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My wife teaches math at a community college level, meaning she often needs to teach students who are paralyzed by fear of fractions (or worse, negative numbers

by j2kun 10y ago

My wife teaches math at a community college level, meaning she often needs to teach students who are paralyzed by fear of fractions (or worse, negative numbers). Many of her students are also adults. She tells me things like "If I ask one of these adult students a question involving negative numbers, and I phrase it in terms of money and debt, they answer it immediately. If I ask them using just numbers, they have no clue." These students do not know how to take a concept they've used their entire lives to balance their checkbooks, and abstract it beyond money. I would conjecture that in most cases of "activities that stimulate your brain", the key to generalization requires another skill: being able to abstract a skill you have learned from one situation, and then specialize it to another situation. And this skill needs practicing. I also conjecture that a small fraction of the population actively does this, and this could explain why the results aren't statistically significant. E.g. meditation actively encourages introspection and generalized mindfulness in any situation, whereas crosswords and Chess are played for their own sake.

gizmo686 10y ago
>If I ask one of these adult students a question involving negative numbers, and I phrase it in terms of money and debt, they answer it immediately. If I ask them using just numbers, they have no clue. This doesn't just happen with students who are bad at math. If you sit in on most introductory advanced math classes (eg. introduction to abstract algebra), you will see the same thing: students imminently understand what is being asked when it is phrased in terms of something concrete, but have more difficulty answering even basic questions when they are asked in the abstract. The main difference, in my experience, is that in advanced classes, a "concrete" example would be something like the set of 2x2 real valued matrixes; so non mathamaticians do not recognize it as being simple. There is also the difference that experienced mathematicians have learned that "simple" things will become simple with enough exposure; and have honed the ability brute force their way through while they get that exposure.
CoryG89 10y ago
So meditation is actively improving your "introspection and generalized mindfulness", but people doing crosswords and playing Chess are just being silly and wasting time? I was with you until I read that. Maybe I just don't buy into the whole meditation thing, but from where I stand, at least Chess seems like it actively improves/encourages/practices strategic thinking skills.
- j2kun 10y ago
  I don't meditate, actually, I was just including that in re some other thread that was mentioning it. I'm saying that yes, Chess does improve strategic thinking skills, but it probably won't help you be more strategic in other situations unless you're good at the "skill of skill transfer."
- ivm 10y ago
  Playing chess builds up your strategic thinking in chess and it's barely transferable to other activities, even to other games. Meditation is about watching your mind and training to recognize your subtle thoughts and emotions. It's universal and can be applied to any activity in one's life because everything is being processed inside our minds.
mikevm 10y ago
I highly recommend watching this: https://www.ted.com/talks/james_flynn_why_our_iq_levels_are_higher_than_our_grandparents?language=en https://www.ted.com/talks/james_flynn_why_our_iq_levels_are_... Flynn believes that the rising IQ scores over the generations are due to us dealing better with abstractions and using logic on these abstractions.
deleted 10y ago
[deleted]
tpeo 10y ago
>"If I ask one of these adult students a question involving negative numbers, and I phrase it in terms of money and debt, they answer it immediately. If I ask them using just numbers, they have no clue." There's an even more extreme example with street kids in Brazil who had de facto knowledge of mathematics (they worked as peddlers) but weren't able to do the same thing they did during daily life in a school setting. I wouldn't say that concept transfer is a skill, however. The two things that come to my mind when I think of the issue of transfer are: the feeling of a student being hung up on a particular problem, anxiously waiting for a solution to come up to his mind; people who seemed to try to tackle lots of different problems from lots of different angles (Wheeler, Feynman). So it seems to me to be more constrained by openess to experience on one hand (the willingness to try and fail) and creativity (willingness to look for and propose solutions) on the other, both of which are more like inclinations than skills. https://www.maa.org/external_archive/devlin/devlin_05_05.html https://www.maa.org/external_archive/devlin/devlin_05_05.htm...
jostylr 10y ago
My belief is that humans are pattern matchers, even in the context of abstraction or logical thinking. The pattern of skill transfer is the experience of transferring skills. That opens the mind to the pattern of colliding different learned patterns into situations that seem not relevant just as patterning the logic leads to being able to develop logical proofs because the pattern of doing logic is being recognized. For example, proving an identity looks like solving an equation. So that is why many students naturally put down a proof that looks like solving an equation. And it can be a proof if the observation is that for each x, the statement holds as all steps are observable. Students rarely make that last step, however, because the pattern they are following breaks down: 1=1 has no expression of x. They kind of just move on at that point. By contrast, someone trained in mathematics would most likely prove an identity by taking one side and transforming it into the other side as they have the experience of that flow of proofs and the goal there is clear: one stops with the right-hand side. It is not logical thinking, but logical pattern application. Transfer skills are similarly learned. We all have them, after all. I have never met anyone bothered by counting markers being a different skill than counting pebbles. But that is a skill transfer too. It just happens at such a young age and is so ubiquitous that we don't even notice it. I would be surprised if meditation helps with any of this. It helps with many other things, such as being more aware of events, particularly emotional states, as that is the pattern being developed, but it is hard to imagine it will help bridge the gap of checkbook balancing to general numbers. What one needs is the experience of numbers in multiple contexts. The pattern in the patterns is the path to abstraction and it no doubt takes a number of patterns to get there. And learning the different kinds of abstractions requires different kinds of patterns.

