(Part 2) Reddit mentions: The best study & teaching mathematics books

Congratulations!!! I'm so happy to hear that!! And a 3.4 GPA isn't bad...you've still got time to bump it up a little but even if you don't it's pretty good.

Yes if you're up to taking the SAT again, go for it! In terms of math review, I would do Khan Academy and tons of practice tests, and write down the answers you got wrong and why. This way you can see over time what your weak areas are and hopefully the extra work of really understanding what went wrong will help you avoid making that mistake again. I used Richard Corn's Math ACT book, which really helped me, so if you want a comprehensive but challenging math concepts review you could try his SAT book: https://www.amazon.com/Guide-Math-SAT-Richard-Corn/dp/0998584908/ref=olp_product_details?_encoding=UTF8&me=

I'm sure you could improve well without it though.

Anyway, congratulations again!! I'm so glad I could help! :) You definitely deserved your great score improvement and I'm sure you'll do even better next time!

I'd recommend against Khan Academy or similar resources in this situation. They are great resources for students who are missing basic skills, or even learning at grade level and struggling a bit. But for a student who is already doing well and wants to do something special, the last thing I'd look for is to give him an early repeat of what he's going to see in math class next year anyway, or the online version of drill worksheets.

Okay, I guess that means I owe some positive suggestions. That's harder given the age, but this is my best try.

• Math circles is the best suggestion here, by far. I hope you can find something nearby.
  
• This book is a great one: https://www.amazon.com/dp/B0095POAX4

I missed a 2400 by a single stupid mistake on the math (damn the number 75 for sneakily being divisible by both 3 and 25!), so I guess I could provide a couple of suggestions:

1. If you're in the 650-730 range and looking for a little help on the math, I definitely recommend this book. Before using it, I could pretty easily get most of the rest of the questions, but the last two or three in a section were always a little tricky and I'd usually miss a couple on a given test. Drilling a ton of those kinds of problems in that book will help a lot, and got me over the hump from averaging around 700-730 to the 780 I eventually got.
   
   
2. For the essay, you want to have a few examples in mind that you can apply to any topic. Ideally, you want one literary or historical example and one "personal story" (which you can completely fabricate, since the graders don't know you) or pop-culture (movies, TV, the news, maybe even music) example. Don't use a literary/historical example that everyone else is going to use though - you want to find a great one that's broadly applicable and fairly well-known, but not so well-known that every 17-year-old in the country is going to think of it. You probably don't want to use George Washington or Adolf Hitler, but think of someone like J. Robert Oppenheimer (the one I ended up using - my topic was about how success brings unforeseen challenges, so I wrote about how he helped develop the atomic bomb, which eventually was used at Hiroshima and Nagasaki and left him conflicted about what he had done), who everyone's heard of but few would think of in those few rushed minutes of planning at 8 AM on a Saturday.
   
   Good luck!

1)
Resources:
Maybe try something like udemy?
https://www.udemy.com/singapore-math/

Or sift through videos here:
http://www.watchknowlearn.org/Category.aspx?CategoryID=4912


If you want to pay for it (or maybe try to find it at a library), this is a great book that goes over the foundational skills taught the singapore math way.
http://www.amazon.com/Why-Before-How-Computation-Strategies/dp/1934026824/ref=sr_1_13?ie=UTF8&qid=1405976198&sr=8-13&keywords=singapore+math


This is a great book about how to teach singapore math based model drawing to solve word problems.
http://www.amazon.com/Step-Model-Drawing-Problems-Singapore/dp/1934026964

Teacherspayteachers also has some free resources:
http://www.teacherspayteachers.com/Browse/Search:singapore+math/Price-Range/Free


2)
Rote practice is necessary, but if you can make it more interesting in any way possible that would probably yield better results. There are plenty of apps out there that make computational practice fun.

You need to make sure he can explain to YOU different ways to solve a problem so he gets practice making those connections on his own and verbalizing it to someone else. It will cement those skills so he can recall the information on his own and independently think of a variety of routes to solving a problem.


