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I assume that the group that spends 100% of their time studying real analysis and 0% of their time doing n-back training will do best in any subsequent real analysis course. Cognitive skill acquisition does not generalise all that much (for a review see VanLehn, 1996). Transfer is often limited. I'm sceptical of any claims that short term training can lead ...


5

Overall, based on my limited research it appears there is no evidence that people who are more logical are more likely to experience depression. There is a theory that people who see the world more accurately (of which rationality would be a component) are more likely to become depressed. It is called depressive realism {1}. However, the theory doesn't seem ...


5

There is a clear association between musical ability and mathematical ability, perhaps best recognised in savantism in people with developmental disabilities. There are limited domains in which savantism appears to occur, including mathematical calculations, reproducing music instantly, recalling specific facts, and perfect-perspective drawing. There are a ...


4

If you define mental disorder as any behavior not applying to (more or less arbitrary) social norms, then yes, the activity you describe would probably be considered mental disorder. However, the same would apply for example to: homosexualism most hobbies asceticism and religious devotion playing and listening to music The last may seem odd, but Plato have ...


4

Dimensions of Human Behavior: The Changing Life Course By Elizabeth D. Hutchison Chapter Language skills Hoff, E. (2006). How social contexts support and shape language development. Developmental Review, 26(1), 55-88.


3

It is generally understood that girls develop a small to moderate deficit in math abilities, compared to boys, over the course of schooling, as measured by mean school grades or test scores (Hyde & Linn, 2006 give a number of .08 standard deviations in favor of men for mathematical problem solving on average, a larger effect favoring elementary school ...


3

In short, algebra and geometry are different type of cognitive abilities. Geometry is more spatial and algebra more verbal-logic. Kestenbaum, C., Williams, T. D., Handbook of Clinical Assessment of Children and Adolescents, NYU Press, 1988.


3

How do the rationality and logical thought processes those with and without ADHD compare? Please explain the source of this difference. Is the difference thought to be caused by dopamine, serotonin or norepinephrine or some other neurological explanation. ADHD is typically associated with a reduction in dopamine and/or norepinephrine. Though the two ...


3

Let me begin by saying that the answer is nowhere near as simple as you or I would like it to be. There are several reasons for this, but the main reason is that there are myriad ways that students can struggle through the material. I became interested in this subject when I was a graduate teaching assistant in the Industrial Engineering program at Iowa ...


2

I have an anecdotal answer with regard to learning Physics. I sat in on a colloquium where a Physics professor discussed his experience with a course that was taught completely through experimentation. Students had to derive their learning of Physics completely through semi-guided experiments, and no lecture. In the beginning of the course, the professor ...


2

Robert Bjork calls this desirable difficulties. That is, students seems to learn best when they are required to encode and retrieve information. Some examples of desirable difficulties include: testing, spacing/interleaving, generating information, changing studying environments, etc. In the long run, these seem to promote long term learning.


2

I'm one of those people who was good at Geometry, but bad at Algebra. Eventually I caught up and was good at both. The question why did bother me for a long time, and it's good to see that I'm not alone. It seems to me that middle and high school algebra is mostly about memorization. Typical questions have only one solution. You have to remember how to ...


2

Yes, you can train your memory to be better at certain tasks, such as remembering numbers. For example Ericcson et. al. (1980) describe a university student who practiced memorizing numbers several times per week for twenty months and could then memorize and recall more than 70 digits reliably. I would not recommend such however if you are looking for ...


2

Some master mathematicians have written on the process of mathematical invention and on some methods of plausible reasoning in mathematics. Here are some references: Jacques Hadamard. An Essay on the Psychology of Invention in the Mathematical Field. George Polya. Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics. Princeton ...


2

I think it is important here to be clear about what John is really capable of doing. If all he is able to do is manipulate the axioms of S correctly, this actually does not get him very far, for at least two reasons. (This is also why theorem proving computer programs have significant limitations.) 1) Suppose we give John a specific theorem P of S and ask ...


2

Short answer It has been argued that infants are born with an ability to recognize, distinguish and even operate on small numbers. Background Speaking from experience (n = 2 :-) toddlers learn to count, first of all. That means they know 2 comes after 1, 3 after 2 etc. In conjunction, we read them stories, like the very hungry caterpillar that ...


2

Intelignece is a combination of nature and nurture, like most human attributes. The exact percentage is not possible to measure, at least with todays knowledge. Extract from the article by Neill, J.T. (2004). "Nature vs Nurture in Intelligence" : In the overfocus on nature vs. nurture issues, the attempts to estimate the relative contribution rests on ...


2

Your hypothesis is not quite true. Even if we restrict discussions to numbers only, conciseness (the term used in literature for your "compactness") is not the greatest for the Western system; the Georgian number system is superior in this respect. I'm reproducing the following table from Chrisomalis' book (p. 391). The Roman system, which is essentially ...


2

The idea that long term memory cannot be ever changes is absolutely wrong, for sure some thing that is learnt and practice for a long time while being a child has a difficulty to change after while, but it is not impossible. About learning you have to know that we have different kind of learning disabilities. Specific learning disorder is a developmental ...


2

No. I can't seem to find a specific study into professional mathematicians or graduate students so far, the studies always seem to group the occupations together. However, Baron-Cohen's team has done an impressive national survey (Ruzich et al., 2015) and recruited nearly half a million people through a UK TV show. They managed to get over 450,394 survey ...


2

This is my first answer here, so bear with me. Suggestions on how to make this answer better are welcome. There are several studies that indicate that men are more interested in things and women are more interested in people. https://pubmed.ncbi.nlm.nih.gov/19883140/ https://www.frontiersin.org/articles/10.3389/fpsyg.2015.00189/full In Scandinavia where ...


1

I asked this question back when I was building a neural model of progression through counting strategies [1]. The quotes in this answer are taken from that publication. Psychologically, there is some evidence of addition speedup being a result of memorisation. Typically, children progress through various strategies before finally memorizing the results of ...


1

Firstly lets define criteria for what difficult learning material is. My interpretation of the matter states that the task of developing mastery or competency in understanding and applying difficult content: Takes an increased amount of time or Demands increased cognitive effort It's relevant to keep in mind The 2 systems that occur in the brain The ...


1

Part of it has to do with the ability to construct a model of reality. Every developer can relate to that. Visible, concrete things are easy to deconstruct in pragmatic terms. But once you get into abstract concepts, it gets harder and harder to bind it with your existing view of the world. Some concepts are also very difficult to grasp if you can't connect ...


1

This website http://www.aboutdyscalculia.org/causes.html provides answers to some of the questions you posed, although I am not sure it is the most up to date information. I would always advise one to do research on more scientific grounds. From my perspective, dyslexia has also been more studied than dyscalculia as its impact in academics seem more easily ...


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