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Comment by fatnoah | Hacker News Reader

I don't know how I feel about this. I've always been good at math, and was one of five kids (out of class of 120) that took Calculus as a senior in high school in the early 1990's. To even take Calculus as a senior, you had to have taken four years of math in the previous three years. I was even the HS Math Champion" for my state.

However, when I took Calculus in High School, it was taught similarly to this. Lots and lots and lots of math foundations, infinite series, areas under curves, and I was able to trudge through it but I didn't really grasp what it all meant or why I was doing it. Finally, about 2/3 of the way through the year, I was working on a problem and had an "oh, shit, this is just about how things are changing". It was a Eureka moment, and entirely based on such a simple statement that was never brought up in lectures or our crusty 1960's texbook.

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> one of five kids (out of class of 120) that took Calculus

I am always puzzled by this. Calculus was 8th - 9th material in Turkey in the 80s. In classrooms with 45 - 50 kids per one over-worked teacher.

We did set theory and Boolean logic in third grade. I think that is far more useful for understanding mathematical thinking than Calculus is.

Same in Canada. ...and then I moved to the US, and the school was a full YEAR behind, and only covered the basics.

...and I feel like it's getting worse.

> It was a Eureka moment, and entirely based on such a simple statement that was never brought up in lectures

Young me picked up the basics of cryptography at seven or eight, a couple of years before classes in the first foreign language began at age nine or ten. In Finland, for the Swedish-speaking minority, the first foreign language to learn is Finnish — often mentioned as one of the world's most difficult languages to learn. Neither the textbook nor the teacher mentioned how languages work, and specifically not how they are in no way related to cryptography. Young genius me concluded that surely the teacher will soon tell us how this crypto works, so we could move on. While waiting for that to happen, I skipped more or less everything. It took a couple of months to realize the actual situation, by that time the damage had been done. Picked up Finnish seven years later, the natural way through a colleague at a summer job.

That little omission had a detrimental effect on my average grades throughout the school years though, and therefore I certainly do not judge anyone's abilities based on their paper qualifications.

Hmmm, something seems to be missing from the explanation there?

Why would the teacher be expected to know anything about cryptography, let alone know that a particular student has any interest in it?

Were you thinking that maybe foreign languages were substitution ciphers, and that you were eventually going to be taught the substitutions you needed?

I think I had a similar thought when I was about six or seven and came across the Cyrillic alphabet printed in the back of a dictionary. I thought "oh wow, I guess if you learn this, then you know Russian!" -- thinking of Russian as something like English transliterated into Cyrillic.

There are phenomena in language that do work a little bit this way (https://en.wikipedia.org/wiki/Relexification, https://en.wikipedia.org/wiki/Avoidance_speech) but usually at the word level and not in contexts that will really help second language learners.

What a great story. I dont think you are alone in this. I also think this applies to more than just math.

Can you elaborate more about that sentence? With example, perhaps?

This actually covers it very well: http://www-math.mit.edu/~djk/calculus_beginners/chapter00/se...

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