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17

Sounds like a form of Synesthesia, in particular it sounds like Number Form Synesthesia mixed with Grapheme-color Synesthesia: A number form is a mental map of numbers, which automatically and involuntarily appears whenever someone who experiences number-forms thinks of numbers. Number forms were first documented and named by Francis Galton in "The ...


8

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 ...


8

The term seems to come from David C. Geary's 1995 article. Here's the abstract with full-text link below: An evolution-based framework for understanding biological and cultural influences on children's cognitive and academic development is presented. The utility of this framework is illustrated within the mathematical domain and serves as a ...


8

I have number Synesthesia, actually, and numbers do indeed appear as a specific pattern inside my head -- I have never not seen numbers this way, and have even drawn my number map for my own edification and to show people what I'm talking about when I try and explain my synaesthesia to them. Numbers are not individual digits to me; they are one huge ...


8

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 ...


6

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.


5

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 ...


3

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 ...


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 ...


3

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 because of ...


3

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., & ...


2

There is a huge amount of research on this topic, particularly in developmental psychology. Siegler: As @Joel has noted, Robert S. Siegler provides a great entry point into this literature (see his list of selected publications with PDFs). He has done a lot of research on the strategies that children use to solve mathematical problems. His research includes ...


2

If you pose the question only to students who have a perfect knowledge of high school calculus, without any knowledge gaps, then they should all give the correct answer. The "problem" is, that you can graduate from high school without having understood all the details about differentiation. Most students don't finish high school with the best mark in maths, ...


2

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

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

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 ...


1

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.


1

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 ...


1

Retaining a large number Can you hold the number 7859385 in your head for an extended period without the image of the number becoming distorted at any point? Long term memory of a single long number: Obviously a large proportion of people remember a few phone numbers that are at least as long as the number you mention. So for long term recall there are ...



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