Aspiring HS Math Teacher: Textbooks for learning Algebra, Geometry, Trigonometry, and Calculus?

Question

I plan to study for 6-12 months to take a high school mathematics teaching license exam. This one to be exact.

Florida Teacher Certification Examinations Test Information Guide for Mathematics 6–12

Been out of school for roughly 8 years. Never took calculus before. Was never really the studious type in school, but managed out alright.

Nonetheless, I am wanting to put a lot of time and effort into re-learning these subjects from the ground up not only to pass the test but also to help me be an effective teacher.

Thus I am looking for the best textbooks to have to help aid me in this process.

Thanks for the recommendations and any advice really. Cheers

Answer 1

Additionally, I would consider using Khan Academy as supplementary practice with the books that people have included on here. Khan Academy includes videos and many practice problems with detailed solutions given. That's how I reviewed high school math after not taking it for a while.

Answer 2

There is an important genre of textbooks on high school mathematics written to be used by students who are preparing for careers in teaching mathematics at the high school level. These textbooks are often written in a more rigorous fashion and cover the material in more depth than the textbooks used by high school students.

A recent example of this is the series of three textbooks by Hung-Hsi Wu, Algebra and Geometry, Rational Numbers to Linear Equations, and Pre-Calculus, Calculus, and Beyond.

Answer 3

If you need it, consider Martin-Gay's Prealgebra & Introductory Algebra; it's about the most complete and clearest presentation I've seen, and moreover provides a template for teaching those subjects when needed (it's my starting point for lectures in those subjects).

For the next step, consider Michael Sullivan's Algebra & Trigonometry; it's a comprehensive and pretty widely-used text.

If budget and time is a consideration, consider the analogous free texts at OpenStax: College Algebra and Algebra and Trigonometry.

Answer 4

I highly suggest "Hurricane Calculus" by John B. Hahn (1995). It was introduced to me in Calc II, but I wish it had been available for my introductory Calculus class. The writing style is not "textbook". Instead it is written more like a person talking to you. There are also many examples at varying difficulty level, which is extremely helpful.

Hurricane Calculus covers the full range of first year college calculus, from the concept of limits to the often complex partial derivatives and multiple integrals. It tells you in plain, simple terms what the basic calculus concepts are, provides you with step-by-step problem solving guidelines, and shows you plent of completely worked out examples. Hurricane Calculus may be the most readable book ever written on the subject. There's very little of the mathematical jargon that often causes confusion. The book is full of examples drawn from actual real world applications. Its easy-going style is aimed directly at the reader who may be new to calculus or needs clarification.

Answer 5

Do you really need to learn all of this material or just brush up for the standardized test you are planning to take? The answer would probably change the advice you get here.

For a full learning effort, the CK-12 series of books is a great start, and will help you re-learn what you feel you forgot.

For your state exam, I recommend going to Amazon and searching on FTCE mathematics 6-12 which will give you the study guides targeted to the exam. When I took my state's 6-12 exams (2 different levels) the study guides gave an overview at a level that made more sense than to go through a text similar to what a student would use.

Answer 6

Edit:

Work your way through Schaum's Outline First Year College Mathematics by Frank Ayres, Jr. I prefer the earlier (1958) edition to later versions. Also, get a used copy not a reprint or electronic one. (print quality suffers on later ones). You can get it quite cheap on Amazon.

This will cover algebra (what used to be called college algebra and is called algebra 2 in high schools now, but don't worry it covers everything in first year high school algebra also), trigonometry, analytic geometry, and precalculus. You would need to get geometry elsewhere. And it is lacking much on vectors (but don't let perfect be the enemy of better!) I would hold off on calculus (even worrying about a text) until you have the basics down solid. But this one book will really help you.

Note that Schaum's is written for busy people, is simple, is great for review, is not a logorheic doorstopper like the texts that are sold to schools. Just WORK PROBLEMS, not passively read. And you will be fine. Oh and all the answers are included.