10 ms·

Learn Difficult Concepts with the ADEPT Method

189 points by jhund 10y ago

deleted 10y ago
[deleted]
vikeri 10y ago
Excellent! I always think that people, like myself, that work with somewhat abstract and/or complex concepts need to improve our ability to explain them. Really happy to see a concrete method to do this.
hodgesrm 10y ago
Great article! This is the most intuitive description of imaginary numbers I have ever read. I'm going to try the same technique with Software Defined Networking (SDN), which has been on my "must figure it out" list for a while. :)
joelg236 10y ago
Fourier transformations clicked for me from your previous articles, this outline really shows the skill of "sharpening" rather than "building" knowledge. Helpful for young kids to adults alike.
- thomasahle 10y ago
  I had the same experience. However later when I encountered new properties of fourier transforms, such as the convolution theorem, fast fourier transform and the fourier transform of boolean functions, I felt my acquired intuition no longer fitted. Did you also experience this? If so, how did you get past it to that "next level"?
karimdag 10y ago
Having skimmed the article I want to ask: How about the first principles method ? How does this [ADEPT] compare to it [fp] ?
- Silhouette 10y ago
  It seems the main point being made by the article is that even if you are going to teach principles, it can be more effective to start by giving some context and motivation before getting into the detailed technical explanations. Deriving results from first principles may well result in better understanding than simply learning results and proofs by rote, but it's still useful to have some indication of why those principles might be useful and relevant as well.
  - kalid 10y ago
    Exactly. Even if teaching or reasoning from first principles, you would explain them via analogies, diagrams, examples, etc. Teaching from first principles solely from the technical definition wouldn't be very pleasant for most.
theobon 10y ago
I'd love to seen an ADEPT method explanation of Laplace Transforms. I got through most of math fairly easily by having a mental model of what was going on and could always check that I was on the right track as it made sense in my mental model. However, when I got to Laplace transforms I never figured out how to visual what that meant. Everything collapsed into transform into the magical space where you can do some things easier and then you can transform out into a new place. I could never be sure of how I got from a to b without a tedious examination of every step to ensure I applied the rules correctly. I'd love to have a mental model for Laplace Transforms. As a generalization, how does one explain things where no good mental model exists?
- copperx 10y ago
  > As a generalization, how does one explain things where no good mental model exists? Papert et al. are convinced that computers ought to help with this problem. The idea is that visualizations, even if they are interactive, aren't very useful. Instead, the learner should iteratively build and play with a simple version of a model (a microworld) until the learner gets into the full-fledged model. Preferably by programming the model itself. It's sad that this idea never caught much traction beyond educating children.
- Noseshine 10y ago
  I have not check out these videos in particular, but when I went through Khan Academy I thought they were doing a remarkable job at explaining. Try https://www.khanacademy.org/math/differential-equations/laplace-transform https://www.khanacademy.org/math/differential-equations/lapl...
- kalid 10y ago
  Kalid from BetterExplained here, my quick intuition: The Fourier Transform breaks a signal into its "cycle recipe" (what circular paths are present?). The LaPlace Transform breaks a signal into its "spiral recipe". Circles are made from a type of exponential (given by e^ix), and spirals are the more general version, where the radius changes (if s=a+bi, then e^is = e^a * e^bi, aka a circular path where the radius changes exponentially). The LaPlace transform actually deals with decaying spirals (negative s) -- why is this useful? Well, perfect circles that never decay (the Fourier Transform) are nice for analyzing audio samples, as in music. (Repeated drumbeat throughout the song.) Decaying spirals model things in the real world, where friction, etc. dampen the signal over time. The Laplace transform can cleanly represent this scenario, whereas you need an infinite number of cancelling terms in the Fourier Transform to represent the "decays over time" setup. Engineering applications prefer Laplace, compression mechanisms may prefer Fourier. (Separately, Laplace/Fourier make differential equations easier to solve by writing functions in terms of exponentials, which are easy to derive/integrate. The Laplace transform is more general and powerful in this regard, since it can handle any rate of decay, including 0. The Fourier Transform is embedded within the Laplace.) Just some quick thoughts from an amateur on this :).
