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I am curious about the experiences of people who had no formal mathematical training in their youth, but learned mathematics as adults.

I imagine that there are a fair number of people in the US who were homeschooled in such a way that mathematics was almost entirely omitted. There is also the phenomenon of "Sudbury schools", in which students are given complete freedom to choose how they spend their time. Many of these students could experience an education which is completely free of instruction in mathematics.

I am curious about how people with this background adapt to mathematics as adults. How long does it take them to "catch up" to their peers who were trained in the normal system? Are there any long term mathematical disadvantages or advantages in this population?

I would like to be made aware of research studies tackling these kinds of questions. If they do not exist, I am serious about trying to undertake such research.

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    $\begingroup$ Peter Gray (psychology, Boston College) has written about about Sudbury schools. Many of the students get into college, so they must do OK on math somehow. Homeschooling here in GA requires that mathematics be taught. Accredited private schools probably have to teach it, too, even if they avoid that invention of the Devil, Cantor’s set theory. I think the first step is to determine whether there are in fact a fair number of people in the US who had no formal mathematical training. $\endgroup$ – user615 Dec 15 '20 at 20:42
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    $\begingroup$ Where have you, ahem, researched to try to find prior research? $\endgroup$ – shoover Dec 16 '20 at 2:38
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    $\begingroup$ I have a few chapters by unschoolers in my book, Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers. naturalmath.com/playingwithmath (pdf version available online, name your own price.) $\endgroup$ – Sue VanHattum Dec 16 '20 at 4:08
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    $\begingroup$ @SueVanHattum Very interesting! I read just the one section written by Lavinia Karl. It doesn't seem like a lack of formal mathematics instruction held her back much! This is exactly the kind of thing I would like to study. $\endgroup$ – Steven Gubkin Dec 16 '20 at 16:57

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