[Viliam1234]

It's not just working hard enough, but also doing the right kind of work. Many people make the mistake of trying to memorize things without understanding. Which may be easy at the beginning when you memorize a fact or two, but it gradually accumulates, especially in math when the old topics never go away as the new ones are introduced. And then the memorizers are actually working much harder, and even that is not enough, so they fail.

So why the aversion to understanding? I suspect part of that is generational; if your parents sucked at math because they relied on memorization, they probably won't introduce you to math as an something worth understanding. It will either be "give up", or "work harder" but in the sense of memorizing harder. Not just your parents, but the entire culture around you will be like that. Another part is that most math teachers at elementary schools actually suck at math; because teachers are many, but people good at math are few and they have many better careers available. But another problem is the insistence of school system on everyone going forward at a predetermined speed -- sometimes understanding takes time, and when you don't have the time, you are forced to memorize; but once you start memorizing, you usually need to keep memorizing, because understanding can only be built on understanding the prerequisites.

Properly taught elementary-school math should be fun, like this: https://www.matika.in/en/ Fun makes people think.

[danielmarkbruce]

A lot of people don't understand what understanding really even entails. They don't know that some people actually understand a topic/idea/whatever, can play around with the ideas in their head, think from first principles on the topic. They've never understood a topic in their life.

[synecdoche]

If passion, or own experience, is missing it may be a case of unknown unknowns for both parents and teachers.

The Matika site looks really nice but I have difficulties comprehending the instructions. Even the very first one for first grade. “Children step by record.” What does that mean? I tried the next one. “During addition we write addends below each other…” What? If all addends are below, no addend is on the top. It makes no sense. Then, “…and the sum below the line” with no line in sight. What, where, which line, how? That was frustrating.

[Viliam1234]

Wow, the English translation sucks much more than I noticed. :(

The whole "stepping" thing is a reference to how they (in the web page author's country) teach basic addition and subtraction at first grade. There is a carpet with numbers on the floor, you start at number zero, and do addition like "2+3" means "two steps forward, pause, three steps forward, now look at the number you are standing on". The carpet is situated so that from the sitting kids' position the zero is on the left, and the numbers increase to the right.

The idea is to turn integers into something "tangible", in a way that can later be extended to negative numbers.

So the instructions should be like: "You start at given number. Right arrow means a step forward to a greater number. Left arrow means a step backward to a smaller number. What number you end at?"

Sorry, I already know all these things by heart, so I didn't notice how the English instructions don't make sense. Guess I should contact the author about it.

[vonunov]

I feel the same way when I'm on hold and a recording tells me "your call will be answered in the order it was received". This isn't about grammatical pedantry -- I don't care that they didn't say in which -- it's about it not making sense. Which, as I said, isn't grammatical pedantry. But it probably is still a bit pedantic. Still, though, how can one thing have an order? What order was my call received in? Is it before or after itself? I get the sense that whoever recorded that didn't spend any time actually thinking about it, or they would have said "Calls are answered in the order [in which] they are received" or something.

[madaxe_again]

Understanding is critical.

I unfortunately spent the entire introduction to calculus in hospital, so missed it - when I came back to school, I was dropped straight into “differentiate this” and “integrate that”. There was no explanation of what either operation was, just the rules that you followed to obtain the result. I had no idea that we were looking at rates of change or at areas under curves. For the first time in my life, I found myself bewildered, and struggling - until a month later I happened to find myself reading a biography of Newton which actually explained what the purpose of calculus/fluxions was - and then it became easy, as it was obvious if a result was nonsensical.

[Viliam1234]

I knew people who somehow missed the information that fractions are the same as division. So they could e.g. reduce the fraction 40/20 to 4/2, then after thinking about it longer also to 2/1, and... then had no idea what to do next.

For me it was completely mind-blowing, how someone could do fractions without understanding what they are? But I imagine, at school they probably could solve some problems, couldn't solve others, got C, moving on to the next lesson.