I have heard a number of reports that some mathematical savants associate particular colors with numbers. It got me wondering, if colors are associated with numbers during mathematical teaching, would this improve ability?

For example, if every time I showed my child the number 2, it was colored red, and every time I showed her 3, it was blue, and so on, would she learn arithmatical skills like addition, subtraction, multiplication, and division faster?

Further, would it matter which colors were associated with which numbers? Should 5 be purple?


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. M. (2009). Using concreteness in education: Real problems, potential solutions. Child Development Perspectives, 3(3), 160–164.

Mayer, R. E., Sims, V., & Tajika, H. (1995). A Comparison of How Textbooks Teach Mathematical Problem Solving in Japan and the United States. American Educational Research Journal, 32(2), 443–460.

Second, in general, associating something you want people to recall with a larger number of cues is going to help recall. (Sorry I don't know a citation for this off the top of my head, but I think it's a general principle of information theory.) In this case, the colors and the numerals are both cues for numbers, which should lead to better recall than if you only had the numerals. However, you are looking at learning arithmetic and not learning the number sequence.

Learning numbers MIGHT go faster with this additional cue. However, I'd be concerned whether there might be some negative impact on ability to use numerals once the color cue is removed, as it inevitably will be.

Presenting numbers together with analogue representations of magnitude does aid in learning arithmetic facts:

Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031.

However, analogue representations of magnitude are a cue that's relevant to the actual meaning of the numbers, while colors are not. I doubt colors would deliver this particular benefit.

With all that said, I haven't considered motivational issues. If children are motivated by brightly colored number blocks, then I'd say go ahead and use them. I doubt that the cognitive effects would be strong one way or the other, so even if negative, they'd probably be outweighed by any motivational benefits.

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  • $\begingroup$ I know that synesthesiacs perform worse in math, but I'm too lazy to look up the research. $\endgroup$ – Indolering Mar 11 '13 at 1:13

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 his synesthesia, which allows him to "see" different numbers as different shapes, sizes, and color. It is worth noting that his ability has also been greeted with skepticism both in pop culture (such as in the best seller Moonwalking with Einstein) and by synesthesia researchers who have studied him personally (Azoulai et al., 2005).

Tammet claims that he sees numbers as shapes, and that to multiply two numbers he sees the shapes "merge" in his head. It's not really clear how you could train someone to do this, if it is possible at all. It is possible that this is just an epiphenomenon, and does not actually help Tammet solve problems.

In fact, associating numbers with colors might actually hurt your performance. Mills et al. (2009) showed that a synesthete performed slower when the numbers in an addition problem were not congruent with her internal perception of them. Thus even if you were able to perform math problems faster, it may only apply when the numbers are congruent with the color-number pairing that you trained on. In the real world, you are most likely to see all numbers in only a single color.

Azoulai, S., Hubbard, E., & Ramachandran, V. S. (2005). Does synesthesia contribute to mathematical savant skills. Journal of cognitive neuroscience, 69. PDF

Mills, C. B., Metzger, S. R., Foster, C. A., Valentine-Gresko, M. N., & Ricketts, S. (2009). Development of color-grapheme synesthesia and its effect on mathematical operations. Perception, 38(4), 591. PDF

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  • 1
    $\begingroup$ +1 Do you think it would be possible to test one's personal internal perception of numbers by doing addition problems and analyzing the performance? $\endgroup$ – draks ... Mar 30 '13 at 23:13
  • $\begingroup$ @draks... yes, i suspect so-- that is very similar to what Mills et al. (2009) is doing. There are also several standardized methods for diagnosing synesthesia though, so if that's your goal I would start there. I don't recall exactly what those tests ask offhand... $\endgroup$ – Jeff Mar 30 '13 at 23:30

Trying to calculate with a sequence of colours is not any easier than calculating with a sequence of digits.

There are alternative explanations for the high prevalence of synesthesia in mathematical savants.

For example:

  1. Synesthesia is common in autism.
  2. Synesthesia is associated with increases in white matter connectivity which might contribute to savant abilities.
  3. Synesthesia is associated with more vivid mental imagery, which could be used to visualize the sequence of steps in a calculation.

Although there is an association between grapheme colour synesthesia and enhanced memory ability, this association is also present for stimuli which do not trigger synesthesia. Therefore we cannot conclude that associating digits with colours will increase the number of digits that can be manipulated in working memory.

On the other hand, some savants have more elaborate forms of synesthesia in which a two or three digit number has its own associations instead of being a combination of the associations for its constituent digits. In this case it is possible for the associations to directly benefit arithmetical ability by acting as a chunking strategy.

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Some very good answers, and i note the important remark of @indolering

I know that synesthesiacs perform worse in math, but I'm too lazy to look up the research. – Indolering Mar 11 '13 at 1:13

However, particularly if we generalize the question slightly to symbols rather than just numbers, it would be bold to assert that aside from motivational effects there is never any pedagogic benefit to be obtained from the use of colouring. We should not neglect the role played by selective attention in following an intricate symbolic argument. (training of visual selective attention is of especial importance in studying complex geometrical figures, and has to some extent been used, i think - but this is well beyond the scope of OP's question).

Also we should remember individual differences. Most trivially, if color were found to be of benefit in learning some mathematical idea or result, one would expect this benefit to be reduced for individuals with some degree of achromatopsia.

One should finally note that whilst the content of mathematics is objective, our conceptualizations depend quite strongly on the development of notation. Many typographical conventions are already in existence which certainly enhance learning of abstract concepts in mathematics.

The unfortunate truth of the matter is that to date the teaching of elementary maths is of a uniformly low quality, which there are reasons for, perhaps. Not least the domination of education theory by an arithmophobic intelligentsia to whom self-esteem is more important than the needs of both children and the society they grow up in.


@caseyr5471 here included the following relevant quotation (italicized) from this paper

The parietal area and prefrontal cortex from the neocortex are the source of ones ability to perform algebra and most other logic and analytic intensive tasks.

In a brain imaging study of children learning algebra, it is shown that the same regions are active in children solving equations as are active in experienced adults solving equations. As with adults, practice in symbol manipulation produces a reduced activation in prefrontal cortex area. However, unlike adults, practice seems also to produce a decrease in a parietal area that is holding an image of the equation. This finding suggests that adolescents' brain responses are more plastic and change more with practice. These results are integrated in a cognitive model that predicts both the behavioral and brain imaging results.

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