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This is a concise description of what happens if I attempt any problem solving task with numbers: [1] I never work out where to start. [2] If by some miracle [and I'm talking Moses parting the waves here] I work out where to start, then there will be some point where I won't work out which area of maths to use.

I have found no answer to [1] or [2]. I did maths at university and in one unit I passed with 55%; I got 90% for the bookwork and almost nothing for the problem solving. In one problem solving task I actually got zero; I never worked out where to start. That was following bad marks at high school maths because of the problem solving component.

I can problem solve with things that are not numbers. I run Linux and have nobody else to help me out. I sort out problems with scanners, printers, bootloaders and many other aspects. I also get scores off the charts for the blocks component of the IQ test. I have always been reluctant to get any help with maths problem solving. Then I got the response from my family "it's OK if you're thick". Then I would scream back "I am not thick". That's one megaton H bomb - maths is so bound up in "being thick" if you can't do it.

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    $\begingroup$ The title is incredibly broad, but the question body seems mostly like just griping about your personal situation. If you can clarify exactly what the question is, that might help? $\endgroup$ – Daniel R. Collins Nov 30 '19 at 16:58
  • $\begingroup$ Have you read How to Solve It by George Pólya or similar books? $\endgroup$ – Rusty Core Dec 1 '19 at 4:35
  • $\begingroup$ yes, they do not help. $\endgroup$ – Snack_Food_Termite Dec 1 '19 at 9:23
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You might want to learn more about a learning disorder called dyscalculia. Students (or people in general), who are diagnosed with this learning disorder, are not "thick", nor "stupid". An analogy you might be more familiar with is dyslexia, in which students struggle with reading and writing, but are in no way inherently "thick", nor "stupid".

You seem to be quite capable, but struggle with numbers and calculations. Over time you may have developed anxiety in relation to seeing numbers involved in any sort of math. I'd suggest you read more about dycalculia, to see whether the description "fits" with your experience, or not. If it does, there are professionals who can work with you to help you demonstrate your potential. There are online support groups, and helpful information on the internet, as well.

Just don't equate "mathematical problem solving skills" with "numerical computation skills".

In any case, it sounds like you are fully capable of mathematical problem solving.

Added: Reading through your question once more, I note your statement, " I have always been reluctant to get any help with maths problem solving." You and your conviction that you can't solve math problems, and your reluctance to get any help, are your biggest obstacles to further progress in math problem solving. There is absolutely no shame in seeking assistance. And your family is not helping you move forward.

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    $\begingroup$ From the question, it sounds as though OP has trouble with figuring out what operations are needed to break down a word problem, rather than the calculations themselves. OP says "I got 90% for the bookwork" which I take to mean equation solving. $\endgroup$ – shoover Dec 1 '19 at 20:31
  • $\begingroup$ @shoover the OP also states "I can problem solve with things that are not numbers [emphasis mine]." $\endgroup$ – amWhy Dec 1 '19 at 20:34
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    $\begingroup$ Excellent answer. Seeking help is a natural part of getting better at math, and one should derive absolutely no shame from doing so. In fact, one should be quite proud if they've attempted a problem, couldn't solve it, asked for help, and then understood the underlying idea behind the solution and learned from it. That's the only real way to improve one's problem-solving ability. $\endgroup$ – YiFan Dec 2 '19 at 0:42
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    $\begingroup$ Regarding dyslexia, here is one article out of many that makes one wonder, how many of those diagnosed with dyslexia are actually dyslexic, and how many of them were simply taught (um, "taught") using non-working and discredited "whole language"/"balanced literacy" approach instead of phonics. II am sure a lot of those diagnosed with dyscalculia were simply badly taught (um, "taught") in elementary school. One will never know the full picture thanks for absence of national curricula. $\endgroup$ – Rusty Core Dec 5 '19 at 20:49
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As written, this seems overly caught up in your personal experience, but I think there's a real question here. A lot of people make it to various stages of education having concluded that they're incapable of learning math, and teachers do need to figure out how to handle students who believe that they just can't learn to do math.

  • More than most subjects, math carries a lot of cultural baggage about how associated it is with being "smart". That means a lot of people have a lot of emotions tied up in their experience of doing math, and those emotions often get in the way of actually doing it. Math class isn't therapy, and we can only do so much about this on our own, but classes need to be set up in a way that gives students space to try things that don't work and to be in the process of learning something while still not fully understanding it.

  • A lot of students pick up some really bad habits from their early mathematics education. (For just one example, my students (mostly first-year college students) frequently think that if you look at a math problem and don't immediately know what to do with it, that means they don't know how to solve that problem.) Helping students identify and break these habits can help a lot, though - especially because of the previous item - sometimes students have a lot of resistance to changing the way they think about math.

  • Learning math inevitably requires some un-learning: we first learn things in a narrow, often very rote way, and then later have to re-learn more conceptual and flexible approaches.* But a lot of people have trouble with that step. Students often approach math with a mindset "the goal is to get to the final answer as quickly as possible", which makes it hard to revisit old "easy" material in light of new ideas. (And, again, that emotional baggage gets in the way: once students identify as having understood something, they're often reluctant to let go of that and realize there's more to understand.)

  • But all that shouldn't discount: neurological differences are real. The way we teach math has some reliance on the way most people's brains learn to automatically do certain kinds of symbol parsing. Some people have brains that either don't do this, or do it differently. A lot of people say, "I just can't do math" and mean "the way I learned to do math is totally failing me". But some people really do have brains that work differently; we're at a very early stage of recognizing this, and still at the level of saying "I guess some people just have dyscalculia". I'm optimistic that in the next decade or so, we'll begin to see alternate approaches to teaching math that are accessible to at least some people for whom math is currently genuinely inaccessible.

*This site sees a lot of hand-wringing around this, so I want to emphasize that I don't think this is intrinsically a problem: I think it's an inevitable part of learning a difficult, abstract subject that we sometimes have to learn fragments of it incompletely, use them as stepping stones to harder things, and then reconceptualize the stepping stone.

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  • $\begingroup$ I can solve hard problems with using computers. For instance I have set up complex things like TOR nodes and ruby on rails. Today I built my printer drivers in Linux from source code. I seem to do better at those problems because they involve concrete steps, even when I have to use some trial and error; sometimes I take 4 or 5 different attempts to build source code from a tar.gz file. It's something that I do in Linux as a last resort if something has not got a deb file. A lot of people could not do any of that. But problem solving with numbers is where I run into road blocks. $\endgroup$ – Snack_Food_Termite Dec 2 '19 at 17:31
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Most of real mathematics is not about numbers at all. If you can solve hardware and software problems that are essentially puzzles then you could probably do better at mathematics if you wanted to and needed to.

You seem to be beyond university. If you don't need mathematics in your life but want to use your problem solving skills in some more abstract settings, search the web for mathematical puzzles and work on the ones that look like fun.

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