Friday's Five is a feature every week where I pick a new topic and list five items that I think fit best. Then I ask you to share your thoughts in the comment section. For an archive of past topics, check the Friday's Five Page.
I believe that as we move further into the 21st Century, understanding mathematics is more vital than it has been at any time in history. Math at its very nature is problem solving and critical thinking, skills that are sorely lacking in many of our students due to the pervasive culture of standardized testing we are forcing them to suffer through.
Here are five fallacies about math that too many people believe to be fact:
1. Math is a series of rules to be memorized. Too many times we teach math as something to be done in order to get a correct answer. (i.e. Divide, multiply, subtract, and bring down in order to get the right answer to a long division problem.) Students start to believe early in their school careers that the key to learning math is to memorize these rules. The key to learning math is understanding why those rules work, though. It's much more important for kids to understand that division means we are putting things into equal groups than the rule mentioned above. The best math students are those who can creatively find different ways to figure out problems.
2. Creativity is important in other subjects, but not math. True math is creative. Rarely do we give students the chance to be creative in our math classes, though. I can't count the number of times I've heard stories of teachers taking points off (we'll save the discussion over the worthlessness of grades for another time) for doing a problem wrong, or not using the correct method to solve a problem. At its very nature, math is about creative problem solving. As Michael P. Goldenberg pointed out, Mathematicians don't calculate. They have computers and calculators to do that for them. Mathematicians solve problems. In our math classes, we should expect and demand that our students act as mathematicians and not calculators. We should allow them to explore different solutions, to fail, and to learn from that failure. We should give them problems that may not have a clear cut answer. We should have them identify problems in their community and try and solve them.
3. Our best math students are the ones who score highest on our state standardized math tests. Those are the students who are best at calculating and memorizing. They are not our best math students. Standardized tests comprised of multiple choice questions and a few short answers cannot measure the understanding of mathematical concepts or the ability of a student to see the world mathematically. While on this subject, it's terrible that we punish kids who do poorly on standardized math tests by forcing them to endure additional bad instruction in math (standardized test prep). We should be teaching them to understand mathematics, not decipher test questions by looking for keywords, finding shortcuts to calculations, and how to format short answer responses. That just makes it harder for them to actually think mathematically.
4. It is acceptable to joke about not being able to pass an 8th (or 5th) grade math test. At least once per week I hear a teacher, parent, or member of the community make the statement that they couldn't pass a middle school math test, don't understand "that math", or say with a smile that they aren't good at math. Why do we, as a society, find this acceptable? A person who can't read on a middle school level is almost illiterate. They would never brag about it in public, and we would never want them teaching a group of students. Math ineptitude is not cause for pride. When students see adults display it as such, they are given silent permission to be prideful of their own stuggles in math. Is that what we want to promote?
5. We should teach things the "traditional way" because that's what parents understand. If parents really did "understand" math, they wouldn't have such a problem with their students actually learning it instead of just doing it. Many times at a parent teacher conference I've had a parent tell me, "I hated math when I was in school and never understood it. I'm bad at math." Then, 30 seconds later they are demanding that I teach their kid the same way that they were taught. Seriously? If you hated math and never understood it, why on Earth would you want your kid to have the same experience? For the past few years I have tried to keep an open line of communication with parents so that when they don't understand something we are exploring in class, they can notify me. When that happens I try to put a video demonstration by myself or a student on the concept on our class wiki so that the parents can see what we are doing. This has worked beautifully; parents and students end up watching the video together and the kids are able to teach their parents about the concepts to reinforce their learning.
Now it's your turn. What are your thoughts on teaching math, misconceptions, and the above thoughts? Have you had some of the same experiences? What other misconceptions do you think are out there about mathematics? Please share with us in the comment section below, and pass the post on to others using Twitter, Plurk, Google+, and Facebook so that we can hear their points of view as well.