Acknowledging the Only “Real-World Problem” We Face in Mathematics
By Edward B. Burger
November 15, 2016
For years I have argued that there are no “problems” in mathematics—there are "questions," "challenges," "conundrums," and even "riddles." Given that most people either live with "mathphobia" or belong to the “I hate math” club, it makes little sense that we would use such a negatively charged word to describe those joyful activities that promote the learning of mathematics. I regularly challenge educators to remove the word "problem" from their mathematical lexicon. There certainly are problems in our world, but, blissfully, there are no problems in mathematics.
However, now I expose a mathematical "real-world problem"—not one within the field itself, but rather in our curriculum: Most students either will never connect with or will quickly disengage with most of the mathematics they face in their formal education. That is, they will let the content drift away from short-term memories as soon as they can (if not sooner).
We as educators implicitly acknowledge this axiom through the design of our standard curriculum. Through my online tutorials with publishers Houghton Mifflin Harcourt and Thinkwell, I have personally journeyed (on video) through our math curriculum from kindergarten through calculus II—and the overlap of material from year to year is enormous. As curriculum fails to engage our students, we re-teach, re-re-teach, and so on, hoping for an eventual happy ending. This truism leads to a thought-provoking question: What if we explicitly acknowledge the reality that most students do not retain most of the technical details we pack into our math courses? Here is a one answer:
Our curriculum and daily class activities could include overt strategies for instilling practices of thinking more effectively so that our students would be empowered to think, create, and connect—not only to allow them to make meaning of important mathematical ideas, but also to apply those practices of mind to all their other studies and endeavors. In The 5 Elements of Effective Thinking, Mike Starbird and I offer some specific practices that can be incorporated in and out of the classroom to attain a deeper understanding and spark creativity.
At Southwestern University we intentionally offer practices of thinking, creating, and connecting throughout our curricular and co-curricular initiatives. Even more extreme, I recently connected these efforts to create a course that I now offer at Southwestern called Effective Thinking and Creative Puzzle-Solving. The course provides a space dedicated to amplifying and sharpening students’ own abilities and talents through these practices of effective thinking and applying those mindsets to the rest of their lives. Through a traditional lens this unusual course might appear to have no “content,” however when seen through the mind’s eye, the course tries to deliver the true vision of impactful learning: A way to grow and flourish for a lifetime—and every class should have this as its ultimate goal.
https://www.nctm.org/blog/realworldproblem/