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Mathematic Text Recommendations

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I may have been able to escape the terror of the Whole Language method of teaching, but Whole Math has certainly killed my ability to work with numbers mentally. Quite embarrassing sometimes, so I would like to remedy the problem by redoing my mathematics education.

The problem is I am not sure which books abide by the appropriate epistemological teaching methods; I fear accidentally purchasing a book that uses the Whole method. A search on Amazon, the site I use the most frequently for books, turns up nothing but what seems to be junk and "Learn Math in 20 minutes a Day!" types.

So could anyone provide me with some book recommendations? The kind of math I want to learn is very elementary. It is purely for my everyday use (just sticking to that which has utility to me). I want to learn about the first branch arithmetic (what numbers are and etc., addition and subtraction, multiplying and dividing) and, when I get to training myself to cook or the likes, measurement. Simple, easy, useful.

Thank you for your time.

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I similarly wanted a conceptual (hierarchically-appropriate) approach to mathematics. I learned about John Saxon's math textbook series after listening to one of Lisa VanDamme's lectures (one of her students mastered calculus through self-study with these books at the age of 12). The books offer day-to-day lessons, quizzes, etc. with an emphasis on proper conceptual hierarchy. I highly recommend them.

I bought his Algebra, Algebra 2, and advanced mathematics textbooks for all under $10 from www.allbookstores.com and half.ebay.com

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Alright, I've taken a look at some of the books at Allbookstores.com, Amazon.com, and even the publisher, but they don't provide any information as to what content is in what book, and some of the titles, at a glance, seem entirely arbitrary (Math 87 and Math 8/7). Where's the beginning (arithmetic) and what's what? :P

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I may have been able to escape the terror of the Whole Language method of teaching, but Whole Math has certainly killed my ability to work with numbers mentally. Quite embarrassing sometimes, so I would like to remedy the problem by redoing my mathematics education.

I don't have any book recommendations, but I do have some suggestions for how to approach this task in general.

My early education in math was also quite poor, and I have been in the process of repairing that fact for about 6 years now. In my case, I struggled with math until my junior year of high school, and then slowly began to improve. I have given a lot of thought to identifying the change in my epistemology which caused this improvement, and I have come to some basic conclusions, which you may be interested in.

First, a large problem with basic math education is the emphasis on learning algorithms by rote. This approach is better than what I have heard about "Whole Math": at least you learn some concepts of method, which can help you in practical situations. You mentioned wanting to "work with numbers mentally", however, and simply memorizing algorithms will do little to help you in this area.

To be clear, I do recommend learning these algorithms (long division, for example) until you can do them quickly. You should especially follow the drill approach in the beginning, in order to become comfortable with the subject. If you really want to increase your ability to think mathematically, you should follow this up by trying to understand as clearly as you can why the algorithm works. If you follow this "practice then understand" approach for all of your mathematical knowledge, you will improve your mathematical reasoning ability tremendously.

By understanding why something works, I mean reducing it to first-principles. You should, for example, be able to understand why the long division algorithm works by reducing it to simple counting, which you can take as the basis for your knowledge of mathematics.

You say that you are interested in a practical knowledge of mathematics. I think that the above approach is very practical for several reasons. First, if you just want to learn the algorithms, you might as well carry around a calculator instead. Epistemologically, blindly using algorithms is barely preferable to relying on a calculator. If you have reduced your knowledge to first-principles, you will not only not be dependent on a calculator, but you will be able to recreate the algorithm if you forget it (and you will be less likely to forget it to begin with). Most importantly, your ability to apply your knowledge will be greatly increased, since you will know exactly which algorithm applies in which situation, and why.

So, whichever textbook you choose, I recommend the following epistemological strategy:

1. Do lots of practice problems, until you are confident.

2. Reduce your knowledge to first principles, until everything you know seems "obvious" to you.

I know this is not exactly what you were asking for, but I hope you find it helpful.

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Thank you West, Mallory, and Mr. Shaw. I appreciate everything.

I have finally found which book I need: Saxon Math 3. That one covers everything I want. It might be embarassing: studying 3rd grade material, but oh well. :)

One final question: Which should I buy? The student workbook or the teacher's manual, or perhaps the whole kit? For those of you that have used Saxon math before, what did you purchase?

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[Kline wrote] quite a few non-text math books as well, including a three volume history of math. If they are as good as his calc book they are worth reading.
I haven't read his calculus book. I have gotten some benefit from his three volume history. However, I think his 'Mathematics: The Loss Of Certainty' is not very sharp in its view of incompleteness and related results in mathematical logic.
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