5 ms·

I just love this guy's ADEPT method of exposition (Analogy, Diagram, Example, Plain English explanation, and just then Technical definition). [1] That is exact

I just love this guy's ADEPT method of exposition (Analogy, Diagram, Example, Plain English explanation, and just then Technical definition). [1] That is exactly how I like to be introduced to any new concept, in special when I'm a complete newcomer to the field and can't relate it to previous ideas in it. Judging by the reactions to the BetterExplained site, other people agree with that. [1] http://betterexplained.com/articles/adept-method/ http://betterexplained.com/articles/adept-method/

kalid 11y ago
Thanks! I was really hesitant to force an acronym (it actually started as ADE) but then I realized I could work my way up to the full technical definition. Really glad to hear it's resonating. (Sometimes things happen out of order, i.e. you start with a plain English definition. But the idea is to have all 5 parts if you want to truly master a concept.)
igravious 11y ago
I've found that I also need to understand the historical context/impetus... I need to be shown and eventually understand why something was developed when it was developed. I need chronology of thought and ideas. For instance, learning about Gödel's theorems without having the Hilbert back-story explained. Learning about Leibniz's and Newton's calculus without learning about infinitesimals. And so on. There's generally a reason _why_ concepts are born _when_ they are born. If you think about your maths classes, sometimes you're instructed to learn a method because it is useful and because it has real-world applications but it I don't think anybody is ever first taught algebraic geometry properly, if I may use that word. I don't think kids are taught the geometry is one thing and algebra is another and that different spaces can have different metrics. Am I making sense here? Do people see what I'm trying to get at? Am I arguing for HADEPT? :) (Historical context, Analogy, Diagram, Example, Plain English explanation, and just then Technical definition)
- kalid 11y ago
  Great point. I find myself looking at the history of the idea when writing up a post. Did you realize negative numbers were only accepted in the late 1700s? That the Fourier Transform was originally rejected as untrue when first presented, by world-famous mathematicians even? (Yet we require students to internalize it without issue in a single lecture.) Historical context is huge. I think I'm now stuck with this ADEPT name but maybe it fits into the Plain English portion :).
  - igravious 11y ago
    > Did you realize negative numbers were only accepted in the late 1700s? I did not know that! This makes total sense. I'd like to know more about that. When you think about it, only whole positive numbers make sense from a quantitative perspective. One thing, two things, three things, and so on. What's half-a-thing? Right? a half-a-thing is still just one thing, if you know what I mean. And how can no thing (nothing) be a number? And how can negative numbers be "numbers". It has always struck me that imaginary numbers are really badly named. Zero and the negative numbers are just as 'imaginary', equally unintuitive from a certain perspective. I applaud what you're doing. I think there is a metric-tonne of dogma and bad naming schemes in the standard maths curriculum. Remember in software engineering they say that naming things is one of the hardest parts of the task? I think the same applies to maths, perhaps more so.
    - kalid 11y ago
      Exactly! There's a quote from a famous mathematician at the time that the negatives "Darken the very whole doctrines of the equations". If positive is good, negative must be evil right? And how can "less than nothing" exist? I love the philosophical implications of it. Ugh, tell me about the naming. "Imaginary numbers?" How about "rotated numbers". Nobody complains "Hey, when will I ever use the second dimension?". But "imaginary numbers" are setup to be eye-rolled.
    - billbrown 11y ago
      I'd recommend "The Joy of x" by Steven Strogatz. It's full of that sort of story.
IkmoIkmo 11y ago
Agreed, but it depends. The analogy can make things harder if you're not intimately familiar with the analogy. Take the below, an excerpt from the explanation on prime numbers for example, and consider you know 0 chemistry (not unlikely if you're reading an intro on prime numbers): ----- > I'm no chemistry expert, but I can see a relationship to the primes. Chemical elements have properties based on their location in the periodic table of the elements: Atoms in group 8A (Neon, Argon) are the noble gases. They don't react and won't blow up in your face. Atoms in group 4A (Carbon, Silicon) bond well. They're great building blocks for other elements. Atoms in group 1 (Sodium, Potassium, etc.) are very reactive. Drop 'em in water and see them explode. And in organic chemistry there's an idea of a functional group: several atoms can determine the class of the entire molecule. For example: Alcohols are a certain carbon-hydrogen chain with an OH group at the end. Methanol, ethanol, and other alcohols share similar properties because of this OH functional group. Those are the basics, if I didn't mess it up. Now let's see what happens when we treat numbers like chemicals. First Example: Guessing Evenness In general, an organic chemical contains carbon (not quite, but it's a good starting point). No matter what elements you mix together, if you never add any carbon then you can't create an organic compound. ----- Anyway, a single example doesn't negate your point. I love analogies in learning, but one has to be careful to pick analogies from a level of understanding (way) below what you're trying to explain. I guess kids are introduced to primes and chemistry at roughly the same age, but I'd have picked a non-academic analogy to explain an academic concept. But even then, it's tricky. For example I've been confused by my fair share of 'sports analogies' in secondary school books, for sports I happened not to have ever tried or knew the rules for. But really, the analogy should be completely supplemental, and if possible marked off in a side box that people can, but not should, read for better understanding if it helps them. I find many school books do this really well, but I haven't seen it translated to web content as much somehow. For example, on Evenness he'll continue by explaining how if you have a factor of 2 in your number (e.g. 24 = 2^3 * 3), then no matter what, the number is even, likening it to an organic chemical which contains carbon no matter what (though, noting a caveat without going into it). I don't think that analogy is very strong, it's confusing if you don't know chemistry, and it's pretty redundant if you do. In fact I'd personally be better of without it, and understood Kalid's normal explanation without issue. Yet I had to read through something about Atoms in group 4A and their properties, unsure whether I could just skip it or whether it was important to grasp some larger point. Anyway I was already familiar with primes but my 12 year old self probably would've been confused with the chemistry analogy.

