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In 1993 my wife and I had a son, and we decided to homeschool him. I took responsibility for my son’s mathematics education. I started by collecting hundreds of used math books (and some new ones), and then I identified the best of them to use as textbooks. I discovered that most of the books were of very low quality, and that only a few of them seemed to be any good. I did not realize until my son was in college that the reason the “good” books were good was because they were based on formal mathematics. My son did not have any noticeable talent for mathematics when he first started learning it. In fact, he was not very good at math at all. I couldn’t directly teach him math because I did not understand it very well at that time, so I had him work through some of the math books I set aside. Before he went to college, he worked through one “Saxon Math” arithmetic book, one book titled “How to Think Like a Mathematician” by Kevin Houston (which dealt with how to do proofs), and a book titled “Fundamental Mathematics” fourth edition by Wade and Taylor (which was based on 1960s New Math). Around a third of the way through the fundamental mathematics book he apparently saw how formal mathematics worked because he started being able to do mathematics quickly, accurately, and with confidence. He did not like math very much up to this point, but as soon as he was able to do math, he began to like it more and more. Before college, my son never took even one math test. When he entered college, he majored in mathematics and physics. He was easily able to do all of the work in the mathematics and physics courses he took. This past spring he graduated with a GPA of 3.9. Since 2008 I have been developing open source mathematics software that students can use to learn how mathematics works at a deep level. Here are some examples of what I have created so far: http://patternmatics.org/test/expression_structure.html
http://patternmatics.org/
https://www.youtube.com/watch?v=kYtsQ_PczlY
http://www.mathpiper.org/ The last link is to an education-oriented computer algebra system. If you (or anyone else) is interested in learning more about this software and my thoughts on mathematics education, feel free to ask questions about it on the MathPiper developer list. |