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Sadly, mathematics classes are like that as well. Instructors start throwing equations on the board, expecting us to somehow connect it all together. The best m

Sadly, mathematics classes are like that as well. Instructors start throwing equations on the board, expecting us to somehow connect it all together. The best math textbook (Theory of Algebra) I ever read had little sections about the person who revealed a particular subject, why they were studying it, and how the subject is used.

gen_greyface 4y ago
Do you remember what the book was called, or the writers.
luuuzeta 4y ago
Sadly many professors fall victim to the Curse of Knowledge. It doesn't help they need to follow a tight schedule and intuition isn't something you can develop in a single lecture. I suppose self-study and repetition is the most likely solution. >The best math textbook (Theory of Algebra) I ever read had little sections about the person who revealed a particular subject, why they were studying it, and how the subject is used. I've found the best type of books provide motivation for concepts, how they have evolved, etc. Take Computer Science for example, many of its concepts were area of research for decades but from a student's perspective it seems these concepts were always here instead of being constantly refined until the states they're now in.
- voidhorse 4y ago
  Exactly, understanding the intentions and history behind a concept is key to achieving comprehension. I've had to teach myself nearly all of the more advanced mathematical concepts I know, and I'm finally starting to reach a point where I feel I have a nice approach toward achieving an understanding: - Learn the definition - Learn the motivations and history - Peruse a few examples - Try to map the above to a brief synopsis that explains the concept in intuitive terms that relate to your own life. Rely on pictures. Finally, I find it helpful sometimes to try and "deduce" identities from "first principles". e.g. assume I didn't know that n^0 = 1. How might I reach that conclusion? If I have an understanding of what exponentiation means I should be able to come up with a few different propositions (these could even be relatively informal) that make such a conclusion make sense. My childhood was rife with mathematics teachers that focused more on rote memorization of identities instead of careful explanation of definitions and development of "intuition". There's pretty much no better way to ensure you'll produce students that dislike and suck at math for the rest of their lives than proceeding by mind-numbing rote memorization.
  - luuuzeta 4y ago
    I think that's a great approach. If possible, you can add another step: Teaching it to someone else. >There's pretty much no better way to ensure you'll produce students that dislike and suck at math for the rest of their lives than proceeding by mind-numbing rote memorization. I couldn't agree more.

gen_greyface 4y ago

Do you remember what the book was called, or the writers.

luuuzeta 4y ago

Sadly many professors fall victim to the Curse of Knowledge. It doesn't help they need to follow a tight schedule and intuition isn't something you can develop in a single lecture. I suppose self-study and repetition is the most likely solution. >The best math textbook (Theory of Algebra) I ever read had little sections about the person who revealed a particular subject, why they were studying it, and how the subject is used. I've found the best type of books provide motivation for concepts, how they have evolved, etc. Take Computer Science for example, many of its concepts were area of research for decades but from a student's perspective it seems these concepts were always here instead of being constantly refined until the states they're now in.

voidhorse 4y ago
Exactly, understanding the intentions and history behind a concept is key to achieving comprehension. I've had to teach myself nearly all of the more advanced mathematical concepts I know, and I'm finally starting to reach a point where I feel I have a nice approach toward achieving an understanding: - Learn the definition - Learn the motivations and history - Peruse a few examples - Try to map the above to a brief synopsis that explains the concept in intuitive terms that relate to your own life. Rely on pictures. Finally, I find it helpful sometimes to try and "deduce" identities from "first principles". e.g. assume I didn't know that n^0 = 1. How might I reach that conclusion? If I have an understanding of what exponentiation means I should be able to come up with a few different propositions (these could even be relatively informal) that make such a conclusion make sense. My childhood was rife with mathematics teachers that focused more on rote memorization of identities instead of careful explanation of definitions and development of "intuition". There's pretty much no better way to ensure you'll produce students that dislike and suck at math for the rest of their lives than proceeding by mind-numbing rote memorization.
- luuuzeta 4y ago
  I think that's a great approach. If possible, you can add another step: Teaching it to someone else. >There's pretty much no better way to ensure you'll produce students that dislike and suck at math for the rest of their lives than proceeding by mind-numbing rote memorization. I couldn't agree more.