by j2kun 10y ago

gizmo686 10y ago

>If I ask one of these adult students a question involving negative numbers, and I phrase it in terms of money and debt, they answer it immediately. If I ask them using just numbers, they have no clue. This doesn't just happen with students who are bad at math. If you sit in on most introductory advanced math classes (eg. introduction to abstract algebra), you will see the same thing: students imminently understand what is being asked when it is phrased in terms of something concrete, but have more difficulty answering even basic questions when they are asked in the abstract. The main difference, in my experience, is that in advanced classes, a "concrete" example would be something like the set of 2x2 real valued matrixes; so non mathamaticians do not recognize it as being simple. There is also the difference that experienced mathematicians have learned that "simple" things will become simple with enough exposure; and have honed the ability brute force their way through while they get that exposure.

CoryG89 10y ago

So meditation is actively improving your "introspection and generalized mindfulness", but people doing crosswords and playing Chess are just being silly and wasting time? I was with you until I read that. Maybe I just don't buy into the whole meditation thing, but from where I stand, at least Chess seems like it actively improves/encourages/practices strategic thinking skills.

j2kun 10y ago
I don't meditate, actually, I was just including that in re some other thread that was mentioning it. I'm saying that yes, Chess does improve strategic thinking skills, but it probably won't help you be more strategic in other situations unless you're good at the "skill of skill transfer."
ivm 10y ago
Playing chess builds up your strategic thinking in chess and it's barely transferable to other activities, even to other games. Meditation is about watching your mind and training to recognize your subtle thoughts and emotions. It's universal and can be applied to any activity in one's life because everything is being processed inside our minds.

mikevm 10y ago

I highly recommend watching this: https://www.ted.com/talks/james_flynn_why_our_iq_levels_are_higher_than_our_grandparents?language=en https://www.ted.com/talks/james_flynn_why_our_iq_levels_are_... Flynn believes that the rising IQ scores over the generations are due to us dealing better with abstractions and using logic on these abstractions.

deleted 10y ago

[deleted]

tpeo 10y ago

>"If I ask one of these adult students a question involving negative numbers, and I phrase it in terms of money and debt, they answer it immediately. If I ask them using just numbers, they have no clue." There's an even more extreme example with street kids in Brazil who had de facto knowledge of mathematics (they worked as peddlers) but weren't able to do the same thing they did during daily life in a school setting. I wouldn't say that concept transfer is a skill, however. The two things that come to my mind when I think of the issue of transfer are: the feeling of a student being hung up on a particular problem, anxiously waiting for a solution to come up to his mind; people who seemed to try to tackle lots of different problems from lots of different angles (Wheeler, Feynman). So it seems to me to be more constrained by openess to experience on one hand (the willingness to try and fail) and creativity (willingness to look for and propose solutions) on the other, both of which are more like inclinations than skills. https://www.maa.org/external_archive/devlin/devlin_05_05.html https://www.maa.org/external_archive/devlin/devlin_05_05.htm...

jostylr 10y ago

My belief is that humans are pattern matchers, even in the context of abstraction or logical thinking. The pattern of skill transfer is the experience of transferring skills. That opens the mind to the pattern of colliding different learned patterns into situations that seem not relevant just as patterning the logic leads to being able to develop logical proofs because the pattern of doing logic is being recognized. For example, proving an identity looks like solving an equation. So that is why many students naturally put down a proof that looks like solving an equation. And it can be a proof if the observation is that for each x, the statement holds as all steps are observable. Students rarely make that last step, however, because the pattern they are following breaks down: 1=1 has no expression of x. They kind of just move on at that point. By contrast, someone trained in mathematics would most likely prove an identity by taking one side and transforming it into the other side as they have the experience of that flow of proofs and the goal there is clear: one stops with the right-hand side. It is not logical thinking, but logical pattern application. Transfer skills are similarly learned. We all have them, after all. I have never met anyone bothered by counting markers being a different skill than counting pebbles. But that is a skill transfer too. It just happens at such a young age and is so ubiquitous that we don't even notice it. I would be surprised if meditation helps with any of this. It helps with many other things, such as being more aware of events, particularly emotional states, as that is the pattern being developed, but it is hard to imagine it will help bridge the gap of checkbook balancing to general numbers. What one needs is the experience of numbers in multiple contexts. The pattern in the patterns is the path to abstraction and it no doubt takes a number of patterns to get there. And learning the different kinds of abstractions requires different kinds of patterns.