What are the best books for re-learning math?

[MelvinDL86]

I am in the process of re-learning math to become a high school math teacher.

In school I never really tried or studied and would make C's or B's. I have pretty much forgotten everything, and plus I want to learn again from the ground up to better my understanding and how new learners learn etc.

So my question is which books do you all recommend that are easy to follow, precise, with the best explanations?

So far I am aware of the "For Dummies" books, "Practical Algebra", "Effortless Algebra", and "How to Ace Calculus: The Streetwise Guide"

Will need to books and materials on all the subjects (algebra 1 & 2, geometry, trigonometry, pre-calculus, and calculus)

Thanks in advance for any advice / recommendations.

 

[Lebombo]

You might get more feedback if you ask this in the Academic Guidance or Career Guidance sections of this forum. I have looked in the Algebra for dummies before. My opinion is there is NO shortcut to becoming proficient in math. Unless you are a natural born mathematical genius with formulas and concepts inherent within your conscious brain circuitry, then you'll need to dedicate lots of time. You'll have to learn each and every math rule, as unimportant or insignificant as one may seem, you will need to know each one for later math levels because they all come into play, sometimes when you least expect it. You may want to start with school assigned official textbooks instead of Algebra for dummies, or express math. And from there, ask questions, seek tutoring, and search for alternate explanations. Don't just memorize formulas without fully understanding them. Nobody can memorize all the formulas if they are only meaningless symbols and letters from which to plug in numbers to arrive at an answer which makes little to sense. You need to know how each formula and rule is derived or else you will not be successful math student let alone math teacher. In regard to the book titles you mention, in my opinion, those types of titles usually imply a brief overview of the math, but not the nitty gritty. I could be wrong though in that there may be non official school approved textooks that are of great use, but you have to get feedback from those who have much more expertise than me. What I do feel confident in mentioning is that seeking to become a high school math teacher in a shortcut "express" fashion is setting yourself up for failure. Math actually becomes very enjoyable when you pace yourself and do not allow yourself to be rushed to such a degree that you have to skip comprehending concepts just to start the next section. Understanding how a formula was developed and learning to derive it myself continually increases my appreciation for math, pulls me in, and makes me want to spend more time learning it (as opposed to trying to memorize letters), which further increases my knowledge. And the same is true for many people. Unfortunately, if you have a full time job outside of math as I have and/or other obligations that make it difficult to spend lots of time studying, don't let it become a reason to conclude that one particular rule or formula is not worth fully understanding. If anything, skip it and be sure to revisit it once you can. But keep in mind, you will soon realize you can't go too far beyond a topic without encountering it once again at a more advanced stage. So even if it takes 3 weeks to finally understand a sub-sub topic, then stick with it because you surely will not be able to understand further topics without understanding previous topics. Each formula builds upon previous concepts, rules, and formulas. Finally, in my opinion, you don't need to read books on how learners learn or "new" learners learn. That time would be better spend learning math by reading math and studying from math books. Good luck.

 

[jimmyly]

Yes you will need better books like lebombo said. Take a look in the textbooks section. There are good books in there

 

[462chevelle]

I am not a mathematical genious or going to school to be a math teacher. but here was my approach to relearning math. I got a college algebra and studied through it not really skimming but not really going in deep depth where I could do about 80 percent of the problems without looking back. then on to the next chapter. so that when I went to class I understood everything on a basic level and whenever something was explained I didn't know for sure before it was completely clear after lecture without much effort.

 

[Raze]

Google Paul's online math notes. I have used it for tutoring people wanting to learn those subjects (or relearn them). It goes from college algebra through differential equations. It is pretty solid, I think.

 

[462chevelle]

x2 pauls notes

 

[BOAS]

I am in the process of re-learning math to become a high school math teacher.

In school I never really tried or studied and would make C's or B's. I have pretty much forgotten everything, and plus I want to learn again from the ground up to better my understanding and how new learners learn etc.

So my question is which books do you all recommend that are easy to follow, precise, with the best explanations?

