If you hadn’t heard, a group of Georgia Tech Mathematicians have proved the Kelmans-Seymour Conjecture, a 40-year old problem. Here is a an article that describes the conjecture and its proof in more detail for those of you interested: “Georgia Tech Mathematicians Solve 40-year old Math Mystery” Now, I personally had no idea what this conjecture was till after reading the article – Graph Theory was not something I spent a lot of time on in college or in my teaching career. What struck me was that this conjecture has been out there for 40 years with people trying to prove it, and it took a collaboration of over 39 years between six mathematicians to prove it:
“One made the conjecture. One tried for years to prove it and failed but passed on his insights. One advanced the mathematical basis for 10 more years. One helped that person solve part of the proof. And two more finally helped him complete the rest of the proof.”
Elapsed time: 39 years.” (Ben Brumfield | May 25, 2016)
Here’s what I love about this – it shows that math is a collaborative endeavor, that takes time and different approaches and insights and that something new can always be discovered or proved. Which is what we should be focusing on in K-12 math education, instead of the idea that there is one answer to a problem. The standards for mathematical practice (part of the Common Core and based on NCTM Principles to Actions) are all about this collaboration, problem-solving, communication. It’s slow to take hold, and politics is working against it, but look at what can be accomplished when mathematicians, i.e. students, work together to problem-solve?
Math is not a single-solution, one-way only, or learn-in-isolation. Let’s support the practices, let’s support teachers, let’s support students and create mathematical learning experiences that promote collaboration, real, relevant problem-solving. It requires teachers being willing to accept multiple approaches and multiple methods of explanation (verbal, written, visual). It requires noise – collaboration is not sitting quietly at your desk. It requires “mess” – using whatever tools or resources help students think about problems. It requires time. But think about the new and different math that students will create and explore – and think about how much better prepared they will be for the mess that is the world. That’s ‘college and career ready’ in my opinion.