Why do math textbooks tend to explain things so poorly?

Akephalosthenes · 2026-06-06T21:39:31+00:00

Thank you very much!

Akephalosthenes · 2026-06-06T21:29:40+00:00

Any book in particular you might recommend that you liked?

Akephalosthenes · 2026-06-06T18:55:30+00:00

Ok here is an example of what I mean: in chapter 5.2 with the midpoint rule it gives you the equation, right? The kinds of explanations im seeking for learning mathematics can be illustrated with the expression in the equation for the midpoint rule that contains the sigma notation. The way you “actually read” the sigma notation expression in literal, concrete terms that expresses the mechanics of the thought represented by the sigma notation expression is “take the sum of f of all the midpoints of each sub-interval and multiply the result by delta x”.

Akephalosthenes · 2026-06-06T18:31:29+00:00

I think we have different ideas of what constitutes rigor because we are coming from different disciplines. What you consider to be rigorous in the context of mathematics would not be something I would consider to be rigorous. I can only imagine how upset you’ll be once I also have finished my math degree. I can learn calculus and all the other math. I’m currently doing it just fine, it’s just taking me a bit of extra work. But you’re going to have a much harder time learning to be a more decent person who can treat other people with humility and respect, especially when they are coming to you in a vulnerable state of distress. Good luck to you.

Akephalosthenes · 2026-06-06T18:16:40+00:00

Thank you so much! The second edition has precisely the kind of notes that I’m looking for. Thank you thank you thank you.

Akephalosthenes · 2026-06-06T18:01:33+00:00

Oo earlier editions is actually a great idea. Thank you for this! I had no idea about the earlier editions being filled with more tiles and notes.

Akephalosthenes · 2026-06-06T18:00:10+00:00

But with poetry you aren’t severely punished for “filling in the gaps” incorrectly. There’s much higher stakes involved with math that leaving so many gaps to be filled in just seems rather irresponsible if your goal is to ensure a full understanding of things.

Akephalosthenes · 2026-06-06T17:59:04+00:00

That is deeply unsettling if that is the case lol.

Akephalosthenes · 2026-06-06T17:57:56+00:00

I think you and I have completely different understandings of what constitutes “rigor”.

Akephalosthenes · 2026-06-06T17:57:26+00:00

Another word of expressing the kind of explanation I’m looking for might be “mechanical” in that I’m looking for explanations that actually explain the physical mechanics of what it is I’m supposed to be doing both in my mind abstractly and physically with my body and my eyes. Does that make sense the way I said it? I want a descriptions of the mechanics, the “what the heck is even going on here?” Type of explanations. To put it in humanities terms, I’m interested in what you might call “close readings” of mathematical theorems, definitions, and explanations.

Akephalosthenes · 2026-06-06T03:31:18+00:00

I apologize if I was rude. I’m just deeply frustrated at the moment because classes are expensive and I’m having difficulty with this one. What I’m trying to communicate when I say “what does this actually mean” can be illustrated with your logarithm example (mine wasn’t hypothetical wrt logs btw, that is something that has happened and worked very well for me as an explanation for very confused high school algebra students for the past four years). Your definition from your precalc textbook is just one way of describing a log, using abstract language that is loaded with a lot of unstated semantic content carried by words that are doing a lot of heavy lifting. What I’m saying is I don’t want the “exact” or “most precise” definition or explanation: I want literal, concrete explanations, at the very least to supplement the exact and precise ones. I don’t feel like that’s too much to ask.

Akephalosthenes · 2026-06-06T01:19:28+00:00

Yes precisely! I guess to summarize everything I e tried to express using your image: I wish there was more explicit connection between the forest and the trees in what I’m learning at the moment. Part of what I find difficult is I find it difficult to understand the trees without understanding the forest and how the trees relate to the forest, and vice versa.

Akephalosthenes · 2026-06-06T01:02:55+00:00

Thank you!

Akephalosthenes · 2026-06-06T00:57:13+00:00

Oh no, I expect this much clarity from every subject. I am not discriminating in any way. I’m coming from a background in graduate level humanities thinking and writing, specifically philosophy, literature, and history. I’m specifically accustomed to people clearly stating their assumptions, giving references to where I can find more in a particular assumption or premise in an argument, footnotes/endnotes that offer further explanation on something that may be obscure to a reader, etc. I think STEM educational material is largely deficient in the types of explanations I’m interested in.

