It was nice to hear that Erika had some personal reaction to my research topic of technology in math education. She struggled in math class, as well as quite a few students in math class over the years, and wonders if more technology would have helped.
I had the chance to read the new proposal by the National Council of Teachers of Mathematics this last week called Catalyzing Change in High School Mathematics. They sent a copy of their proposal to all members of the NCTM for review and comment. One aspect of this new direction in mathematics education is to incorporate more technology, not just in the realm of graphing calculator use, but to use more interactive technology that will deepen understanding of math content. It’s not sufficient to use a great tool such as a graphing calculator, but technology in terms of apps and software can be utilized. If a student wants to understand how quadratics behave, for example, students can use an app that has a general quadratic function graphed, but has “sliders” that modify parameters (A, B, and C) of the quadratic function y = Ax^2 + Bx + C. By allowing students to consciously make adjustments to the parameters, and observe the results, they can solidify their understanding of how quadratic functions in general behave. Simulations can also be run to observe behaviors of patterns. Statistics is an area that utilizes this method quite a bit. The list can go on.
If teachers can use these types of apps and software, we can make some significant changes in math education nationwide for the betterment of student success and achievement. If one of our goals in school is to produce problems solvers, one way to accomplish this is to allow students to use the tools of mathematics, namely technology, to assist them in their endeavors. This is another area that the NCTM wants teachers and schools to focus on, solving “real world” problems. Gone should be the “recipe” or “cookie cutter” type story problems in most high school math texts have currently. Students need to be able to solve unexpected problems and use their knowledge of mathematics to solve them. I like the new direction the NCTM is pursuing.