10

I don't know of research that answers this question directly, but I'm going to guess the answer is no, it wouldn't help, based on the following reasoning. First, people tend to learn math less well when superfluous visual richness is added. I think adding color to numbers counts as superfluous visual richness. Brown, M. C., McNeil, N. M., & Glenberg, A. ...


9

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 ...


9

Well that looks like the behavior of any person with a strong passion and focus for his work. There are plenty of these around! I guess it would be more common in any field of work were people already have dedicated a significant part of their life to it, and where it is almost a prerequisite. Being a mathematician selects and cultivates people able to ...


8

There's a very small percent of people who enjoy the adrenaline of mental exhaustion. While that signals most people to stop, there are people who will continue exhausting themselves. This isn't physiologically healthy. You need to recognize when you're worn out and rest. Don't get hyper-focused on your problem.


6

Difficulty of an item could be operationalised in a variety of ways: probability of getting the item correct, amount of time required to complete, amount of resources required to complete, etc. Item response theory perspective That said, in the item response theory literature item difficulty is typically synonymous with a parameter related to probability ...


6

I would say it is highly unlikely. The report that you reference is the savant Daniel Tammet who has performed many impressive mental feats, including holding the European record for most recited digits of pi. He has been popularized in the media in such documentaries as "Brain Man". He claims that he is able to accomplish such mathematical feats ...


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 ...


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 ...


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

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

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

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 ...


3

I imagine this question is tricky for students for a several reasons. Question wording: The question may suggest to the student that it is possible to differentiate $x!$. Or they may assume from the wording that some meaning is meant where it is possible to differentiate. For example, alternatively, you could ask a set of questions, one for each functions, ...


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 ...


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

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

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

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

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 ...


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