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As a Brit, I was never any good at mental math at school, I still cannot do that hardest one without a calculator. But later on, I swam like a fish in water in

As a Brit, I was never any good at mental math at school, I still cannot do that hardest one without a calculator. But later on, I swam like a fish in water in geometry, trig, logic and loved algebra and moved from the last of my year to one of the top. I was doing integration etc a good two years before it was being taught in the higher classes. These skills are good for programming and computers. There was a limit; basically theorems, multi dimensional stuff and unreal? math, primes, pure math etc were completely out of my scope. Strange I guess, perhaps these are connected with being good at mental arithmetic? My point is that I also think it's bizarre on the British obsession with mental maths early on, when for many algebra might be better and easier.

mkl95 5y ago
In my country (and I'd say this happens in some other EU countries), you do a ton of basic algebra as a kid, then take some rushed calculus and linear algebra 1-2 years before uni. Once you pretend you have mastered the basics, there is a sudden, strange focus on advanced Calculus heuristics and obscure linear algebra techniques, effectively making most people hate these subjects. The way you are taught the stuff is basically a crime against Mathematics since it drives talented people away from STEM careers.
javajosh 5y ago
I felt the same way, but I noticed professors I admired often doing arithmetic in their head, clearly because they enjoyed doing it. So since then I make an effort to mentally calculate. And you know what? It's a more interesting hobby than you'd think. Whatever technique you adopt (or grow, in my case), it's a good, concrete, occasionally useful exercise in breaking down a problem into smaller parts, and then combining those simple results into something else. Or maybe it's vanity. But I will say it's depressing to see all the cashiers (in the US) that can't seem to do any kind of math in their head, not even to minimize change (which seems totally ubiquitous in many other parts of the world; in fact, some cultures are aggressive about optimizing your change - China comes to mind).
- confidantlake 5y ago
  I feel that in the US any cashier that could do mental math would soon move on to a better paying job.
pulkitsh1234 5y ago
I still have a hard time in mental arithmetics. During my school days, this is one of the things which had instilled the "math phobia" in me. I never really took an interest in math, until I started doing competitive programming in college. I had to literally build a new understanding of division, multiplication, modulus, etc., it's difficult to explain. But I feel really ashamed in admitting that I still suck at math, probably because I just hated it during school days and no one was there to guide me. I don't really like blaming things on others, but I am not sure what else I could've done to learn math.
2muchcoffeeman 5y ago
I think mental arithmetic is one of those things that simply requires vast amounts of practise. I’m quite slow at it, but when I’m forced to do a lot of it, say for keeping score. I quickly get faster. I too was much better at applied maths and stats. It was fairly easy for me. But my brain just shuts down doing pure math.
TheMightyLlama 5y ago
I'm in exactly the same position at the age of 40. I've attempted to memorise the times table to no avail. It seems to me one of those things that you need to know cold. And then from there you can look at other things. To me mathematics is a thing of beauty I just find I havent found the right handle to grasp it with. I ask myself what would be the order in which one could most easily absorb the material. Does it really start with rote learning?
- wheelinsupial 5y ago
  > I ask myself what would be the order in which one could most easily absorb the material. Does it really start with rote learning? What are you trying to learn and why? Math starts with axioms, which are some statements that everything else is built from. Axioms, as far as I understand, can't be derived. These are the most basic building blocks. Then through logic and deductions other machinery is built up. There is a certain amount that does need to be internalized or memorized, but that is the same for learning the alphabet. In math classes, at least at the university level in Canada, knowing the statement of definitions and theorems covered exactly is somewhat important. If it's a proof based course this is more important, but the theorem will tell you where it's applicable, so knowing that helps. Math builds. It took me until a third year complex analysis course to build up enough courage to ask a prof how he solves problems. Basically he said he has a hierarchy of theorems in a given field. When he sees a problem he will go through each of them starting with the easiest to apply and check the assumptions. If it applies, then he will use it and get the result. If not, move on to the next one. He goes and looks up the exact statements and how to go through with the calculations and checks. If you forget something, look it up. Eventually after solving enough problems you'll build up some intuition and muscle memory for the problems. As to how to progress, I am not sure. Some mathematicians say you kind of just pick things up and then connect the threads later on. It's not always possible to march through in a linear manner because there isn't an absolute ordering in what to learn. There should be an appendix in the back of a textbook that reviews or outlines what's required for the book. There will be a few questions that rely on outside knowledge, but one can still learn the majority of the concepts without going to far afield for review. Start with what you want and fill in the rest of the gaps by working backwards. I wouldn't worry about memorizing the times tables (unless maybe you're interested in number theory?) if you're trying to learn math. Know algebra, functions, and graphing as a minimum, then start to learn what you want... I would just use a calculator or pencil and paper to multiply things out on homework. If this is for personal benefit, then don't hesitate to get some numerical methods involved to help learning the material.

