I used a similar approach to learning chemistry at university level (undergraduate to PhD level, although my PhD drifted a bit from pure chemistry into computing and education). There were lots of situations where, to solve a problem, you needed the appropriate applied formula. Many (most?) students tried to memorise these formulae and the situations they applied in. I struggled to memorise them, so instead focused on how to derive the applied formula from a much smaller set of basic equations. Often there’s a mental trick that makes it easier—e.g. to derive the equation for surface tension of a liquid, you think about what happens if you split a cylinder of liquid in half. I found it a lot easier to remember that sort of thing than an equation. (I’ve not used that particular equation since an exam in 1991 or 1992, but I can still vividly remember the mental model to derive it.)
I can’t say that my approach was a better one in terms of getting good marks. When you have to answer specific questions—which you know will be drawn only from the set of situations you were taught—it’s much easier and quicker to produce the appropriate equation from your memory and apply it. With my approach, you have to spend valuable exam time deriving the equation before you can apply it. (You rarely got marks for deriving the correct equation.)
However, it has been enormously useful for dealing with real world problems beyond the constrained world of exams. My basic approach—work out what I want to know, think of all the equations that might help, then do a bit of thinking and dimensional analysis to see how to get an equation to relate them—is applicable even when you’ve never seen the precise equation you need. Or, indeed, when nobody has ever seen it, which is often the situation when you’re doing genesis research. It’s also extremely helpful for understanding when your equation might not be appropriate, since you only get the equation when you’ve thought a fair bit about the situation you’re trying to apply it to.
Also, in the real world these days, it’s trivial to look up an equation. If you’re doing any serious work that might require formulae, you’ll almost always be sat at a computer with an internet connection. It might be marginally quicker to produce the equation from memory, but the generic skill of being able to look up the right equation is much more widely applicable. It’s also, I suspect, less prone to trivial errors (e.g. misremembering a sign) for most people.
I’ve switched to this approach with maths over time. These days I wouldn’t dream of doing any serious algebra or calculus by hand—much easier, quicker and less error-prone to stick it in to Mathematica, Wolfram Alpha or whatever. Those systems know more tricky integrals than (almost?) any human. But I don’t do any research in maths, I just use maths in my research.
This ready access to information and symbolic mathematics certainly wasn’t the case when the people who taught me learned their basics—it was only becoming the case for some people when I learned them (early 90s). Luckily I was one of the early ones. Sadly, it appears to be taking a long time for the world of formal education to catch on to this shift in how knowledge work happens.
My intuition is that my focus on turning things in to transferable knowledge makes it more transferable. My subjective experience is certainly that this generic approach is valuable across domains, and it feels that that’s part of what’s enabled me to work in many different domains. But I’m not sure I have convincing evidence that it’s the case.
It definitely feels more personally satisfying to me, when I feel that I understand what I’m doing, rather than following a recipe, and have the skills to get to work on a totally-novel situation. But that’s a personal preference that is not universally shared. Though my guess is that it’ll be more widely shared among LWers than among the general population.
If you’re in a position to choose between these approaches (learn deeply and how to apply vs memorising large amounts), I’d strongly recommend learning deeply and how to apply it. It may well not get you the best exam marks, but it’ll set you up better for dealing with new situations, and that’s a more valuable long-term skill.
I used a similar approach to learning chemistry at university level (undergraduate to PhD level, although my PhD drifted a bit from pure chemistry into computing and education). There were lots of situations where, to solve a problem, you needed the appropriate applied formula. Many (most?) students tried to memorise these formulae and the situations they applied in. I struggled to memorise them, so instead focused on how to derive the applied formula from a much smaller set of basic equations. Often there’s a mental trick that makes it easier—e.g. to derive the equation for surface tension of a liquid, you think about what happens if you split a cylinder of liquid in half. I found it a lot easier to remember that sort of thing than an equation. (I’ve not used that particular equation since an exam in 1991 or 1992, but I can still vividly remember the mental model to derive it.)
I can’t say that my approach was a better one in terms of getting good marks. When you have to answer specific questions—which you know will be drawn only from the set of situations you were taught—it’s much easier and quicker to produce the appropriate equation from your memory and apply it. With my approach, you have to spend valuable exam time deriving the equation before you can apply it. (You rarely got marks for deriving the correct equation.)
However, it has been enormously useful for dealing with real world problems beyond the constrained world of exams. My basic approach—work out what I want to know, think of all the equations that might help, then do a bit of thinking and dimensional analysis to see how to get an equation to relate them—is applicable even when you’ve never seen the precise equation you need. Or, indeed, when nobody has ever seen it, which is often the situation when you’re doing genesis research. It’s also extremely helpful for understanding when your equation might not be appropriate, since you only get the equation when you’ve thought a fair bit about the situation you’re trying to apply it to.
Also, in the real world these days, it’s trivial to look up an equation. If you’re doing any serious work that might require formulae, you’ll almost always be sat at a computer with an internet connection. It might be marginally quicker to produce the equation from memory, but the generic skill of being able to look up the right equation is much more widely applicable. It’s also, I suspect, less prone to trivial errors (e.g. misremembering a sign) for most people.
I’ve switched to this approach with maths over time. These days I wouldn’t dream of doing any serious algebra or calculus by hand—much easier, quicker and less error-prone to stick it in to Mathematica, Wolfram Alpha or whatever. Those systems know more tricky integrals than (almost?) any human. But I don’t do any research in maths, I just use maths in my research.
This ready access to information and symbolic mathematics certainly wasn’t the case when the people who taught me learned their basics—it was only becoming the case for some people when I learned them (early 90s). Luckily I was one of the early ones. Sadly, it appears to be taking a long time for the world of formal education to catch on to this shift in how knowledge work happens.
My intuition is that my focus on turning things in to transferable knowledge makes it more transferable. My subjective experience is certainly that this generic approach is valuable across domains, and it feels that that’s part of what’s enabled me to work in many different domains. But I’m not sure I have convincing evidence that it’s the case.
It definitely feels more personally satisfying to me, when I feel that I understand what I’m doing, rather than following a recipe, and have the skills to get to work on a totally-novel situation. But that’s a personal preference that is not universally shared. Though my guess is that it’ll be more widely shared among LWers than among the general population.
If you’re in a position to choose between these approaches (learn deeply and how to apply vs memorising large amounts), I’d strongly recommend learning deeply and how to apply it. It may well not get you the best exam marks, but it’ll set you up better for dealing with new situations, and that’s a more valuable long-term skill.