If you are a math teacher or have ever taken a math course of any kind, this video by Conrad Wolfram should be of some interest to you.
I don’t teach K – 12, but I do have a hard time letting go of the idea that somewhere, sometime in their lives students needs the basics of mathematical operations and ideas…add, subtract, multiply, divide…number sense…logic..mathematical intuition…and no calculators. Not for awhile anyway. I am talking elementary school here. Let young students get a feel for numbers and a confidence with them sans a computing device.
Memorizing times tables in second grade is no more difficult or unnecessary than learning a language when you are young. At least those learnings stay with you for your entire life, or, they don’t if you miss that day in school. I joke with my students that, “I was absent the day we did the upper 12’s, so I never learned them.” Absolutely true. Ask me what 6×12 is, and I can’t tell you right off. BUT, I understand multiplication and realize that multiplication is just repeated addition so I can quickly go to 5×12 = 60 (since I was present for 5 x 12 day) and add 12 to get 72. The memorized tables serve their purpose as does the understanding of how numbers and operations work together.
What I would like to see is an application of some of Conrad’s ideas in our community college, college prep classes. (I am not so sure about teaching through programming…but the idea of using computers as computing devices is what interests me). These are the classes of arithmetic, introductory algebra, and intermediate algebra taught in community college as preparation for the college math course. In my opinion, and many of my colleagues might disagree, if students have not learned their times tables by the time they reach my arithmetic class in community college, then I am inclined to believe that I am not going to teach that to them in the short time they are with me. What I would rather do is teach them to become a) extremely proficient with a well-designed tool (calculator or computer) and b) engage them with problems that apply the results of using that tool.
If this idea were well designed and implemented throughout the college-prep curriculum, then we might see a new crop of students that can think critically and solve problems as opposed to those that forget the steps for all the processes that, to them, are disconnected and meaningless.