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18

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 ...


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

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

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., & ...


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

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

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

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 ...


4

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

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 ...


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

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 ...


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

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

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

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

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

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 ...


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

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 ...


1

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.


1

Learning is a very complex process, do not expect to find precise answers like “5 exercises are required to learn a new subject”. There are many factors that affect learning, just to name a few: Your existing knowledge. Your engagement with the subject. How you learn. Deep Vs shallow processing. The complexity of the subject. Your personal characteristics ...


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 ...



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