3)
This is probably a huge factor in his scores, and super important to work on nixing bad habits. I used to do this ALL THE TIME and it's a hard habit to break. One thing you can do to show him the difference between his way and your way of doing things: Give him a quiz at the start of session. Then focus the session on minimizing mistakes and slowing down, not skipping steps. At the end, give him another mini quiz w/ similar questions & difficulty. The next session, have them graded and most likely there will be a big difference between the first and last, and the difference will most likely be preventable errors. (If it's not...then it would be a first!). Show him both quizzes and ask him why he did better on the second one, process with him the importance of doing the steps every time and double checking work, etc.

It will also help if you have him explain to you why he got a problem wrong, and to keep track of the reasons. Once he sees how many he is missing because of little errors, he will better understand the impact of skipping ahead and not checking his work. (This worked for me when I was studying for the GRE. It's hard to see the big picture, I only see the current moment. Tracking the big picture helped me connect my actions to the future consequences)

4)
Lame techniques are awesome because they remember them and it's fun to tease them a bit. :)

Can you take some successful strategies from your experience as a history teacher and amend them to work in a Math classroom? I think it's okay to be honest about the fact that you don't have experience in a Math classroom, as long as you can show that you do have relevant experience that you will be able to adapt and build on. It may also be helpful to observe some Math teaching so that you get more strategies and ideas to discuss in interviews and to use when you do get hired. A good book that can give you an overview of a common, very successful way to run a Math lesson is Five Practices for Orchestrating Mathematics Discussions.

I highly recommend The Beauty of Everyday Mathematics, which has a terrible name, but is otherwise a very good book. It's aimed at exactly you, I think, and it's not afraid to do the math.

I would also recommend Towing Icebergs..., which has a similar feel. Both use calculus in fun ways.

I bought the ETS "Official Guide" and went through the quantitative reasoning section and made notes on any math concepts I needed to brush up on (I haven't done any geometry since high school, which was...uh...a few years ago). I wanted more practice problems, so I bought a Kaplan book that just covers GRE math and that's what I'm working through now. It's this one: https://www.amazon.com/Math-Workbook-Kaplan-Test-Prep/dp/1625232993/ref=mp_s_a_1_3?ie=UTF8&qid=1543244179&sr=8-3&pi=AC_SX236_SY340_QL65&keywords=kaplan+gre+math&dpPl=1&dpID=511IWfCnykL&ref=plSrch

Once I finish with this workbook I'll probably do the two free practice tests on the ETS website, and then if I'm still not happy with my scores I might pay for the two additional practice tests.

As far as making it fun, I'm just a weirdo who genuinely enjoys doing math problems. I'm super fun at parties, lol.

this one

and

this one

and yes I keep them on my shelf. Personally, the pre-calc is still helpful from time-to-time and the Math Power book I keep because it made me love mathematics.

It depends on what kind of math you want to learn. If you want to get up to speed on your basic math, khan academy is the way to go. However, I think that is probably a waste of your time. The math that you will see in high school and the first year or too of college has very little to do with what a mathematician might consider 'real math.' Frankly I found it boring as hell and I majored in math undergrad and grad.

If I were you, I would start with something interesting and if you end up really liking math, go back and pick up algebra and calculus. So check out the two books below:

This book will walk you through really high level stuff in an easy to understand way. As a grad student I would hang out in this class because it was rather fun.

This book is a history of math/pop math book. As an undergrad it put the field into perspective. Lots and lots of really useful information for anyone, especially someone who is interested in being well learned.

Certainly:

1. http://www.amazon.fr/Math%C3%A9matiques-L1-complet-exercices-corrig%C3%A9s/dp/2744075590/ref=pd_sim_b_6?ie=UTF8&refRID=05YXG1RX5QVDXH554N93
   
   
2. http://www.amazon.fr/Math%C3%A9matiques-Cours-complet-exercices-corrig%C3%A9s/dp/2744072257/ref=pd_bxgy_b_text_y
   
   
3. http://www.amazon.fr/Math%C3%A9matiques-L3-Analyse-exercices-corrig%C3%A9s/dp/2744073504/ref=pd_bxgy_b_text_y
   
   
4. http://www.amazon.fr/Math%C3%A9matiques-L3-Alg%C3%A8bre-exercices-corrig%C3%A9s/dp/2744073512/ref=pd_bxgy_b_text_z
   
   The first and second link are all-in-one books for the first and 2nd year of university respectively. The 3rd and 4th links are the all-in-ones for the third year for analysis and algebra respectively. They're pretty damn good, and it's like reading a Bourbaki but with colored boxes and random historical blurbs that you'd expect to find in a freshman calculus book like Stewart.

