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Higher Math for Beginners (1987)

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Re: Higher Math for Beginners (1987)

#71

Post by Jensson »

Mandelmus wrote: post #22
Jensson wrote: post #19

Earlier quoted context omitted.

Has it actually improved though? Every study I've seen says students are worse at maths today than 30 years ago, so to me it doesn't look like all that pedagogy research improved things. If things actually got better we should have strong evidence supporting that. Images are prettier, sure, but do students who study using modern books actually understand the material better after the course is done?

I think attention spans have shortened (which is arguably devastating for maths), and the materials considered "state of the art in modern pedagogy" are the ones that take that into account in ways that a book from 1987 does not.

As someone who had a hard time focusing in school, modern books with lots of text actually made it harder to focus than books with less text and more information per word. I can read 20 words and then think about those, I can't read the same information if it is spread out and hidden within a 2000 words text.

So maybe kids has problems focusing partially due to modern pedagogy? Every word you write down has a cost to the reader, and the less attention span the reader has the more that cost matters. Drown them in too many words and they will just zone out since their attention span didn't last long enough for them to reach the important parts of the text.

Re: Higher Math for Beginners (1987)

#72

Post by pfortuny »

Mandelmus wrote: post #22
Jensson wrote: post #19

Earlier quoted context omitted.

Has it actually improved though? Every study I've seen says students are worse at maths today than 30 years ago, so to me it doesn't look like all that pedagogy research improved things. If things actually got better we should have strong evidence supporting that. Images are prettier, sure, but do students who study using modern books actually understand the material better after the course is done?

I think attention spans have shortened (which is arguably devastating for maths), and the materials considered "state of the art in modern pedagogy" are the ones that take that into account in ways that a book from 1987 does not.

Drill exercises require very little attention time but are the keybto learning a topic and understanding it. This is nothing new but it is usually despised because “boring”…

Re: Higher Math for Beginners (1987)

#73

Post by ivansavz »

TheFreim wrote: post #45
k__ wrote: post #39

My experience with learning math is that the first months are all about backtracking. You have to fill all your holes. It's basically one big graph of concepts. The tricky part is, most beginners simply don't know how to navigate that graph. They see complex numbers with their exponentials and cos/sin forms and shut down. They can learn all these concepts no problem, but finding what they need to learn defeats them.

Last time I took math courses was high school, algebra 2 or geometry. Do you have any resources you can suggest for not only going forward but also filling in the gaps that I've forgotten or never filled?

disclaimer: self-promotion ahead, highly relevant but still...

> RE: resources for filling in the gaps

I recently published a book titled No Bullshit Guide to Mathematics that has precisely the goal of reviewing concepts form high school math for adults. Context: I was a private tutor at university for many years, so I know how common it is for university students not to remember anything from high school and struggle a lot, even though a few weeks of review would bring them back up to speed.

The book's websie is here https://nobsmath.com/ and you can see an extended PDF preview of it here https://minireference.com/static/excerpts/noBSmath_v5_previe... (see my other comment for links to the concept maps).

Once you have the high school math review done and solved some exercises and problems, you'll be in good shape for the other two books in the series No Bullshit Guide to Math & Physics, which covers mechanics and calculus, and the No Bullshit Guide to Linear Algebra. You can easily find links if you search for them and see reviews on the amazons.

Re: Higher Math for Beginners (1987)

#74

Post by codetrotter »

yuuu wrote: post #66
codetrotter wrote: post #9

Earlier quoted context omitted.

The book in the updated link [1] does not have the problem that the old link had I think, if you were talking about how for example on page 358 the page had become split so that the rightmost part of the page had been cut off and placed on the left side of the page. I didn’t check the other pages because I’m on mobile, but since page 358 looks good in the new link the others might too. [1]: https://archive.org/detail…

Thanks for getting me flagged by completely overhauling your comment without recognizing its original content.

wut?

Re: Higher Math for Beginners (1987)

#75

Post by BeetleB »

BossingAround wrote: post #17
qsort wrote: post #15

Earlier quoted context omitted.

Why would you say that? The kind of mathematics that book presents has barely changed in the last 200 years. I would doubt there's much difference to speak of at all.

Because while the field of mathematics has probably not changed, the field of didactics has changed drastically, and the student expectations in 1980s and 2021 will be also drastically different.

I doubt math professors who write textbooks that are not meant for the mass public (i.e. not part of a state mandated curriculum) follow the field of didactics.

I've read math textbooks from the 60s onwards. I do not see a trend vs time.

Re: Higher Math for Beginners (1987)

#77

Post by hdjjhhvvhga »

scythe wrote: post #62
hdjjhhvvhga wrote: post #43

Earlier quoted context omitted.

Having read numerous books on various aspects of mathematics written by the academia, my pet theory is that there are two kinds of people who write incomprehensible math books: - Senior professors who actually suffer from the curse of knowledge and really forgot how it is not to know certain things, so they make tons of assumptions that are obvious to them. - Junior profs who could actually explain the topics in an a…

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; dis…

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.

Re: Higher Math for Beginners (1987)

#78

Post by mindcrime »

ivansavz wrote: post #73
TheFreim wrote: post #45

Earlier quoted context omitted.

Last time I took math courses was high school, algebra 2 or geometry. Do you have any resources you can suggest for not only going forward but also filling in the gaps that I've forgotten or never filled?

disclaimer: self-promotion ahead, highly relevant but still... > RE: resources for filling in the gaps I recently published a book titled No Bullshit Guide to Mathematics that has precisely the goal of reviewing concepts form high school math for adults. Context: I was a private tutor at university for many years, so I know how common it is for university students not to remember anything from high school and struggl…

Nothing wrong with a little self-promotion now and then. FWIW, I appreciate it, and I just ordered a copy of your No Bullshit Guide to Mathematics.

Re: Higher Math for Beginners (1987)

#79

Post by gopher_space »

ivansavz wrote: post #50
k__ wrote: post #39

My experience with learning math is that the first months are all about backtracking. You have to fill all your holes. It's basically one big graph of concepts. The tricky part is, most beginners simply don't know how to navigate that graph. They see complex numbers with their exponentials and cos/sin forms and shut down. They can learn all these concepts no problem, but finding what they need to learn defeats them.

> It's basically one big graph of concepts True that. I have created a bunch of concept maps for my books in order to show readers this graph. It's really useful to find your way in a new field, to keep track of your progress, and also to look ahead into the the concepts that are coming up. Here are the links to the concept maps: High school math: https://minireference.com/static/conceptmaps/math_concepts.p... Mechan…

I work alongside different industries and a hobby of mine is getting the people I work with to break down their domain for me. You've given me some good examples for organization, I have a lot of different media but everything would translate to concept maps, but I don't understand the 'graph' term you and OP are using. I found two definitions, neither of which seem like a perfect match.

Is this an analogy? Would I be able to apply the concept to my project if I dug into it?

Re: Higher Math for Beginners (1987)

#80

Post by mindcrime »

amelius wrote: post #63

Why is this called "higher math"? It mostly covers high-school calculus and physics. And how would you call more advanced math?

There really isn't any universally accepted definition of what "higher math" means. To mathematicians it seems to be something of a synonym for "proofs based maths", but for the rest of us, plenty of people use "higher math" to refer to Calculus and up. But in that sense, "higher" will always just be relative to where you already are, so honestly it's not a particularly useful term. But personally I don't think it's anything worth getting to worked up about.
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