So far I am aware of the "For Dummies" books, "Practical Algebra", "Effortless Algebra", and "How to Ace Calculus: The Streetwise Guide"

Will need to books and materials on all the subjects (algebra 1 & 2, geometry, trigonometry, pre-calculus, and calculus)

Thanks in advance for any advice / recommendations.

Calculus made easy - Silvanus P Thompson, Martin Gardner

That's an excellent book for introductory calculus in my opinion.

 

[johnqwertyful]

http://carlossicoli.free.fr/L/Lang_S.-Basic_mathematics-Addison-Wesley(1971).pdf

Best book on basic math I've ever seen

 

[shelly22]

This book has been helping a lot of persons I think it might help you a lot.

https://www.amazon.com/dp/B00AQKZ6D0/?tag=pfamazon01-20

 

[jedishrfu]

Don't forget KA Stroud's books on Engineering Mathematics. Its broken into two parts:
- foundation topics (high school math review)
- program topics (college level calculus, diff eqns..)

What's unique about his approach is he uses small frames where some fact is explained, a problem is presented and the answer appears immediately in the next frame, sometimes with the reasoning to go with it. His book is designed for self-study at whatever pace you need and is a good review of key concepts.

https://www.amazon.com/dp/0831134704/?tag=pfamazon01-20

I've considered jumping to it myself but have refrained until I finish the Schaum's Vector Analysis book I'm currently struggling with. (trying to learn stuff from decades past)

 

[Abscissas]

My experience

Well, so far I've been doing about the same, except i never really learned it more slept through the classes. BUT i have found some very helpful sources, like khanacademy and The complete idiots guide to algebra, now the latter is somewhat iffy as i havn't finished it. I can say though the author explains the reasoning behind the equations and the whys of what your doing. Its filled with corny jokes which dosn't really bother me and it gives a lighthearted mood to the book. The information in it is pretty good but i don't have anything to compare it to. I don't think its good on its own but combined with something else like khanacademy (which i have nothing bad to say about it is wonderful and anyone and everyone learning should go to it) it is efficient especially if you take notes.

 

[Jorriss]

http://carlossicoli.free.fr/L/Lang_S.-Basic_mathematics-Addison-Wesley(1971).pdf

Best book on basic math I've ever seen

I came here to recommend this same text.

 

[mal4mac]

Why not go through the recommended high school textbooks? But be careful:

http://www.textbookleague.org/103feyn.htm

 

[Abscissas]

Why not go through the recommended high school textbooks? But be careful:

http://www.textbookleague.org/103feyn.htm

That made me loose faith in any school textbooks forever.

 

[mal4mac]

Don't forget KA Stroud's books on Engineering Mathematics...

Isn't that a bit too advanced? Might be better spending time on "how new learners learn etc.", with books like:

Why Johnny Can't Add Math by Morris Kline
Mathematics: A Very Short Introduction by Timothy Gowers

...plus actual school textbooks, based on "best evidence" that they work, from actual research on efficacy, for example:

http://www.bestevidence.org.uk/assets/Secondary_math_Oct_21_2008.pdf

This recommends the "Saxon math back-to-basics textbook" as the best resource, why not start there?

 

[AJKing]

I am in the process of re-learning math to become a high school math teacher.

Hey!

I passed high school math with a low C.

Years later, under new motivation, I relearned my math at Khan Academy. The mixture of watching succinct lectures and answering hundreds of questions for 2 weeks straight helped me achieve 98% when retaking Math 11 and Math 12.

I now study Mathematical-Phys and work as a Physics lab tech.

So, again, KhanAcademy.org/exercisedashboard
Start from the top.

 

[jedishrfu]

Isn't that a bit too advanced? Might be better spending time on "how new learners learn etc.", with books like:

Why Johnny Can't Add Math by Morris Kline
Mathematics: A Very Short Introduction by Timothy Gowers

...plus actual school textbooks, based on "best evidence" that they work, from actual research on efficacy, for example:

http://www.bestevidence.org.uk/assets/Secondary_math_Oct_21_2008.pdf

This recommends the "Saxon math back-to-basics textbook" as the best resource, why not start there?