saeranv 10y ago
When I was taking linear algebra and calculus in university, I found that there was a lot of focus on deriving formulas from underlying principles, with the notion that this constituted a "fundamental" understanding of the mathematic concept. I got quite good at being able to derive formulas for anything, and did well enough to scrape by on my exams. However the concepts didn't really stick with me. Going through Khalid's site I quickly discovered I had a terrible intuitive understanding of mathematical concepts, almost embarrassingly so. Somehow, derivation from first principles doesn't quite capture intuitive insights for me, especially once I start worked at higher levels of abstraction removed from easily understood foundations (i.e. multi-dimensional vectors). The two things that I found most helpful in relearning math is (1) building up a foundation for mathematical concepts through betterexplained's intuitive method and (2) turning it into code as soon as possible. For the latter, I have a side project that is a sort of platform to test all my various ideas, from city performance modeling, to procedural form generation, where I am constantly trying to rework or tweak with new math formulas. It's amazing how much more efficient and useful this is as a learning method.
- Silhouette 10y ago
  Unfortunately, university lecturers in many subjects, including mathematics, are often doing that job only because they have to as part of their main research position, not because they actually want to or have any aptitude for it. There are some great lecturers who are happy exceptions, but they are few and far between in my experience. The sooner traditional universities and their ineffective, anachronistic teaching practices die out as the main form of tertiary academic education, the better. They could be replaced tomorrow by some combination of recorded lectures given by presenters who are actually good and in-person tuition given by people who can actually teach and care about their students' education, and I suspect absolutely nothing of value would be lost. The students would be both better educated and probably much better off financially, while the academics with a talent for research but not for teaching could make better use of their time and skills.
  - rahimnathwani 10y ago
    "academics with a talent for research but not for teaching" Apparently, good teaching doesn't require specific talent. It is a learned skill: http://www.economist.com/news/leaders/21700383-what-matters-schools-teachers-fortunately-teaching-can-be-taught-how-make-good http://www.economist.com/news/leaders/21700383-what-matters-...
bbcbasic 10y ago
Hard to fully get the Haskell Monad with analogies. The way to understand them is to use them. Coming to think of it same for OO. All those silly Dog is an Animal examples spring to mind.
- a_imho 10y ago
  I agree, if you want to learn something, you have to spend your time and focus on it. There is really no other way. I can accept it can be more digestible for many if it is packaged nicely in method X. Helping people learn is a very noble goal, but it should come with a fair warning there is no shortcut in understanding.
kitd 10y ago
Interesting article. I think I'm going to try explaining git branching/merging to newcomers via interpretative dance in future.
kristianp 10y ago
Anyone want to explain the Y combinator with this method? I find the wikipedia article on it completely inscrutable.
zump 10y ago
Does anyone have a link that summarizes this new field of "learning methods?" How does it compare to "How to Solve It"?
wingerlang 10y ago
Cool. I am currently learning something new and something that have stuck with me is the "if you can explain it, you know it". So while I am learning I am writing a set of instructions about what I am learning and some of what I have written down seems to resemble parts of this article. Some analogy, visualisations and plain english.
supergirl 10y ago
Analogies are dangerous in math. They give you the illusion that you understand, but you actually don't.
- kalid 10y ago
  Only if you stop at the analogy :). Last step is Technical Definition.
copperx 10y ago
I see one thing missing from the ADEPT method, which is "what's the story?" in the literal sense. Storytelling is one of the most powerful learning techniques and even a self-learner can create a story about the concept to be learned. The story doesn't need to be picturesque; even a dry story is much more useful than just the facts and description. Some of the examples they provide are stories ("Academic progress on imaginary numbers took off only after the diagrams were made!"), but the notion of teaching with a story isn't made explicit in the steps of the method.
- kalid 10y ago
  Great point. I enjoy using stories, history, humor as effective tactics for presentation. ADEPT is mainly about the raw ingredients I find helpful.

