This web site is a collection of explanations of stuff that comes up a lot, and that isn't often explained well in textbooks. I concentrate on what's going on conceptually, not just how to do the steps of a problem. I hope you'll be enlightened about things that may always have seemed mysterious. Because I'm doing it in my spare time (what little there is), I can't claim to be comprehensive. Mostly the topics are things I've already thought a lot about.
These pages usually have pictures, diagrams, and examples. Some of them have interactive geometric diagrams that you can change to see what happens in different, related examples.
I wrote all the pages, unless otherwise noted. I have a Ph.D. in mathnoted. I have a Ph.D. in math (research in arithmetic algebraic geometry), so I guarantee that these pages are mathematically correct.* (Occasionally the first edition of a page will have a slip-up.If you find an error, let me know so that I can fix it.)
If you don't find what you're looking for, check Ask Dr. Math at the Math Forum. There is a large collection of answers to frequently asked math questions, and if you don't find the answer to your question, you can send it in, and someone will problably eventually post an answer.
Another place to check at the Math Forum is Teacher2Teacher,
"a resource for teachers and parents who have questions about teaching
math. T2T offers an archive of answers, pages of public discussions, and
a form for submitting questions."
Alternative algorithms (methods for calculating)
- Some alternative methods for subtraction
- tml">subtraction
- Long division Some very easy to understand ways of doing long division, leading up to the usual way. From my lecture notes for my course on math for elementary teachers.
- An e-mail essay on alternative algorithms for arithmetic by Rex Boggs, a high school math teacher in Australia. This was part of a long discussion in the math-teach discussion group on whether all students should learn thoroughly a standard technique (algorithm) for each arithmetic operation.
Slopes of perpendicular lines
Tessellations and symmetry