Another idea for math study is to look at proofs and try to distinguish between steps that are just mechanical calculation vs steps that are leaps of insight.
With book-based arguments, like a work of philosophy, I find it helps to identify the point of a paragraph and then think beyond it. I like to do that with “Question Notes,” writing one question per paragraph where the paragraph in the text could be a valid answer to the question itself.
In an equation, I often start by imagining how the result changes as the variables change, or why the variables are as they are.
I wonder if this could be productive applied to strictly empirical findings, like the structure of RNA polymerase? Often I find that the textbook will present a structure, then point out the inferences from that structure to its function (and in biology, often the reverse—mRNA and genes were known to exist long before we identified their structure).
In any case, I agree that this is a whole other mode of relating with a text—one that I use, but haven’t focused on as a technique, perhaps because it’s not something that’s as easy to define and apply mechanically. Thanks.
Another idea for math study is to look at proofs and try to distinguish between steps that are just mechanical calculation vs steps that are leaps of insight.
With book-based arguments, like a work of philosophy, I find it helps to identify the point of a paragraph and then think beyond it. I like to do that with “Question Notes,” writing one question per paragraph where the paragraph in the text could be a valid answer to the question itself.
In an equation, I often start by imagining how the result changes as the variables change, or why the variables are as they are.
I wonder if this could be productive applied to strictly empirical findings, like the structure of RNA polymerase? Often I find that the textbook will present a structure, then point out the inferences from that structure to its function (and in biology, often the reverse—mRNA and genes were known to exist long before we identified their structure).
In any case, I agree that this is a whole other mode of relating with a text—one that I use, but haven’t focused on as a technique, perhaps because it’s not something that’s as easy to define and apply mechanically. Thanks.