As math education evolves, the teaching methods change to suit the needs of today’s learners. This happens as a result of the research of mathematicians and math educators (sometimes, one in the same) for more effective ways to teach mathematics.
Today’s students are so “right now” that many of them are not really interested in the whys of mathematics. They want the bottom line so they can complete homework assignments or pass tests. Most of my students are not interested in how a formula was derived. They want the formula and they want to know how to apply it. There are rare cases when a student questions a concept and wants to know why it works. In this situation, I take the time to explain the concept and prompt the student to figure it out on their own. Once this is done, the student can relate to the concept and apply it easily, because it now makes sense.
Today, we are all so concerned with following and keeping up with standards, scoring high on standardized tests, and getting students into the next grade by any means necessary, that we do not take the time to implement more meaningful methods of math education into our curricula.
In an ideal education system, secondary students would be separated based on their interest in specific fields (language, science, math, history, etc.). Within that field, the teacher would have the autonomy to structure their courses to strengthen their students’ understanding. In mathematics, this would make room for reinvention based problems that would bring math to life for the students. As a mathematician, I wish everyone could understand mathematics on a higher level. Unfortunately, most students are not interested and some educators are neither equipped nor concerned enough to make such changes in their classrooms, even when the opportunity is present.
As a math educator, I think the concept of reinventing math is brilliant. I believe it would have strengthened my understanding of so many mathematical concepts when I was a student. I believe that math educators should learn math in this manner so that they can be more effective educators. The more we understand a concept (and reinvention can help) the more effective we can teach that concept.
What do you think about reinvention as a method for teaching math?