What are your views on homeschooling? How can they do better at math? originally appeared on Quora - the knowledge sharing network where compelling questions are answered by people with unique insights.
There are many reasons parents choose to teach their children at home and boosting math scores is not typically the main reason for making that decision. So I do not assume that my comments will deter parents from homeschooling their children -- nor should they. But I do want to offer a caution.
At the University of Illinois, I teach courses to prepare elementary teachers to teach math. I once had an older student who had previously homeschooled her children. After taking the course, she told me that she deeply regretted teaching her kids without knowing the things she learned in our class, including standard math misconceptions and the most effective representations of fundamental math ideas. As one example, we discussed that students sometimes think the "=" sign means "the answer is," and this can be diagnosed by asking students questions, such as 4 + 6 = _ + 3. If a student puts 10 in the blank, then he or she has a fundamental misconception and needs to learn that "=" means "is the same as." As another example, we learned that 8÷2 could be thought of as "How many groups of 2 are in 8?" or "If you divide eight into two groups, how many would be in each group?" In the first case, the picture of the solution should show four groups of 2, and in the other circumstances, it should show two groups of 4. These ideas are a specialized type of knowledge that teachers learn, yet other adults, even those who are excellent at math, do not possess this knowledge.
Many homeschooling parents assume that they can teach elementary math content because they remember basic math well enough. I caution parents against this assumption. The small "class size" and high teacher/parent motivation can help compensate for lack of cutting-edge pedagogical knowledge, but if parents fall back on the way they were taught math, they are likely to teach children how to do procedures without actually making sense of mathematics. Children who learn in that manner will struggle when they encounter more advanced mathematics as well as standardized tests that contain non-routine problems, including the SAT.
My main advice for parents is to make sure their children make sense of math and do not simply memorize rules and follow procedures to get answers. Fortunately, several textbook series have been funded by the National Science Foundation to promote student reasoning and sense-making, such as Math Expressions (grades K-6), Connected Mathematics Project (grades 6-8), and Core Plus (grades 9-12). I highly encourage parents to choose such a curriculum if they are teaching math to their children at home.
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