189 points by jhund 10y ago

deleted 10y ago

[deleted]

Excellent! I always think that people, like myself, that work with somewhat abstract and/or complex concepts need to improve our ability to explain them. Really happy to see a concrete method to do this.

hodgesrm 10y ago

Great article! This is the most intuitive description of imaginary numbers I have ever read. I'm going to try the same technique with Software Defined Networking (SDN), which has been on my "must figure it out" list for a while. :)

joelg236 10y ago

Fourier transformations clicked for me from your previous articles, this outline really shows the skill of "sharpening" rather than "building" knowledge. Helpful for young kids to adults alike.

thomasahle 10y ago
I had the same experience. However later when I encountered new properties of fourier transforms, such as the convolution theorem, fast fourier transform and the fourier transform of boolean functions, I felt my acquired intuition no longer fitted. Did you also experience this? If so, how did you get past it to that "next level"?

karimdag 10y ago

Having skimmed the article I want to ask: How about the first principles method ? How does this [ADEPT] compare to it [fp] ?

Silhouette 10y ago
It seems the main point being made by the article is that even if you are going to teach principles, it can be more effective to start by giving some context and motivation before getting into the detailed technical explanations. Deriving results from first principles may well result in better understanding than simply learning results and proofs by rote, but it's still useful to have some indication of why those principles might be useful and relevant as well.
- kalid 10y ago
  Exactly. Even if teaching or reasoning from first principles, you would explain them via analogies, diagrams, examples, etc. Teaching from first principles solely from the technical definition wouldn't be very pleasant for most.

theobon 10y ago

I'd love to seen an ADEPT method explanation of Laplace Transforms. I got through most of math fairly easily by having a mental model of what was going on and could always check that I was on the right track as it made sense in my mental model. However, when I got to Laplace transforms I never figured out how to visual what that meant. Everything collapsed into transform into the magical space where you can do some things easier and then you can transform out into a new place. I could never be sure of how I got from a to b without a tedious examination of every step to ensure I applied the rules correctly. I'd love to have a mental model for Laplace Transforms. As a generalization, how does one explain things where no good mental model exists?

copperx 10y ago
> As a generalization, how does one explain things where no good mental model exists? Papert et al. are convinced that computers ought to help with this problem. The idea is that visualizations, even if they are interactive, aren't very useful. Instead, the learner should iteratively build and play with a simple version of a model (a microworld) until the learner gets into the full-fledged model. Preferably by programming the model itself. It's sad that this idea never caught much traction beyond educating children.
Noseshine 10y ago
I have not check out these videos in particular, but when I went through Khan Academy I thought they were doing a remarkable job at explaining. Try https://www.khanacademy.org/math/differential-equations/laplace-transform https://www.khanacademy.org/math/differential-equations/lapl...
kalid 10y ago
Kalid from BetterExplained here, my quick intuition: The Fourier Transform breaks a signal into its "cycle recipe" (what circular paths are present?). The LaPlace Transform breaks a signal into its "spiral recipe". Circles are made from a type of exponential (given by e^ix), and spirals are the more general version, where the radius changes (if s=a+bi, then e^is = e^a * e^bi, aka a circular path where the radius changes exponentially). The LaPlace transform actually deals with decaying spirals (negative s) -- why is this useful? Well, perfect circles that never decay (the Fourier Transform) are nice for analyzing audio samples, as in music. (Repeated drumbeat throughout the song.) Decaying spirals model things in the real world, where friction, etc. dampen the signal over time. The Laplace transform can cleanly represent this scenario, whereas you need an infinite number of cancelling terms in the Fourier Transform to represent the "decays over time" setup. Engineering applications prefer Laplace, compression mechanisms may prefer Fourier. (Separately, Laplace/Fourier make differential equations easier to solve by writing functions in terms of exponentials, which are easy to derive/integrate. The Laplace transform is more general and powerful in this regard, since it can handle any rate of decay, including 0. The Fourier Transform is embedded within the Laplace.) Just some quick thoughts from an amateur on this :).

