What book would you recommend to significantly improve my problem solving skills? I am a straight-A student (going to the ninth grade) and do nearly perfectly in math, the problem is that my school (like many other schools I suppose) makes you memorize the steps, the formulas, etc. and just apply that to similar questions, and since I’ll probably be opting for IGCSE and eventually A levels, I find it necessary to significantly improve my critical thinking skills because I never had adequate practice for that. I’m sorry for all that background, but I would like your recommendation of books/websites that would help me.
Do you think these books are appropriate:

*

*How to Solve It by Polya

*The Art of Problem Solving Vol. 1: The Basics & How to Solve It Vol. 2: And Beyond

*Problem Solving Strategies by Engel

*Problem-Solving through Problems

*Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving

Do you think that Solving Mathematical Problems by Tao is enough for me to significantly improve?
 A: The ruling class doesn't want critical thinkers.
It wants trained workers.
Apparently you've outstripped your school's ability to educate you.  So move on from the Dummy Down Dunce Dance school you're currently attending.  Learn math on your own.
Choose the topics that most interest you and study them.
That is where you'll excel.  Skip that I've got to curriculum, it's just baggage.  If you bump into something that you like but lack the background, then you'll be motivated to study the background material.
Skip that high school stuff and look for a community college that'll accept you.  You'll likely be happier there.  Visit a community college, meet with a math teacher, and find what opportunities be there for you.  I have a friend who got so bored with high school, she attended a community college instead where she was happier.  I also know a self tutored math student who was accepted into a liberal arts college based upon his success in a college math exam.
PS. Skip the most modern text books and look for books written for mathematicians where the cook book method is ignored in preference to concepts, theorems and proofs.
Good luck with your struggle living in a country where being of above average intelligence is a handicap and with your new adventure beyond high school into adult education.
PSS.  If you want a tutor, I'll give you a throwaway email address by which you can contact me.  I have successful experience tutoring both elbow to elbow and by phone. Being retired, I've no need of payment.
I also suggest you use this web cite for questions and when you get stuck understanding a concept or a formula.
A: Yes, I think the Art of Problem Solving is a good book series.
I have not heard of Solving Mathematical Problems by Tao, though, but I do know that you can practice your mathematics skills by completing AMC Tests from past years here.
https://artofproblemsolving.com/wiki/index.php/AMC_Problems_and_Solutions
A: I wrote a book that may be helpful, as it covers the mental process of problem solving, something rarely taught in school. It has a series of engineering problems solved with the top-down approach, as a boot camp for the reader to get the hang of it.
It's titled "The Top-Down Approach to Problem Solving", ISBN 979-8464073296. You can find it on amazon as paperback and ebook.
I hope you like it.
