
  • Also, I would encourage to look at some people like Greg Ashman and John Stillwell who argue that a lot of problem solving is domain specific. And that "general problem solving" is a skill we all have (maybe even just evolutionarily within our brain architecture) but that it is not very strong. And that improvements in "problem solving skill" are often domain specific, not general and transferrable. The upshot being that you don't want to train for better problem solving overall, but better calculus problem solving. At least read their arguments, since you wanted the other side. – guest philosopher Apr 01 '23 at 00:56

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First, metacognition may sometimes actively interfere with task performance. Second, the costs of engaging in metacognitive strategies may under certain circumstances outweigh its benefits. Third, metacognitive judgments or feelings involving a negative self-evaluation may detract from psychological well-being.

binish shahzadi
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    I think these are very valid points! Can you find some literature to back them up? Welcome to the site, and thanks for the answer! I think one place one might find mention of this is in the writings of Wittgenstein to the philosophy of mathematics. According to him, we mostly learn what not to think about when learning math. – Jon Bannon Dec 31 '21 at 17:22