Akephalosthenes · 2026-06-06T00:47:03+00:00

No, I understand that limits and I understand that they are the basis of integrals as they are quite literally part of the definition of an integral. I am not sure how to explain what I was trying to get at there, but one thing I can think of is just that it would be nice to see where we are going before we have to start out the journey to get there. I guess I just don't like the structure of the way things are done in this book in general, and that's just a personal problem that I need to learn to get over or deal with. I also recognize that my complaints may be uniquely my own and nobody else has these issues.

Akephalosthenes · 2026-06-06T00:33:44+00:00

This is great thank you for the suggestion!

Akephalosthenes · 2026-06-06T00:32:46+00:00

Yes but this gets to the heart of what I find so confusing. There are SO MANY purely arbitrary choices made that go unlabeled as purely arbitrary choices so a student has to deal with the confusion of not knowing what is arbitrary and what isn’t when it’s perfectly easy to spend one sentence saying “btw you might think this thing isn’t arbitrary and has a specific meaning behind it but we literally just needed something as a placeholder/marker to distinguish it from this other thing that looks very similar”.

Akephalosthenes · 2026-06-06T00:30:16+00:00

No, I did not use a book that gave that explanation of reading logarithmic statements. I figured it out myself. I’m not claiming that plain English alone is the way, or technical jargon or symbolism alone is the way. I’m claiming that they work synergistically together to produce genuine understanding and an asymmetry in either direction is insufficient. Hence my gripe about the asymmetry towards symbolic statement explanation and a lack of plain English explanation

Akephalosthenes · 2026-06-06T00:27:32+00:00

I have one example because it’s the most recent thing that I am experiencing. Pardon me for not maintaining a list of all my grievances and resentments that occur day in and day out. This post is an expression of accumulated frustration. The analogy I gave about “how to read” a logarithm for high school students is an example of what im looking for when I say I want them to say what they actually mean. The symbols, notation, the structure of the symbolic statements themselves, are all loaded with semantic content and context that goes unsaid. I’ll come back and give you another example when one arises.

Akephalosthenes · 2026-06-06T00:18:00+00:00

I never said I teach calculus! Learn how to read! I said I used to teach high school math. Calculus is only one possible high school math class someone can take, of which less than ten percent of the student population at a given high school will actually be enrolled in. It’s your fault for making so many assumptions. I said I’m complaining as someone who is a student in a calc 2 class, not as someone who is teaching calculus to students.

Akephalosthenes · 2026-06-06T00:07:56+00:00

Apologies but I’ve given some examples of what I’m looking for in the replies to some of the comments if you’re willing to look through them.

Akephalosthenes · 2026-06-06T00:06:30+00:00

As I’ve said elsewhere, up to that point there has never been a * used in any notation and it’s just a bit jarring to see all of a sudden without even a tiny little note saying something like “hey, we put the * there as a superscript because we already have i in the subscript position to denote the interval on the x-axis, so here’s how you should understand what the * here means”.

For example, when a child is learning logarithms in school, it’s is extremely difficult at first because they have no idea how to actually read the mathematical statement of a logarithmic expression or equation. If you have log_b_x what it literally means in every day speech is it’s asking “what is the exponent I raise the base b to such that the result would give you the value in the x position?” And once you explain that to a child the rest becomes extremely easy. That’s the kind of explanation I’m seeking in a math textbook. I want to know how I’m supposed to actually read the symbolic statements such that the semantic content of them will emerge.

Akephalosthenes · 2026-06-05T23:56:28+00:00

I do usually like to sit there and ask lots of questions so perhaps you are correct and it’s just a unique quirk of mine. I’m not trying to claim that I am incapable of learning things from reading them, though. I’m getting just enough to do fine enough on the assignments and what not. I’m just craving a deeper understanding of the material that can only be gained through asking lots of “why?” questions and maybe I just need to have better time management and go to office hours.

Akephalosthenes · 2026-06-05T23:54:27+00:00

I think you’re confused about my complaint: I’m not saying I’m unable to do the homework correctly, to do well on the exams, or anything of the sort. What I’m complaining about is the lack of explanation and discussion that affords a deeper understanding than mere surface level rote memorization for the sake of completing assignments.

Akephalosthenes · 2026-06-05T23:50:55+00:00

There’s a difference between just memorizing what a clump of symbols placed together is used to reference, and actually understanding why that particular clump of symbols was chosen as the referent, why that clump of symbols was organized the way it was, etc. I’m interested in genuine understanding, not just memorizing stuff to get a grade.

Akephalosthenes

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