I’m starting this thread as a spin off from another discussion. Here are some comments, links, and ideas I have about math in middle school & high school. I hope others will add to it and it’ll be a useful resource.
Studying math (or science) isn’t like studying any other subject. You’ll read the material at a MUCH slower pace than for any other subject. Ideally, a student will read text examples with a pencil and paper and will cover up the work (fold a page in half) and try to work the problem ahead of the example, looking at the next step in the text explanation after writing what you think the next step is. Pay CLOSE attention to the EXPLANATIONS given. That’s the sort of thing I say in class as I’m doing examples.
I once spent about 3 hours reading 3 pages in a math text. It took me that long to really take in what was happening. Lots of scratch paper is useful! I also like doing math on unlined paper because it seems to allow me to write larger and more neatly. It’s when I start skipping too many steps that I find myself making careless errors.
For taking math notes, I used to have my students keep a math journal. I’m trying to attach the pdf I’d hand out with an explanation of what I was looking for. The practice problems a student does really don’t need to be kept, but a set of explanations of how to do certain problem types would be very useful for later reference. (not working, but PM me with your email & I'll send the pdf)
I really liked the book Winning at Math by Paul Nolting. It’s out of print now, but it looks like some cheap used copies are available – and our library has some.