When I was in seventh grade my math teacher lent me some books to read:

• Fantasia Mathematica, by Clifton Fadiman (and there's a sequel, The Mathematical Magpie);
  
• A History of Pi, by Petr Beckmann;
  
• and some introductory book about topology, explaining the Möbius strip, the four-color theorem, the Klein bottle, the projective plane, and maybe some other stuff, whose title I have since forgotten.
  
  I credit these books for sparking my interest in math.
  
  Other books I'd recommend include Imaginary Numbers by William Frucht, Flatland/Sphereland by Edwin A. Abbott/Dionys Burger (and Flatterland by Ian Stewart), The Penguin Dictionary of Curious and Interesting Numbers by David Wells, A Passion for Mathematics by Clifford A. Pickover, The Mathematical Tourist by Ivars Peterson, and any book by Martin Gardner or Raymond Smullyan. Also most books by Ian Stewart would be good, but he also writes higher-level math textbooks, so watch out for that.

If you are interested in teaching mathematics at this age/stage, then I encourage you to check out a book like this one. You may also wish to read about Number Strings. There are a lot of interesting ideas surfacing in elementary school mathematics education - the time/place where arithmetic is covered - but it is not as widespread as it should or could be.

For high-school contest mathematics, there is:

• A Decade of the Berkeley Math Circle: The American Experience (MSRI Mathematical Circles Library)
  
  The following is very good for non-contest mathematics, but I don't know of a corresponding book targeted to boys:
  
  
• Math Girls
  
  For each of these, also take a look at the related books to see if something else is more interesting to your son.

If you like to solve problems then I would recommend this book. It's a neat little introduction to problem solving, the questions it will ask you will be more difficult than A-level maths but the knowledge needed for them is far less than needed for A-level. The PDF is also easy to find on Google.

Look up the works of Piaget, Vygotsky, and von Glasersfeld. Compare them to the works of Skinner and Gardener. You will see the difference real research makes.

Some info, for those interested:
http://en.wikipedia.org/wiki/Constructivist_epistemology
http://www.amazon.com/RADICAL-CONSTRUCTIVISM-Studies-Mathematics-Education/dp/0750705728
http://www.youtube.com/watch?v=YozoZxblQx8

Linked because he's my favorite.

Basic Math for Adults

This seems like what you are looking for. Combine this text with khan academy, and I think you should have a good foundation. Remember to take notes while watching lectures and practice tons!

Start with the official book, which has 4 official tests including answer explanations: https://www.amazon.com/Official-Subject-Mathematics-Level-Study/dp/1457309327

Then move onto the Dubai tests. If you need more help with strategy, then I can recommend the Princeton Review book and/or the Barron's book.

The columnist is a completely clueless fscktard who somehow missed the concept of researching before writing an article. Danica McKellar is a math major who actually has an Erdos number of 4, and is a math advocate. The most cursory net search would have showed her that McKellar is a math advocate, not some bubblehead. And why is she reviewing a book that was published over a year ago as if it were brand new? Heck, McKellar's newest book, Kiss My Math, is hitting the stands next month! I hope this was posted as a wry joke to poke fun at the columnist Chloe Angyal for writing without a clue.

For math, we love these books

I'd recommend asking the school/teachers, but each board usually publishes a book for each qualification. These are usually available at shops like Waterstones and online. For example, here is the Edexcel GCSE Maths book (for this year, I think). So just find out which qualifications are being done (and also which exam board) then buy accordingly.

https://www.amazon.com/Hard-Elementary-School-Glenn-Ellison/dp/1489507175