# Learning math / mathematical reasoning as an adult

For a very, very long time, I've had a strange but persistent envy of people who have good "logical" thinking skills or who can do math well. I wish that I was the type of person who could play chess to even a passable degree, as I'm convinced a toddler could beat me. But most of all, I wish I could learn something like calculus, which has held a strange allure for me even as a young kid. But I was failing math as early as the fifth grade, and do not remember even an iota of information about geometry or trigonometry. Ultimately, I dropped out of school altogether.

A year or so ago I started in the "pre-K" mathematics category of Khan Academy, because I had such a low opinion of my own abilities. Sure enough, I breezed by it, but even found some parts of the second or third grade curriculum difficult. It's like I was born completely without numerical ability, but I don't want to go so far as to say I have something like dyscalculia, as I at least read analog clocks and musical notation on a daily basis, and have no problem discerning if a number is bigger or smaller than another. I'm also decidedly not aphantastic; quite the opposite. Something I do have is an *extreme* distrust or even hatred of my own critical thinking abilities. If I mess up simple arithmetic, I'll beat myself up mentally for being "stupid," or an "idiot," and so on for way too long. It's a habit I learned early. Complicating matters is that I'm in my mid-twenties, so my neuroplasticity is probably not great. In fact, one of my deepest fears is that it's too late for me to learn *any* new subject to a competent degree.

This might be a ridiculous thing to say, but I'm hoping someone can reassure me that it's possible to learn math as an adult, even for a "hopeless" case like me. If you've been in a similar situation and have found particular resources helpful, I'd really like to see them. Khan Academy wasn't really my thing, but if it's more or less the best option for someone like me, I'll try it again.

I think that as an adult you really have to embrace top down learning (whereas in bottom up learning you start from the basics and build upwards, top down learning starts with "I want to do X" - from there, you keep going down the knowledge stack until you learn how to do X). Top down learning

isless efficient, but once you leave schooling years, without all that time only dedicated to learning and an environment that forces you to learn things that seemingly have no use for years on end, it's hard to do bottom up learning.So I would try and find a top level goal in math and explore downwards. Keeps you interested.

Just a note, but math != arithmetic. I would consider myself pretty okay at math - I took and got good scores in calc 3, diffeq, linear algebra, all the other mandatory CS math classes + also took abstract algebra, real analysis and others for fun in college.

But I am absolute ass at arithmetic. Once I got a question worth 1/3 of a midterm wrong in abstract algebra because I said 5 + 2 = 8 . If you go higher up the multiplication table I'd have to think for a second.

In the end, it doesn't matter - you get calculators in real life.

It's comforting to hear so many people saying that they struggle with arithmetic but excel in calculus and algebra. I also never stopped to consider that the bottom-up approach might be detrimental to an adult learner, but what you've written makes a lot of sense. Thanks very much.

I pretty much agree with what @stu2b50 said. (And I have a similar background - CS degree, took calc 1-3, diff EQ, etc.) I almost failed calc 3 the first time I took it because it was just so abstract and the problems so boring. I may be misremembering, but it felt like every damn problem was phrased as some amount of water flowing into a bucket at some speed, and some amount of water flowing out of the bucket at some other speed. I was so sick of buckets and water by the midterm I nearly dropped the class! It didn't seem useful to my actual life at all.

In addition to noting that math does not equal arithmetic, also note that logic does not equal math. You can be good at one and bad at the other. Also, there are different types of logic, so it might help to clarify what you mean. I took "logic" classes in college for my CS degree. They were things like Boolean logic, and understanding how to put together simple circuits. (Computers even have a component named an "arithmetic logic unit" or ALU.)

Much later in life, I started listening to skeptical and critical-thinking-related podcasts and learned more about the type of logic you use on a day-to-day basis to understand the world and specifically arguments that people are presenting to you. It's more "philosophical" logic than "math" logic, though they are related. (And for the record, I find most philosophy to be utterly boring. Can't stand it!) I found learning the philosophical logic very helpful in my everyday life. It made discerning which of the myriad things in life to worry about easier. It might help with your feelings of being "stupid" for not knowing something that most adults really don't use anymore. (Also, it turns out there are a ton of arithmetic tricks that make some of the arithmetic simpler if you can spot when to use them. My spouse is often impressed when I do some mental math, and then I point out that I just broke things out into a couple groups and figured each one out separately, and then she's not impressed anymore. "Oh, well I could have done that!")

Hey don't badmouth philosophy in my presence! Western Logic was invented by a philosopher, you know? đź¤¬

Mathematical logic is a way more recent afterthought :P

Iâ€™m no expert but I do have advice:

If youâ€™re curious about calculus, go ahead and read about it. There are conceptual introductions aimed at beginners that will at least help you understand what itâ€™s for. If you donâ€™t quite get it because you donâ€™t understand the vocabulary then you might try reading about some prerequisites.

Actually knowing how to do math means practicing by doing exercises. The people who are really good at math

likedoing exercises and seek them out because they like solving those sort of puzzles. Much like with music you want to look for exercises suited to your skill level and that you enjoy.Unlike music, itâ€™s not a performance, so donâ€™t worry about doing things fluently. If you make a mistake and then notice it and fix it then thatâ€™s good enough.

Solving hard puzzles means getting stuck sometimes and being comfortable with being stuck. Maybe you wonâ€™t solve something right away, but you can keep it in mind and come back to it later after you learn something else that helps solve the puzzle.

