Through Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here
Test Yourself Math — June 24th, 2013
This problem relates to an article on the changing landscape of retirement. How far will $1 million in retirement savings take you?
This is “Crocheted H-Fractal Blanket”, by Kyle Calderhead, on display at the 2012 Bridges Math and Art Conference at Towson University.
I am very proud of my students, Ahmed and Jason, who presented their peer-to-peer math enrichment program MathMatters! at this year’s TEDxNYED conference.
Ahmed and Jason created a program where NYC high school students travel to middle schools and run workshops on advanced and extra-curricular mathematics. Their goal is to spread the beauty and fun of mathematics to younger students.
Ahmed and Jason put together a team of 20 high school students to develop and deliver fun and engaging lessons on Number Theory, Game Theory, Graph Theory, and many other topics. And although they are graduating this year, Ahmed and Jason have ensured that MathMatters! will live on by training the next generation of student-leaders. They also hope to continue to grow the program while at college.
You can learn more about their program MathMatters! here, and you can watch their full TEDx talk here.
A common debate in math education centers on the extent to which students should memorize things, like multiplication tables, the quadratic formula, or the division algorithm.
There are many sensible arguments against memorizing algorithms. While memorizing algorithms might produce good results in a typical math class, mathematics makes the most sense when it is understood as a coherent, interconnected system of thought. We want students to be resourceful and creative problem solvers, and this requires that students understand the context and the connections, not merely the steps, of the procedures they learn.
Occasionally this argument is taken to the extreme and teachers altogether discourage memorization of algorithms and procedures, claiming that it’s pointless for students to have the procedural knowledge without understanding the context.
While there is some merit to this argument, I was recently reminded how valuable it can be to blindly memorize algorithms.
A friend invited me to go rock-climbing, something I had never done before. We arrived at the gym, and my friend, an experienced climber, showed me how to identify the beginner trails on the wall and encouraged me to get climbing right way. Over the next hour I attempted a few trails, and met with more frustration than success.
After a particularly discouraging attempt, I sat down next to my friend to rest. He told me that he noticed I was getting stuck in the middle of the trail and was having difficulty finding the next hold. He suggested that I examine the trail before I start the climb and memorize the sequence of moves needed to make it to the top.
By memorizing the wall-climbing algorithm, I was freed from trying to do too many things at once. I could focus on developing the fundamental techniques — proper holds, balance, body position, different reaches — without worrying about what the next step should be.
Ultimately we want the ability to be on an unfamiliar wall, or in an unfamiliar problem, and have the confidence and skill to figure out what to do next. But this skill is really a combination of many skills, and it can be challenging, and frustrating, to try to develop them them all simultaneously.
Sometimes memorizing things — like a sequence of handholds, or the quadratic formula — can help us get to the top. And it can help prepare us for the day when memorizing won’t be enough.
Nothing as compelling, nor challenging. as trying to capture infinity.