kalid 11y ago

Thanks! I was really hesitant to force an acronym (it actually started as ADE) but then I realized I could work my way up to the full technical definition. Really glad to hear it's resonating. (Sometimes things happen out of order, i.e. you start with a plain English definition. But the idea is to have all 5 parts if you want to truly master a concept.)

igravious 11y ago

I've found that I also need to understand the historical context/impetus... I need to be shown and eventually understand why something was developed when it was developed. I need chronology of thought and ideas. For instance, learning about Gödel's theorems without having the Hilbert back-story explained. Learning about Leibniz's and Newton's calculus without learning about infinitesimals. And so on. There's generally a reason _why_ concepts are born _when_ they are born. If you think about your maths classes, sometimes you're instructed to learn a method because it is useful and because it has real-world applications but it I don't think anybody is ever first taught algebraic geometry properly, if I may use that word. I don't think kids are taught the geometry is one thing and algebra is another and that different spaces can have different metrics. Am I making sense here? Do people see what I'm trying to get at? Am I arguing for HADEPT? :) (Historical context, Analogy, Diagram, Example, Plain English explanation, and just then Technical definition)

kalid 11y ago
Great point. I find myself looking at the history of the idea when writing up a post. Did you realize negative numbers were only accepted in the late 1700s? That the Fourier Transform was originally rejected as untrue when first presented, by world-famous mathematicians even? (Yet we require students to internalize it without issue in a single lecture.) Historical context is huge. I think I'm now stuck with this ADEPT name but maybe it fits into the Plain English portion :).
- igravious 11y ago
  > Did you realize negative numbers were only accepted in the late 1700s? I did not know that! This makes total sense. I'd like to know more about that. When you think about it, only whole positive numbers make sense from a quantitative perspective. One thing, two things, three things, and so on. What's half-a-thing? Right? a half-a-thing is still just one thing, if you know what I mean. And how can no thing (nothing) be a number? And how can negative numbers be "numbers". It has always struck me that imaginary numbers are really badly named. Zero and the negative numbers are just as 'imaginary', equally unintuitive from a certain perspective. I applaud what you're doing. I think there is a metric-tonne of dogma and bad naming schemes in the standard maths curriculum. Remember in software engineering they say that naming things is one of the hardest parts of the task? I think the same applies to maths, perhaps more so.
  - kalid 11y ago
    Exactly! There's a quote from a famous mathematician at the time that the negatives "Darken the very whole doctrines of the equations". If positive is good, negative must be evil right? And how can "less than nothing" exist? I love the philosophical implications of it. Ugh, tell me about the naming. "Imaginary numbers?" How about "rotated numbers". Nobody complains "Hey, when will I ever use the second dimension?". But "imaginary numbers" are setup to be eye-rolled.
  - billbrown 11y ago
    I'd recommend "The Joy of x" by Steven Strogatz. It's full of that sort of story.

IkmoIkmo 11y ago

Agreed, but it depends. The analogy can make things harder if you're not intimately familiar with the analogy. Take the below, an excerpt from the explanation on prime numbers for example, and consider you know 0 chemistry (not unlikely if you're reading an intro on prime numbers): ----- > I'm no chemistry expert, but I can see a relationship to the primes. Chemical elements have properties based on their location in the periodic table of the elements: Atoms in group 8A (Neon, Argon) are the noble gases. They don't react and won't blow up in your face. Atoms in group 4A (Carbon, Silicon) bond well. They're great building blocks for other elements. Atoms in group 1 (Sodium, Potassium, etc.) are very reactive. Drop 'em in water and see them explode. And in organic chemistry there's an idea of a functional group: several atoms can determine the class of the entire molecule. For example: Alcohols are a certain carbon-hydrogen chain with an OH group at the end. Methanol, ethanol, and other alcohols share similar properties because of this OH functional group. Those are the basics, if I didn't mess it up. Now let's see what happens when we treat numbers like chemicals. First Example: Guessing Evenness In general, an organic chemical contains carbon (not quite, but it's a good starting point). No matter what elements you mix together, if you never add any carbon then you can't create an organic compound. ----- Anyway, a single example doesn't negate your point. I love analogies in learning, but one has to be careful to pick analogies from a level of understanding (way) below what you're trying to explain. I guess kids are introduced to primes and chemistry at roughly the same age, but I'd have picked a non-academic analogy to explain an academic concept. But even then, it's tricky. For example I've been confused by my fair share of 'sports analogies' in secondary school books, for sports I happened not to have ever tried or knew the rules for. But really, the analogy should be completely supplemental, and if possible marked off in a side box that people can, but not should, read for better understanding if it helps them. I find many school books do this really well, but I haven't seen it translated to web content as much somehow. For example, on Evenness he'll continue by explaining how if you have a factor of 2 in your number (e.g. 24 = 2^3 * 3), then no matter what, the number is even, likening it to an organic chemical which contains carbon no matter what (though, noting a caveat without going into it). I don't think that analogy is very strong, it's confusing if you don't know chemistry, and it's pretty redundant if you do. In fact I'd personally be better of without it, and understood Kalid's normal explanation without issue. Yet I had to read through something about Atoms in group 4A and their properties, unsure whether I could just skip it or whether it was important to grasp some larger point. Anyway I was already familiar with primes but my 12 year old self probably would've been confused with the chemistry analogy.