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A reinforcing point to this is that I still have a lot of my textbooks from undergrad/grad school. And while I hadn't studied any math for 20 years or so, it w

A reinforcing point to this is that I still have a lot of my textbooks from undergrad/grad school. And while I hadn't studied any math for 20 years or so, it was interesting when I went through some of these books -- how much easier it is to understand some of these concepts now. I don't know what it is that helped me understand these concepts, twenty years after graduating, better than I did when I was studying it everyday. But I would NOT attribute it to the textbook, given it is literally the same one.

sound1 5y ago
> I don't know what it is that helped me understand these concepts, twenty years after graduating, better than I did when I was studying it everyday. But I would NOT attribute it to the textbook, given it is literally the same one. Probably additional skills and experience you picked up all these years by solving/understanding hard problems
- Jtsummers 5y ago
  And more time for it to be mulled over. It was frustrating, but in college I found that the 16 week semester was rarely enough to actually learn something, only enough time to commit it to memory. It was often a year or more later that I'd have a sudden eureka moment while studying a separate topic. Perhaps something that was applying the unlearned material (like Physics I and Calculus, which were a semester apart for me since I took Chem I my first semester in college) or something related but not exactly the same (like Concrete Mathematics by Knuth et al. leading me to a realization about some aspects of calculus).
- dionidium 5y ago
  I had the experience of trying to relearn some math just a few years after first learning it in college and it was similarly much easier to learn it all a second time. I don't think I had a whole bunch of new experience. I think rather there must be some kind of residual understanding, even if it can't all be articulated cold.
  - legerdemain 5y ago
    Could this be a cognitive advantage of getting older?
stackbutterflow 5y ago
I had the same experience. I think it's because school dumps on us solutions to problems we haven't had yet. It's difficult to correlate abstract concepts to tangible problems. But 20 years later those formulas are actually painting a picture of things we've experienced. It's like reading someone else putting perfectly into words thoughts you had. It clicks only if you had those thoughts; to other people it is devoid of meaning.
atoav 5y ago
This is IMO what makes teaching well incredibly hard: you not only need to understand the topics at hand better than people who just apply it, you also need to remember the time before you understood what tou are teaching.
- Arrath 5y ago
  This is something my mentor had to come to grips with when I started, and something I've been working through the last few years as my team grows. It is very difficult to take that step back and divorce myself from years of experience and tough lessons, and to present the subject matter in a way that can be grasped without an innate understanding that took me years to reach.
janto 5y ago
Maybe the ideas you learnt were "settling in" over the past 20 years.
shriek 5y ago
Same here as well. From what I've found out is that, I know the problem space much better now, meaning, I know how some of it applies in real life and I can better visualize it now than when I was just trying to finding the right answer for grades. Maybe that's just for me but that's my reasoning anyway.
swiley 5y ago
Spaced repetition, just with a very long space.

sound1 5y ago

> I don't know what it is that helped me understand these concepts, twenty years after graduating, better than I did when I was studying it everyday. But I would NOT attribute it to the textbook, given it is literally the same one. Probably additional skills and experience you picked up all these years by solving/understanding hard problems

Jtsummers 5y ago
And more time for it to be mulled over. It was frustrating, but in college I found that the 16 week semester was rarely enough to actually learn something, only enough time to commit it to memory. It was often a year or more later that I'd have a sudden eureka moment while studying a separate topic. Perhaps something that was applying the unlearned material (like Physics I and Calculus, which were a semester apart for me since I took Chem I my first semester in college) or something related but not exactly the same (like Concrete Mathematics by Knuth et al. leading me to a realization about some aspects of calculus).
dionidium 5y ago
I had the experience of trying to relearn some math just a few years after first learning it in college and it was similarly much easier to learn it all a second time. I don't think I had a whole bunch of new experience. I think rather there must be some kind of residual understanding, even if it can't all be articulated cold.
- legerdemain 5y ago
  Could this be a cognitive advantage of getting older?

stackbutterflow 5y ago

I had the same experience. I think it's because school dumps on us solutions to problems we haven't had yet. It's difficult to correlate abstract concepts to tangible problems. But 20 years later those formulas are actually painting a picture of things we've experienced. It's like reading someone else putting perfectly into words thoughts you had. It clicks only if you had those thoughts; to other people it is devoid of meaning.

atoav 5y ago

This is IMO what makes teaching well incredibly hard: you not only need to understand the topics at hand better than people who just apply it, you also need to remember the time before you understood what tou are teaching.

Arrath 5y ago
This is something my mentor had to come to grips with when I started, and something I've been working through the last few years as my team grows. It is very difficult to take that step back and divorce myself from years of experience and tough lessons, and to present the subject matter in a way that can be grasped without an innate understanding that took me years to reach.

janto 5y ago

Maybe the ideas you learnt were "settling in" over the past 20 years.

shriek 5y ago

Same here as well. From what I've found out is that, I know the problem space much better now, meaning, I know how some of it applies in real life and I can better visualize it now than when I was just trying to finding the right answer for grades. Maybe that's just for me but that's my reasoning anyway.

swiley 5y ago

Spaced repetition, just with a very long space.