saeranv 10y ago

When I was taking linear algebra and calculus in university, I found that there was a lot of focus on deriving formulas from underlying principles, with the notion that this constituted a "fundamental" understanding of the mathematic concept. I got quite good at being able to derive formulas for anything, and did well enough to scrape by on my exams. However the concepts didn't really stick with me. Going through Khalid's site I quickly discovered I had a terrible intuitive understanding of mathematical concepts, almost embarrassingly so. Somehow, derivation from first principles doesn't quite capture intuitive insights for me, especially once I start worked at higher levels of abstraction removed from easily understood foundations (i.e. multi-dimensional vectors). The two things that I found most helpful in relearning math is (1) building up a foundation for mathematical concepts through betterexplained's intuitive method and (2) turning it into code as soon as possible. For the latter, I have a side project that is a sort of platform to test all my various ideas, from city performance modeling, to procedural form generation, where I am constantly trying to rework or tweak with new math formulas. It's amazing how much more efficient and useful this is as a learning method.

Silhouette 10y ago
Unfortunately, university lecturers in many subjects, including mathematics, are often doing that job only because they have to as part of their main research position, not because they actually want to or have any aptitude for it. There are some great lecturers who are happy exceptions, but they are few and far between in my experience. The sooner traditional universities and their ineffective, anachronistic teaching practices die out as the main form of tertiary academic education, the better. They could be replaced tomorrow by some combination of recorded lectures given by presenters who are actually good and in-person tuition given by people who can actually teach and care about their students' education, and I suspect absolutely nothing of value would be lost. The students would be both better educated and probably much better off financially, while the academics with a talent for research but not for teaching could make better use of their time and skills.
- rahimnathwani 10y ago
  "academics with a talent for research but not for teaching" Apparently, good teaching doesn't require specific talent. It is a learned skill: http://www.economist.com/news/leaders/21700383-what-matters-schools-teachers-fortunately-teaching-can-be-taught-how-make-good http://www.economist.com/news/leaders/21700383-what-matters-...

bbcbasic 10y ago

Hard to fully get the Haskell Monad with analogies. The way to understand them is to use them. Coming to think of it same for OO. All those silly Dog is an Animal examples spring to mind.

a_imho 10y ago
I agree, if you want to learn something, you have to spend your time and focus on it. There is really no other way. I can accept it can be more digestible for many if it is packaged nicely in method X. Helping people learn is a very noble goal, but it should come with a fair warning there is no shortcut in understanding.

kitd 10y ago

Interesting article. I think I'm going to try explaining git branching/merging to newcomers via interpretative dance in future.

kristianp 10y ago

Anyone want to explain the Y combinator with this method? I find the wikipedia article on it completely inscrutable.

zump 10y ago

Does anyone have a link that summarizes this new field of "learning methods?" How does it compare to "How to Solve It"?

wingerlang 10y ago

Cool. I am currently learning something new and something that have stuck with me is the "if you can explain it, you know it". So while I am learning I am writing a set of instructions about what I am learning and some of what I have written down seems to resemble parts of this article. Some analogy, visualisations and plain english.

supergirl 10y ago

Analogies are dangerous in math. They give you the illusion that you understand, but you actually don't.

kalid 10y ago
Only if you stop at the analogy :). Last step is Technical Definition.

copperx 10y ago

I see one thing missing from the ADEPT method, which is "what's the story?" in the literal sense. Storytelling is one of the most powerful learning techniques and even a self-learner can create a story about the concept to be learned. The story doesn't need to be picturesque; even a dry story is much more useful than just the facts and description. Some of the examples they provide are stories ("Academic progress on imaginary numbers took off only after the diagrams were made!"), but the notion of teaching with a story isn't made explicit in the steps of the method.

kalid 10y ago
Great point. I enjoy using stories, history, humor as effective tactics for presentation. ADEPT is mainly about the raw ingredients I find helpful.