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My objection to this argument is that it seems to present "comprehensible" as the default outcome, and then derive confusion as a result of problematic thinking

by scythe 5y ago

My objection to this argument is that it seems to present "comprehensible" as the default outcome, and then derive confusion as a result of problematic thinking. Anyone who has actually tried to teach students knows this is false. Merely trying to be understood fails with high probability. The average math or physics grad student upon entering already knows more than they have any chance of explaining thoroughly; distinguishing between senior and junior professors puts that line much further away than it really is. It's plausible that a sort of follow-the-template dynamic entrenches bad pedagogy, but I would think that the reason authors defensively stick to the old patterns is not because they worry about being judged, but rather the concern that they will do students a disservice if they are not "better than the Beatles": https://pubmed.ncbi.nlm.nih.gov/22378269/ https://pubmed.ncbi.nlm.nih.gov/22378269/ In other words, rather than risk being blamed for using a progression that works poorly, it's safer to follow the old patterns, so that tradition is blamed instead — nobody ever got fired for teaching IBM^W the geometry sandwich.

hdjjhhvvhga 5y ago
OK, a fair point. Let me be specific. What I consider a good math book for undergraduate students should have the following: - Explain the reason first instead of jumping into the definition straight away. I'm not taking about applications in physics etc., just a simple sentence like, "We have to learn series first in order to understand limits, and limits are necessary for understanding differentiation." Just one short sentence is enough to create a map in my mind and actually give me a decent reason to learn the topic. Seems obvious? Most math books chapters start with a definition. - Give examples. Really. How am I going to even remember the topic if you have failed to give even one example? - Give exercises for self-study. This is where the actual learning happens: at this point I can text whether I understood the theory or not. Moreover, it is through exercising that retention happens. Without exercises I can force myself to learn 50 pages and have only a vague memory of it the next day. - Provide the solutions to the exercises. I get it, if it's a textbook, you want to separate them - that's fine. But not providing them at all means the books is only half-useful for self-study. If a book has all these, I already consider it decent enough. Additional points for explaining particularly difficult points in more detail (good profs know well where their students are lost most often). If it makes sense, providing examples of practical application in sciences is always useful as it gives me some mental anchors connecting ideas and helping them to stick.

by scythe 5y ago

hdjjhhvvhga 5y ago

OK, a fair point. Let me be specific. What I consider a good math book for undergraduate students should have the following: - Explain the reason first instead of jumping into the definition straight away. I'm not taking about applications in physics etc., just a simple sentence like, "We have to learn series first in order to understand limits, and limits are necessary for understanding differentiation." Just one short sentence is enough to create a map in my mind and actually give me a decent reason to learn the topic. Seems obvious? Most math books chapters start with a definition. - Give examples. Really. How am I going to even remember the topic if you have failed to give even one example? - Give exercises for self-study. This is where the actual learning happens: at this point I can text whether I understood the theory or not. Moreover, it is through exercising that retention happens. Without exercises I can force myself to learn 50 pages and have only a vague memory of it the next day. - Provide the solutions to the exercises. I get it, if it's a textbook, you want to separate them - that's fine. But not providing them at all means the books is only half-useful for self-study. If a book has all these, I already consider it decent enough. Additional points for explaining particularly difficult points in more detail (good profs know well where their students are lost most often). If it makes sense, providing examples of practical application in sciences is always useful as it gives me some mental anchors connecting ideas and helping them to stick.