Or, if you are doing two credits worth of work, it would be perfectly reasonable to do "world history I" and "world history 2" both for 1 credit. Or you could do one "ancient history" and one "modern history" or any number of other combinations, depending on how fast you go through and how much work you do.

Ah, I was going to post, but forgot. Algorithm, if you're looking for more fun and interesting reading in this general area, you might try "e: the story of a number", by Eli Maor. I was given it for Christmas this year and enjoyed it. Parts of it require knowledge that you won't have yet (especially calculus), but since you clearly aren't thrown off by that, you may enjoy it.

What? It's a program that is designed for students in their last two years of high school, that for some reason (probably liability) also requires them to be 16. Undoing the skip the public school did has allowed him to participate in his last two years of high school, exactly as intended. I will also point out that (unless I misread her posts) he is now registered at the grade level he would have been, had he been enrolled in public school and not skipped. I really don't see anything unethical here.

This is craziness. And I don't get it at all. Example: In our "quantitative literacy" university class (read "math for people who hate math and just need one course to get a degree") we do mortgage calculations. Many people each year will come up with a monthly payment that is ridiculously far off (we are talking $3.54/month or $90,000/month far off), circle it, and move on. Example: When computing area in a word problem, people will get a negative answer and not realize that that cannot be a real answer.

If you're in a mandatory testing state, you may consider recording him in the "redshirted" grade, and bumping him up towards Jr. High if he's still doing very well. It is generally easier to bump up than hold back. This does NOT mean that you need to not teach him this year! There is nothing preventing you from doing K curriculum with a boy who's labeled as PK, or 3 curriculum with a boy who's labeled as 2.

This is very kindly said, and I agree 100%. I would cut every subject except reading (assuming reading is still not mastered), if I had to, to make sure math was getting done and done right.

I see nothing wrong with moving ahead to work on something else for a while, planning to come back.

I believe what he's referring to as "textbook school mathematics" is "the mathematics in the most commonly used school textbooks" not "the mathematics in any textbook." I think he could have chosen a better name for it.

I do agree with what he has to say about algebra/geometry integration, specifically with the slope of the line. This is one of the issues that I see, that we are in such a hurry to get everyone "through" algebra 1, that rather than taking the time to explain WHY these things work, we just say "Here is how to find the slope of a line. Memorize it. Do homework about it." and so students come to college with no understanding as to why, for example, a horizontal line has 0 slope. I also agree with him about needing better-educated elementary teachers. I did not at all like his explanation of fraction addition. It seemed, though, that part of what he thinks is that we should *first* teach adding fractions by using denominator times denominator as the common denominator, and afterwards teach reduction to the LCD. About that, I'm not sure I agree, but I can see his point.

Second the recommendation for Stewart, if you want a physical book. If you are okay with an ebook and either reading it online or printing it out, you can get Gilbert Strang's calculus text online here: http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ You can download chapter by chapter or the whole textbook as a single file.

You won't find any argument here. I would much prefer to just use parentheses or dots for multiplication.

Older versions of Saxon used to recommend skipping 87 and going for Algebra 1/2 if the student did well. Newer versions reverse this recommendation, saying that you should do 87 and then do algebra 1/2 if the student does not display mastery. If your 87 book says that pre-algebra is included, that's the one you should use.

The only problem with this is that (as shown by the OP) it can easily lead to confusion and students falsely thinking that addition comes before subtraction, and multiplication before division. That's why people are trying to come up with newer mnemonics which eliminate that confusion.

Some states are moving towards having "math content specialists" in elementary, as we already have reading content specialists. I wholeheartedly approve -- for a classroom situation, where the teacher has many students and cannot just say "hold on while I ask the hivemind", but needs to come up with multiple explanations for multiple levels of misunderstanding "on the fly".

I would start giving him one problem at a time, on separate sheets of paper or a whiteboard.

Some people are now advocating using GEMS -- grouping, exponents, multiplication, subtraction -- and remembering that multiplication/division are the same operation, as are addition/subtraction.

At almost all universities, Calculus with Analytic Geometry is another name for the standard calculus sequence. Very few will have *both* 'calculus with AG' and 'calculus' listed -- although they may have 'calculus with AG' and 'calculus with applications' listed. Analytic geometry used to be included as a separate course in high schools (it covered some of the stuff which is now included in the calculus sequence and some of the stuff which is now included in precalculus) but gradually became integrated into other courses rather than a course of its own.

