Well it's happened again. A couple of recent tweets have me thinking about my days in the classroom and my role as a mathematics teacher. In this tweet Karl Fisch is looking for advice to help his students overcome some challenges in their math class.
Frustrated. I'm not being successful helping my students when they don't immediately get something. They just stop and give up.— Karl Fisch (@karlfisch) April 3, 2012
In particular he is struggling with creating a culture or a mindset for his students of determination. It also reminds me of the theme from yesterday’s #mathchat.
The topic is: "How do/should we measure success in mathematics, and in schools?"#mathchat— Colin Graham (@ColinTGraham) April 2, 2012
In my days at Cary Academy I remember a conversation the math department had about what were the specific characteristics we wanted our students to develop through their experiences at Cary Academy. I have always felt that one of the most important skills (if it is even a skill) that we could encourage our students to develop is a sense of determination, a sense of patience, and the stamina to be able to attack a problem without becoming frustrated. However society or at least the educational environment seems to teach our students the exact opposite when it comes to mathematics. If we examine most of the problems that we share with our students either through homework, classwork, or on high-stakes tests, there's an expectation that every problem can be solved in one or two minutes. For example when you look at the SATs, students are expected to complete 44 multiple-choice questions in 50 minutes, which means 68 seconds per problem. Because so much of what we do in schools is driven by end-of-course testing and high-stakes testing, that philosophy becomes entrenched in our classrooms.
During my final years of teaching, I had a great opportunity to work with students who had completed the standard course of study in mathematics, through first-semester Calculus. This allowed me a rare opportunity to approach mathematics in a very different way. It allowed me to build my curriculum around problems whose solutions were non-trivial. It was always challenging in the first few weeks of the course to get students to transition from the pattern of behavior established in their previous 11 years of mathematics to my new philosophy. So to start each year on the first day of class I gave them a problem, and I basically said “Go!” The goal was for students to find great challenge in the problem, to not have a simple recipe to throw at the problem, and to encourage them to work in groups to develop a strategy for solving the problem. Typically, this first problem would last a few days. Having worked through a couple problems like this I would then have a conversation that this class would be more likely to have problems that would last a week then it would be to have problems that last 2 minutes. Indeed, I even explained that there may be some problems that we would spend a week on for which I didn't know the answer and for which we may not find an answer. Ironically, I was still required to have a timed exam, and my greatest challenge was to create 3 or 4 problems that could be answered in the two hours, that did not simply destroy the culture I worked so hard to create.
While no longer in the classroom on a daily basis, I do have the opportunity to work with my own two kids (Cameron 4yo. and MacKenna 6 yo.), and I can't help but feel sorry for them because I know that I bring this philosophy to my relationship with them. Recently we attended Science Night at my daughter’s school. The experience is really a great opportunity for kids to explore science before any formal science curriculum instruction has begun. However, the night is a great challenge for me. Each year the teachers setup science experiments in their rooms, six in total, and the event lasts 90 minutes. As has been the experience both times that we've done this, I get frustrated when my daughter seems to “pair-up” with a classmate in the first room. As a result she wants to stick with her friend and complete tasks quickly so they can move on to the next classroom. Unfortunately she does so by sacrificing curiosity and inquisition. In particular this year one of the problems was to use a limited amount of money to purchase supplies that would enable her to build a packaging solution for a raw egg, such that it could be dropped from a height of 8 feet without cracking. It was a bit awkward as I sat down and began to work with her, answering her questions with more questions, and prodding her with “Whys and Hows.” Her classmate and indeed the child’s mom seemed to become impatient with us for spending so much time at this task. At one point I even heard the mother say we needed to hurry up so that we could get to the other stations. For me it was far more important for MacKenna to do one station really well than it was to expose her to all the different experiments. Someday I hope she'll appreciate that philosophy and not hold it against me that she couldn't hang out with her friends as they raced from room to room.
So back to the original tweets, I am not sure how to help Karl. He is bound by a curriculum for which he has little control and is subject to external measures. Maybe he can show the video of the 13-year old who just completed a 1080 on his skateboard after numerous wipe-outs, or he can find a way to introduce his kids to Fermat’s Last Theorem and Andrew Wiles’ determination. As for my answer to the #mathchat topic, I hope our measurement of success includes some indication of stamina and determination for pursuing that which is not easy.