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As many of you are aware there is a critical period in the visual system. There is also one in the auditory system with the learning of perfect pitch. After working with GED adult learners, it has come to my attention that a large subset of the students difficulty can be traced back to a difficulty learning multiplication tables. My experience with these students is that encouraging them to learn multiplication tables should be avoided, and instead to focus on them using calculators.

From what I've read, the students that fall into this category are said to have dyscalculia. What I am wondering is, that of the students that fall into this category, do a subset of them have the ability to learn multiplication tables initially, but due to them not doing so and the critical period closing, forever now have an inability to learn them as adults? Does anyone know of any research that has been done in this area and can anyone think of a way this hypothesis could be tested?

It came to mind that we could see how well that adults that know their multiplication tables could extend them, but as I feel it is likely the case that those adults could in fact often extend their tables, the hypothesis really then would be that the critical period involves the use of a particular system in the brain, that if not used and expanded on during the critical period becomes dysfunctional and is unable to be corrected post that period.

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  • $\begingroup$ Would looking at twins be able to resolve this question? $\endgroup$ May 13 at 19:09

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A distinction can be made between "strong" and "weak" critical periods, see e.g. https://en.wikipedia.org/wiki/Critical_period

Critical periods are a consequence of neurodevelopment. At some stages of neurodevelopment, there are specific events that occur that will never occur again because of specific physical changes.

For most things, though, neuroplasticity is possible indefinitely, it just may take more time and effort. The adage "you can't teach an old dog a new trick" is not an absolute; children and puppies may learn more quickly but that doesn't mean adults cannot learn. Maybe a familiar analogy would be if you have a lot of things to plug into a power strip, behind your desk or around your TV perhaps. The first time you set things up, it's pretty easy to keep things orderly: you have a bunch of receptacles and plugs and can, say, start from left to right and fill them all in. But, over time, as your devices change and you replace old ones with new, things get to be more of a tangled mess. The things that are already connected create a barrier to making those new connections.

I do not know about multiplication tables specifically, but that's something that seems extremely unlikely to have any "strong" critical period. Multiplication tables are "brand new" on an evolutionary timescale, they're not something humans are wired to understand specifically unlike, say, binocular vision.

I think with your adult learners, there are a couple things going on. One: selection bias. You're working specifically with people who struggled with this when they were younger, too. Two: they've had a lot of experience coping in the world since then, and have learned their own ways to deal with numbers that are not the typical way kids are taught math. Any heuristics that have been useful to them are going to be the first things that their brain tries to do; you're asking them to suppress what they've learned and replace it with something new, which is harder than learning from scratch.

You might want to step back and figure out, pedagogically, what skills you are actually trying to teach, and question whether memorization of multiplication tables actually has any value for those pedagogical goals.

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