If you think youâ€™re bad at math because you struggled with it in school then I want to first say that most of what I remember from math classes tells me itâ€™s not taught very well. I have a CS degree (which is a specialized math degree) and frequently realize a far more intuitive way to teach some aspect of geometry or calculus. 3blue1brown on YouTube does a great job with those kinds of things, but Iâ€™m not sure if it requires too much prerequisite math knowledge to enjoy.

In order to teach a generation of students how to do calculus the teacher really needs to have a deep understanding and love for the subject. They need to be able to not only explain the subject but also understand all of the wrong ways a student might approach it, with a dozen ways to bring that student back on track.

I had an excellent calculus teacher in high school. He really thought that the subject was interesting and managed to explain concepts in an intuitive manner. Our society should value people like him more. Heâ€™s probably doing well enough financially, but isnâ€™t nearly getting a fair proportion of his net impact on GDP. The top 1% from a graduating class will mostly go into a high growth business sector. I wish more could become teachers.

To add to the comments here about the difference between arithmetic and mathematics, from a slightly different perspective: I'm a physicist, also have some publications in theoretical computer science, and would reasonably consider myself to be good at maths, yet my ability to do simple arithmetic is rather poor. When thinking about numbers abstractly, or the relations between them, I'm fine; I can also think about simple arithmetic, and reason through it slowly and methodically. But doing arithmetic at a speed that people would consider even remotely reasonable requires completely different skills and knowledge, primarily memorization of many special cases, that just seem pointless and boring compared to the wonders elsewhere.

The difficulty with arithmetic is actually very common amongst people with experience in higher mathematics. There was a common joke when I was a graduate student that the best option for figuring a restaurant bill at a table of researchers was to give it to the person in the

leastmathematical discipline, and certainly never to mathematicians. More concretely, on a project a few years ago, my two collaborators and I, all in physics or theoretical (not engineering) CS, realized that, the day before, all three of us had simultaneously come up with and agreed on the wrong answer to a basic, two-digit subtraction problem where both numbers were divisible by 5.It's also important to distinguish between speed and ability. I am not quick with mathematics and reasoning, and never have been. Of the problems they could solve, a secondary student could likely solve them much faster. The difference is that I can slowly solve those problems, and also slowly solve problems they couldn't. This is not uncommon. As a student, when I moved from classes that cared about solving many easy and almost-identical problems at a time quickly, where grading judged us, even if unintentionally, on how quickly we could work, to classes that cared about solving a few hard problems at a time without regard to speed, where grading judged us on whether or not we could solve the problem at all, it completely changed my enjoyment of the field.

Sadly, many classes in primary and secondary schools are very much focused around presenting mathematics as a field built around repeatedly solving many identical problems at speed, which is enormously boring, and not particularly useful at anything but misrepresenting the field. The result is that many people who excel in those classes are seen as being talented in maths, choose to pursue it as a consequence, and then hit a point where they start struggling to understand, while people who would be talented in understanding difficult concepts are driven away from the field by being seen as slow, and finding the classes difficult and boring. (The difficulty of how scholarly fields are presented in school, as opposed to what being in them is actually like, is a significant problem generally, unfortunately, and not something that is easy to solve.)

Thanks for taking the time to respond. I never stopped to consider that arithmetic and higher math require two different skill sets, so it's encouraging to see it echoed so strongly in the comments here.

â€śIâ€™m in this picture and I donâ€™t like it.â€ť Honestly I think some people donâ€™t believe I studied math after seeing me struggle to compute a tip for a minute and then reach for my phoneâ€™s calculator.

Just throwing out community college courses as an option. Most colleges will have a placement exam that will put you at the right level as well. Math is something you learn only by doing, and it can be hard to identify exercises that help you really nail a concept and ones that are just rote calculation.

If what youâ€™re looking for is reassurance, Iâ€™ll leave you this: the person that got me interested in mathematics (I have a degree in it) was a former marine that went to school after leaving the marines, started in a remedial mathematics course at a community college, and ended up with a doctoral degree in mathematics focusing in number theory. Until he found the right teachers he also believed he was bad at math, and when I met him as a professor he still counted on his fingers to do arithmetic. The thing that mathematicians donâ€™t tell you is that math isnâ€™t really that hard, you just need proper guidance and perseverance to learn it.

That sounds surprisingly similar to the story of Barbara Oakley in her book A Mind For Numbers: How to Succeed at Math (Even If You Flunked Algebra). OP may enjoy that and also Iâ€™ve seen people recommend Mindset - The New Psychology of Success by Carol Dweck. Itâ€™s about how to get into the mindset of succeeding instead of failing when something is hard.

I'd add also for OP to consider his learning style and focus on that. Maybe he's not good at just reading, maybe he needs to touch something to learn it (thus music makes sense because he can touch the notes to make them), maybe he needs to visualize the problem to understand it. If you can find out your learning strengths OP you can do it!!

For the critical thinking bit (not math) I recommend starting with the Illustrated Book of Bad Arguments, followed by Gary Hardegree's excellent

Introduction to Symbolic Logic(alternatively namedSymbolic Logic: A First Coursein book form). It used to be available for free on his website, I'm pretty sure it still is, but my connection is crap right now so I can't find it. It is worth looking for. If you have any trouble do tell me, I still have the PDFs somewhere.I know that this thread is a little old â€” but perhaps some of us could start a study group. I think that one of the most important success factors offered by a good school environment is peer support (and pressure).