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8

Research papers require references to verify where your data comes from. Schoolkids don't care where you get your data, extra references or footnotes just irritate them. If the presented information is incorrect, you are the one who should bear the grilling. Regarding footnotes vs inline references, as a reader - and a former schoolkid as we all were - I ...


1

My advice is to use the least obtrusive method, probably 4, from your list. And to also minimize the number of citations. What you are considering a feature (oh goodie, we get footnotes) is really more of a bug or at least a pill for someone not already used to wading through research papers. You've got enough headwinds already by combining two difficult ...


2

I think the best thing for a beginner is to focus on concrete interesting mathematics. You definitely do not want to do any abstract stuff at this point unless it is motivated by some concrete problem. I recommend "Nets, Puzzles and Postmen" by Peter Higgins, and later on "How to Prove It" by Daniel Velleman. The first book is a really ...


4

You mention Art of Problem Solving. They have a great curriculum for kids called Beast Academy. You could get that for him, and just be there for when he has questions. It is a lot of fun for many of the kids using it. Also, you could play games with him. (You may have to squelch your desire to teach, just a bit.) I love Blokus and Katamino. There are also ...


1

Take a look at Polya's classic "How to solve it". What you are asking is "how do I teach creative problem solving", and for that, sorry to say, there is no royal road. In any case, it isn't fair to expect your kid to solve a problem you struggle with...


5

You'll probably get a better answer after the question is closed, edited for clarity, and reopened. I have had multiple experiences of this for students for whom English is not their first language. "What is 'ferris wheel'"? Taking a trigonometry test and we were using the ferris wheel in a test question. ('We', but I did not author the test. I was ...


3

I should disclaim I haven't managed to solve this equation yet, even with your description. What were your failed attempts like? What was your own approach to this problem, and can't this approach help your son? Overall my approach for a problem like this would be: in general, to solve for N variables you need N independent equations. Here the problem gives ...


1

Pretty open-ended questions since there aren't any specifics, so I'll give my scenarios: I wouldn't allow another chance if it was mathematically-related word that would have been seen in a previous year. For example a high school student asking what a "numerator" is, or a "sum", or a "factor" etc. (I don't think it's unfair to ...


1

It is not formally described as an AP Calculus course, but it is supposed to map roughly onto Calculus AB. It sounds like there isn't a clear definition for the level of the course or the content that needs to be covered. It may be beneficial to poll the students to find out how many are planning on skipping Calculus II in college and moving straight to ...


2

Reasons to study Newton's method: -It's an application of derivatives -It is a good example of numerical methods -It can help strengthen understanding of relationship between derivative and tangent line -It's likely going to be on the AP test I've put these roughly in order of how important they are to your situation; as nice as it is to get greater ...


7

AP classes have become much more common these days, and at many schools the result has been that very few students actually pass the AP exam with a grade that would allow them to skip the course in college. The trouble is that even if 90% of your students fall in this category, you also have a duty to serve the other 10%. Those students are going to be ...


9

If time constraints are so dire that you risk not getting to cover integrals and the fundamental theorem of calculus, then I'd cut Newton's method (and probably much more) since I don't see how you could pass the test without knowing those former topics. But, if you cut Newton's method from the teaching, wouldn't it still come up in practice AP tests that ...


1

It looks to me like your student just has a different, but valid, idea for approaching the problem. If your student made both of the suggested changes, (1) including all ways of ordering the colors, and (2) dividing by $9!$ rather than $(3!)^3$, they would get the same answer as you got. The main downside to your student's approach is that including all ways ...


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