Last week I had an experience of how a math lesson could be so much more authentic than a traditional textbook math lesson as I taught my robotics class.
As Dan Meyer points out in his TED talk (http://www.youtube.com/watch?v=BlvKWEvKSi8) many current math textbooks make the problem solving process too easy and unrepresentative of using math in the “real world” to solve problems. For years I have been using Geometer’s Sketchpad (http://www.keypress.com/x24070.xml), Fathom (http://www.keypress.com/x5656.xml), LoggerPro (http://www.vernier.com/products/software/lp/) and Autograph (http://www.autograph-math.com/) as software tools for students to use in constructing their own math discoveries. In one lesson students used LoggerPro to analyze videos of water balloon launches and determine the quadratic equation whose graph would match a parabolic ballon trajectory. They used their analysis to determine the best angle to launch a water ballon at to maximize the distance flown. To test their analysis I became their target at the maximum distance they calculated.
When I design lessons to encourage what Dan Meyer calls “patient problem solving” I usually start with the math concept I am trying to teach and then brainstorm different real world problems where knowing that concept would help to solve the problem. Recently I realized the best math lessons might come from starting with the problem first.
Last week my students in middle school robotics had to calculate the degrees the wheel of their robot must turn in order to make the robot execute a 90 degree, 60 degree or 30 degree swing turn. They quickly realized they were dealing with 2 circles; the wheel’s circle and the turning circle. Students then determined that by using the ratio of the circumferences of the two circles they could calculate the number of degrees the wheel must turn in order to make a given degree swing turn. The best part of this real world problem solving math lesson is they did not have to ask me if they got it right. All they had to do was run their program that they designed with their calculations to see if they got the correct turn from the robot.
So the next time I teach the circumference formula in my math class I might just get the robots out!