Well, a basic knowledge of calculus is often prerequisite to taking a serious stat course, which might be required if she went for psychology or sociology. A stat course without a calculus prereq spends a lot of time saying "because I said so, that's why" because the underpinnings involve calculus. Calculus is also used more than you'd think in economics, especially if one goes for an advanced degree. But if her interest is history or english or drama, well, eh, I can't really think of an application of calculus to those off the top of my head. I would see nothing wrong, though, with doing a "calculus for business and social sciences" course instead of an AP course. I think this'd be a lot more applicable. However, I doubt she'd get college credits for it, so if your goal is to have her get college credit for it, this wouldn't work unless she took it as dual enrollment. If, on the other hand, you want an understanding and appreciation for all the things that calculus is used for within other majors, that might work for you. Textbooks for this are commonly found used and cheaply so on amazon. Another idea might be a course in finite mathematics with applications. This is usually a university-level course with a prerequisite of college algebra, however, again, she probably wouldn't be able to get college credit for it. The applications usually focus on business, social science, and life science, and textbooks are available cheaply on amazon. As a matter of fact, Lial does both an applied calculus and a finite mathematics text, as well as a combined text. Another idea might be a mathematics for liberal arts course. I really like Jacobs' Mathematics: A Human Endeavor for liberal arts courses, but there are again many options. These types of courses tend to focus more on logic, mathematical reasoning/thinking, and appreciation than on strictly technical skills, but even if her technical skills are strong this might be an enjoyable course. And finally, completely off the beaten track, she might enjoy a course based on a book called "math through the ages:a gentle history for teachers and others", recently published by the MAA. It's a book on the history of math which includes a fair amount of actual math, designed for future math educators but also very accessible to high-school students.

I am not sure, because I am not familiar with the typical sequence of topics from physics books. They do appear to have resequenced the calculus course as well. They definitely do kinematics first, but they appear to have done a very early exposure to 3-d calculus and vectors and postponed some of the typical calc 2 stuff into calc 3. I think this would work as long as the university was also able to run a non-integrated sequence for transfer students. Here's the website for the book, where you can find the table of contents (this is for both books, I don't remember where the actual split was). http://www.pearsonhighered.com/educator/academic/product/0,1144,0201473968,00.html

Here's a link for the first part of a two-book series that was to integrated calc2/mechanics and calc3/e+m for an integrated course taught at some universities. The prerequisite would be calc 1 and a high school physics course (conceptual should be fine). I believe the book is longer in print, but it might be interesting if you can find one at a university library. I borrowed it through ILL and read it myself, but it was a while ago. http://www.amazon.com/Integrated-Physics-Calculus-Volume-1/dp/0201473968 Some of the lower reviews say that the calculus material (especially the stuff that doesn't apply to physics) is on the weak side, but that the applications are great. As I already knew calculus before reading the book, I am not really able to evaluate that. Therefore, were I to use this, I would probably supplement with any standard calculus textbook in an older edition. (Stewart is what I would use because I already own it, but there are many other acceptable ones.)

Honestly I think you'd be better off getting a book like kitchen table math (sold by the AOPS people) and working out your own games/crafts based on what your son actually likes. It would be one heckuva lot cheaper, cover more grades and probably be more useful.

Gosh, it does look expensive. It might be worth it if he looooves arts and crafts and haaaates math, but unless HE (not you) is really into the crafty stuff it might just seem like a way to make math take even longer. Does he do any better when math is integrated into real-life activities? or does he say 'That's MATH!' and shut down when you ask him to cook?

Algorithm, how much math have you had? What are you formally studying now? This would help with recommendations for further reading.

Faith, I've known people who graduated from high school with an F in one course and took a completely different course to earn the credit. Is there anything he finds less tedious than chemistry that might work for him to get that 3rd credit? If he already has earth science or bio, as far as I can read he just needs one more credit in ANY science. Other than that, I also see nothing wrong with giving credit once he can pass a chemistry end-of-course exam.

Remember that the program was aimed to challenge gifted middle school students, so if your kid isn't yet to that level it will probably be more than challenging.