[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.