mkl95 5y ago

In my country (and I'd say this happens in some other EU countries), you do a ton of basic algebra as a kid, then take some rushed calculus and linear algebra 1-2 years before uni. Once you pretend you have mastered the basics, there is a sudden, strange focus on advanced Calculus heuristics and obscure linear algebra techniques, effectively making most people hate these subjects. The way you are taught the stuff is basically a crime against Mathematics since it drives talented people away from STEM careers.

javajosh 5y ago

I felt the same way, but I noticed professors I admired often doing arithmetic in their head, clearly because they enjoyed doing it. So since then I make an effort to mentally calculate. And you know what? It's a more interesting hobby than you'd think. Whatever technique you adopt (or grow, in my case), it's a good, concrete, occasionally useful exercise in breaking down a problem into smaller parts, and then combining those simple results into something else. Or maybe it's vanity. But I will say it's depressing to see all the cashiers (in the US) that can't seem to do any kind of math in their head, not even to minimize change (which seems totally ubiquitous in many other parts of the world; in fact, some cultures are aggressive about optimizing your change - China comes to mind).

confidantlake 5y ago
I feel that in the US any cashier that could do mental math would soon move on to a better paying job.

pulkitsh1234 5y ago

I still have a hard time in mental arithmetics. During my school days, this is one of the things which had instilled the "math phobia" in me. I never really took an interest in math, until I started doing competitive programming in college. I had to literally build a new understanding of division, multiplication, modulus, etc., it's difficult to explain. But I feel really ashamed in admitting that I still suck at math, probably because I just hated it during school days and no one was there to guide me. I don't really like blaming things on others, but I am not sure what else I could've done to learn math.

2muchcoffeeman 5y ago

I think mental arithmetic is one of those things that simply requires vast amounts of practise. I’m quite slow at it, but when I’m forced to do a lot of it, say for keeping score. I quickly get faster. I too was much better at applied maths and stats. It was fairly easy for me. But my brain just shuts down doing pure math.

TheMightyLlama 5y ago

I'm in exactly the same position at the age of 40. I've attempted to memorise the times table to no avail. It seems to me one of those things that you need to know cold. And then from there you can look at other things. To me mathematics is a thing of beauty I just find I havent found the right handle to grasp it with. I ask myself what would be the order in which one could most easily absorb the material. Does it really start with rote learning?

wheelinsupial 5y ago
> I ask myself what would be the order in which one could most easily absorb the material. Does it really start with rote learning? What are you trying to learn and why? Math starts with axioms, which are some statements that everything else is built from. Axioms, as far as I understand, can't be derived. These are the most basic building blocks. Then through logic and deductions other machinery is built up. There is a certain amount that does need to be internalized or memorized, but that is the same for learning the alphabet. In math classes, at least at the university level in Canada, knowing the statement of definitions and theorems covered exactly is somewhat important. If it's a proof based course this is more important, but the theorem will tell you where it's applicable, so knowing that helps. Math builds. It took me until a third year complex analysis course to build up enough courage to ask a prof how he solves problems. Basically he said he has a hierarchy of theorems in a given field. When he sees a problem he will go through each of them starting with the easiest to apply and check the assumptions. If it applies, then he will use it and get the result. If not, move on to the next one. He goes and looks up the exact statements and how to go through with the calculations and checks. If you forget something, look it up. Eventually after solving enough problems you'll build up some intuition and muscle memory for the problems. As to how to progress, I am not sure. Some mathematicians say you kind of just pick things up and then connect the threads later on. It's not always possible to march through in a linear manner because there isn't an absolute ordering in what to learn. There should be an appendix in the back of a textbook that reviews or outlines what's required for the book. There will be a few questions that rely on outside knowledge, but one can still learn the majority of the concepts without going to far afield for review. Start with what you want and fill in the rest of the gaps by working backwards. I wouldn't worry about memorizing the times tables (unless maybe you're interested in number theory?) if you're trying to learn math. Know algebra, functions, and graphing as a minimum, then start to learn what you want... I would just use a calculator or pencil and paper to multiply things out on homework. If this is for personal benefit, then don't hesitate to get some numerical methods involved to help learning the material.