3 ms·

I liked math up until my pre-calc teacher told me I couldn't go any further until I memorized two dozen different trigonometric identities and was able to imme

I liked math up until my pre-calc teacher told me I couldn't go any further until I memorized two dozen different trigonometric identities and was able to immediately identify which to use.

BenFranklin100 2y ago
This is actually not a bad way to go. Understanding which is then followed by rote memorization of basic identities and formulas frees up your brain to focus on higher level concepts. Like the tennis amateur who didn’t make pro because they never bothered to drill on the fundamentals, many people get bogged down in higher level math and physics courses because they’ve long lost or never developed a fluency with the basics needed to derive and understand the advanced concepts.
- raincole 2y ago
  I would have downvoted this comment one year ago. But my perspective changed. "Memorizing to free up brain space" is very real.
  - pictureofabear 2y ago
    This is a good example of why upvotes and downvotes don't always work well when you have class imbalances (more young people than old people or vice versa). We upvote or downvote mostly based on intuition, but wisdom is not always intuitive--we don't always recognize it when we see it.
- bikenaga 2y ago
  "It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments." - Alfred North Whitehead, "An Introduction to Mathematics", pp. 45–46
  - BenFranklin100 2y ago
    Very nice, thanks.
dboreham 2y ago
There are stupid people everywhere, unfortunately. Also sadly except in unusual circumstances (e.g. they have a trust fund to live off), pre-calc teachers are not going to know much about mathematics.
- syndicatedjelly 2y ago
  Those trig identities were tremendously useful throughout Calculus. Having them readily accessible in memory was very helpful, from what I recall. Why do you think this pre-calc teacher was “stupid”?
  - deleted 2y ago
    [deleted]
  - thoaw342 2y ago
    I never took "Pre-Calc" and got easy A's in the calculus series. In my opinion, college calculus is poorly named and instead should be named "Pre-Calc" and the real calculus course is then physics.
    - oaktowner 2y ago
      This gibes with my experience in college -- I did more calculus in my physics courses than in my calculus courses.
    - syndicatedjelly 2y ago
      I'm not sure what you mean by "real" calculus course. Physics applies calculus to solve certain problems. To claim one subject is more "real" than the other doesn't make sense to me.
- qball 2y ago
  Oh, don't worry; university professors do this too. Most of those courses are not calculus, it's just advanced algebra, and we do those trying for success in them a disservice with the dishonesty.
extraduder_ire 2y ago
I've always found needing to rote-memorize formulae and identities kind of contrived in an academic setting, unless you're being quizzed on how to derive them. This is probably due to the education I got. Every maths or science exam in my country hands copies of this booklet out for reference: https://www.examinations.ie/misc-doc/BI-EX-7266997.pdf https://www.examinations.ie/misc-doc/BI-EX-7266997.pdf
- pictureofabear 2y ago
  So you get this booklet to reference on tests? If so, that sounds fantastic. It's the concepts that matter. Either way, thanks! I'm saving this. It's a wonderful reference.

I liked math up until my pre-calc teacher told me I couldn't go any further until I memorized two dozen different trigonometric identities and was able to immediately identify which to use.

BenFranklin100 2y ago

This is actually not a bad way to go. Understanding which is then followed by rote memorization of basic identities and formulas frees up your brain to focus on higher level concepts. Like the tennis amateur who didn’t make pro because they never bothered to drill on the fundamentals, many people get bogged down in higher level math and physics courses because they’ve long lost or never developed a fluency with the basics needed to derive and understand the advanced concepts.

raincole 2y ago
I would have downvoted this comment one year ago. But my perspective changed. "Memorizing to free up brain space" is very real.
- pictureofabear 2y ago
  This is a good example of why upvotes and downvotes don't always work well when you have class imbalances (more young people than old people or vice versa). We upvote or downvote mostly based on intuition, but wisdom is not always intuitive--we don't always recognize it when we see it.
bikenaga 2y ago
"It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments." - Alfred North Whitehead, "An Introduction to Mathematics", pp. 45–46
- BenFranklin100 2y ago
  Very nice, thanks.

dboreham 2y ago

There are stupid people everywhere, unfortunately. Also sadly except in unusual circumstances (e.g. they have a trust fund to live off), pre-calc teachers are not going to know much about mathematics.

syndicatedjelly 2y ago
Those trig identities were tremendously useful throughout Calculus. Having them readily accessible in memory was very helpful, from what I recall. Why do you think this pre-calc teacher was “stupid”?
- deleted 2y ago
  [deleted]
- thoaw342 2y ago
  I never took "Pre-Calc" and got easy A's in the calculus series. In my opinion, college calculus is poorly named and instead should be named "Pre-Calc" and the real calculus course is then physics.
  - oaktowner 2y ago
    This gibes with my experience in college -- I did more calculus in my physics courses than in my calculus courses.
  - syndicatedjelly 2y ago
    I'm not sure what you mean by "real" calculus course. Physics applies calculus to solve certain problems. To claim one subject is more "real" than the other doesn't make sense to me.
qball 2y ago
Oh, don't worry; university professors do this too. Most of those courses are not calculus, it's just advanced algebra, and we do those trying for success in them a disservice with the dishonesty.

extraduder_ire 2y ago

I've always found needing to rote-memorize formulae and identities kind of contrived in an academic setting, unless you're being quizzed on how to derive them. This is probably due to the education I got. Every maths or science exam in my country hands copies of this booklet out for reference: https://www.examinations.ie/misc-doc/BI-EX-7266997.pdf https://www.examinations.ie/misc-doc/BI-EX-7266997.pdf

pictureofabear 2y ago
So you get this booklet to reference on tests? If so, that sounds fantastic. It's the concepts that matter. Either way, thanks! I'm saving this. It's a wonderful reference.