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There exist a large number of reasons why "mathematics is difficult". If one exclude "subjective reasons" such as:

"math anxiety, math fear,..."

and education factors as:

"inadapted math programs, books, teaching level, ..."

and focus only on mathematical cognitive process as:

  • difficulties in the memorization process.

  • difficulties linked to the misunderstanding of terminology.

What other reasons (in one line please) can we give?

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    $\begingroup$ I've found that a very big reason, at the university level at least, is that students underestimate the time commitment for study that is needed to develop mathematical expertise. This is similar to the time commitment needed to develop language fluency. Also, students are not always familiar with what it means to understand mathematics. E.g. students often think plugging things into formulas accurately is sufficient for understanding. $\endgroup$ – Jon Bannon Jan 28 '17 at 14:29
  • $\begingroup$ I'm not sure I understand. Wouldn't "Inability to link concepts" broadly apply to many areas of study? It is difficult to pin down the idea of "cognitive process", isn't it? Someone more qualified than I am would need to answer this... $\endgroup$ – Jon Bannon Jan 28 '17 at 15:16
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    $\begingroup$ There is less to memorize in math than in most fields, so that shouldn't top your list, or even be on your list. I think I disagree with your second item also. $\endgroup$ – Sue VanHattum Jan 28 '17 at 15:50
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    $\begingroup$ To build on Sue's comment, "Thinking that math involves mostly memorization" could itself be at the top of the list of difficulties. (Professorial colleague of mine: "I went into math because it had the least memorization of any field I could find."). $\endgroup$ – Daniel R. Collins Jan 28 '17 at 17:16
  • $\begingroup$ According to this Working Memory and Mathematics article, "Working memory refers to a mental workspace, involved in controlling, regulating, and actively maintaining relevant information to accomplish complex cognitive tasks (e.g. mathematical processing)". So, it's difficult to believe that memory play a minor role in the construction of mathematical reasoning. $\endgroup$ – sapienz Mar 3 '17 at 6:54
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difficulty in understanding the interrelation of mathematical constructs.

or

difficulty of fitting a mathematical problem on just one line

or

difficulty in compressing the problem to a communicable slogan

etc.

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Gaps in basic knowledge which make progressing difficult

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Difficulty to keep the thinking abstract e.g. using symbols instead of "real" world objects

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