I mentioned the book because it uses a programmed learning approach that is excellent for people relearning math. The first half of the book covers high school and the second half first and second year college which as a high school teacher would be good know in case a student wants to know about making the next step into college level math.

 

[kh.ebraheem]

** You'll have to learn each and every math rule, as unimportant or insignificant as one may seem,

** you will need to know each one for later math levels because they all come into play.
** Don't just memorize formulas without fully understanding them. Nobody can memorize all the formulas if they are only meaningless symbols and letters from which to plug in numbers to arrive at an answer which makes little to sense. You need to know how each formula and rule is derived or else you will not be successful math student let alone math teacher.
** "nitty gritty". I
** Math actually becomes very enjoyable when you pace yourself and do not allow yourself to be rushed to such a degree that you have to skip comprehending concepts just to start the next section.
** Unfortunately, if you have a full time job outside of math as I have and/or other obligations that make it difficult to spend lots of time studying, don't let it become a reason to conclude that one particular rule or formula is not worth fully understanding.
** If anything, skip it and be sure to revisit it once you can. But keep in mind, you will soon realize you can't go too far beyond a topic without encountering it once again at a more advanced stage.
** So even if it takes 3 weeks to finally understand a sub-sub topic, then stick with it because you surely will not be able to understand further topics without understanding previous topics.

Good luck.

Really, you did help me alot, nice words
you make me stick more and more in my way to master, learning every detail and every derivation.


Thanks

 

[kazzy]

I picked up a book called "Manga guide to Linear Algebra" and found it really helpful. I know its dramatically different from the books already mentioned here, but I found it really helped me prepare for the class. Paul's notes is good too though.

 

[jstad]

Something that you may want to consider is signing up for a university math class but only take that one class for the semester. Go to lecture and anything that you are confused on, write down in your notes and look up later. Paul's Online Notes, Kahn Academy are all great. PatrickJMT on YouTube is incredible. It will be a lot of work (hence why I suggest only taking that one class), but if you keep at it, the concepts begin to stick like glue.

The process I described above really never stops though. Learning and improving is a constant process.

As far as good books for self study, apparently Euler's books on algebra are great (and from what I've read on Amazon's "book preview" feature, I agree). I want to buy them myself but they're a little too pricey.

 

[urbano]

You'll have to learn each and every math rule, as unimportant or insignificant as one may seem, you will need to know each one for later math levels because they all come into play, sometimes when you least expect it. …... Understanding how a formula was developed and learning to derive it myself continually increases my appreciation for math, pulls me in, and makes me want to spend more time learning it (as opposed to trying to memorize letters), which further increases my knowledge. And the same is true for many people. Unfortunately, if you have a full time job outside of math as I have and/or other obligations that make it difficult to spend lots of time studying, don't let it become a reason to conclude that one particular rule or formula is not worth fully understanding. Each formula builds upon previous concepts, rules, and formulas. .

I'm in a similar situation, in that I have gone to learning maths again as an adult and while the odd piece of maths form here and there has stuck with me, I often can just plug in numbers to a formula and get an answer. ..BUT…if you asked me why it worked that way I'd be stumped and possibly not know the answer.

I personally believe it is where a lot of teaching falls over , in that it does;lt teach the why things work the way they do, just rather they work so do it his way.

2^-6 = 1/2^6 for example. I can follow a rule that says to do this, but am not sure why it works , as in I couldn't stand in front of a class and give talk on why this works..


Is anyone able to give example soy how they dive a bit deeper into equations to work out how the equation actually works and what is really going on .

So far I been resorting to looking at "Better explained"

 

[mal4mac]

2^-6 = 1/2^6 for example. I can follow a rule that says to do this, but am not sure why it works , as in I couldn't stand in front of a class and give talk on why this works...

Isn't that just a definition? Like 10^2 just means "stick a 1 with two 0s after it"? A better example might be 7^37^5= 7^3+5. Try explaining that (especially with fractional indices...) Physicists can just say, "looks reasonable, I'll use that..." Only specialists in this area of mathematics need to why it works in all the gory detail.

 

[Alicelewis11]

I could not be right however in that there may be non official school affirmed textbooks that are of incredible utilization, yet you need to get input from the individuals who have significantly more skill than me. What I do feel positive about specifying is that trying to turn into a secondary school math educator in an alternate way "express" form is setting yourself up for disappointment. Math really gets to be exceptionally agreeable when you pace yourself and don't permit yourself to be raced to such a degree, to the point that you need to skip appreciating ideas simply to begin the following segment. Seeing how an equation was created and figuring out how to determine it myself consistently expands my thankfulness for math, pulls me in, and makes me need to invest more of a chance learning it (instead of attempting to remember letters), which further builds my information. Furthermore the same is valid for some individuals. Shockingly, on the off chance that you have a full time work outside of math as I have and/or different commitments that make it hard to invest loads of time mulling over, don't let it turn into motivation to presume that one specific standard or equation is not worth completely understanding. On the off chance that anything, skip it and make certain to return to it once you can. In any case remember, you will soon understand you can't go too a long ways past a theme without experiencing it by and by at a more exceptional stage. So regardless of the fact that it takes 3 weeks to at last comprehend a sub-sub theme, then stay with it in light of the fact that you most likely won't have the capacity to see further themes without comprehension past points.

 

[mal4mac]

So my question is which books do you all recommend [for aspiring high school maths teacher] that are easy to follow, precise, with the best explanations?

Not many recommendations here! I think this is because none of books are easy to follow, precise or with good explanations - at least not all of the time! Some of them hardly any of the time. A wonderful essay by the mighty Feynman is crucial here:

http://www.textbookleague.org/103feyn.htm

As you have the practical, and onerous, task of preparing to be a school math teacher *now* I would take a pragmatic/defensive approach. (i) find out which textbooks you are most likely to be using in your teaching and study them (watch out for rubbish that Feynman has spotted - like adding the temperature of stars! Or converting from base 5 to base 7). This is the kind of stuff that probably turned you off math and got you those Cs and Ds. Now, as an adult, you just have to accept that the state expects you to teach such useless stuff and that you need to suck it up (like forcing you to wear a tie...) When you don't understand something, which given the state of textbooks will be often, then head to the nearest public library. At school I survived by supplementing my textbook by perusing just about every math book, and encyclopedia, in my public library. So if you, say, can't understand "differentiation" (or how best to explain it to schoolkids) look up differentiation in every "likely" book in your school and public library (and university library if possible) until it clicks. No joy? Well we have the internet these days, so search for the particular problem you are stuck on, or ask questions here. This approach - study the set text and blitz the library for points you get stuck on - got me As (lot of hard work though!)

 

[Axel Harper]

I used to compete in math competitions in middle and high school and I've heard incredible things about the Art of Problem Solving series. Unfortunately, I never did get the chance to read them myself, but they cover everything from prealgebra to calculus. These books aren't cheap though, so I would recommend trying to find them in a library.

 

[Alicelewis11]

You may need to begin with school appointed authority reading material rather than Algebra for shams, or express math. What's more from that point, make inquiries, look for mentoring, and quest for interchange clarifications. Don't simply remember equations without completely understanding them. No one can remember all the recipes if they are aimless images and letters from which to module numbers to land at a response which bodes well. You have to know how every recipe and guideline is determined or else you won't be fruitful math learner without taking into consideration math instructor. Concerning the book titles you specify, as I would like to think, those sorts of titles typically infer a brief diagram of the math, yet not the bare essential. I could not be right however in that there may be non official school affirmed textooks that are of extraordinary utilization, yet you need to get input from the individuals who have significantly more skill than me. What I do feel positive about specifying is that looking to turn into a secondary school math instructor in an alternate route "express" mold is setting yourself up for disappointment. Math really gets to be extremely charming when you pace yourself and don't permit yourself to be hurried to such a degree, to the point that you need to skip appreciating ideas simply to begin the following segment...