I’ve always told my students tales from my life. Sometimes as part of the chitchat of milling around with students before or after class, and occasionally during class if the tale seems to fit in somehow with the lesson. I’ve told students about learning to quilt and knit. I told students about learning to be a cyclist. In teaching my tutor training course I’ve talked about misunderstandings from my own life that illustrate the need to listen carefully and ask questions to be sure you understand the situation.
I also frequently use analogies, both to help my students to learn mathematics, but also to help my students understand what it means to study mathematics. Many people think that math knowledge is developed in a fashion similar to learning to fly, by being sprinkled with pixie dust. That is, they believe that if they are shown how to do math, they will magically be able to do mathematics themselves. So I try to explain that’s like expecting to learn to play the violin by watching someone play 3 days a week, or learning to draw by watching an artist make sketches, or learning to drive by riding in a car. Of course watching an experienced person do a task plays a role in helping to learn the task. But, you won’t learn to do the task yourself until you put in a significant amount of time and effort to practice. I’ve tried many times to get that idea across to my students.
One day the perfect incident happened in my life that led to the perfect analogy.
My youngest daughter is quite stubborn at times. I think she might get that from me. 🙂 When she was 5 years old, and after already attending swim lessons for 2 years, she one day decided that she was done with swim lessons. At the pool that day she literally climbed up my body to try to avoid getting in the pool.
This incident happened just a few days before my students took an exam. The exam had mixed results. Some students who seemed to be understanding the material in class weren’t doing homework on a regular basis and predictably didn’t do well on the exam, or not as well as they could have.
When I returned the exams to the class, I was planning to remind them that homework and practice were important. I started with having them fess-up to studying or not. I wanted them to be honest, so I started by turning my back to the class and asked them to raise their hands if they’d studied for the exam. Then keep their hands raised if they’d studied more than an hour. More than two hours. Then I asked them to raise their hands if they’d done all the homework. I then asked them to all lower their hands. Then I turned around and asked if one of the students would summarize what they’d learned. The student representative said that most of the class studied, but only about half had studied more than two hours and very few had done all their homework.
I started to then go into a speech about how important practice was for learning math. Then I thought that sounded awfully similar to what I’d said to them at the beginning of the quarter. Then I realized they’re just like my daughter, they don’t want to get in the water and swim. So, I told them the story of my youngest daughter clinging to me and refusing to get in the water at swim lessons. I then asked the class if she would ever learn to swim. Then someone in the back of class yelled out “Throw her in the water!” I couldn’t have planted a better response. “Yes she needs to get in the water,” I responded.
I then went on to tell my students that I wasn’t sure what the math pool was or what it looked like, but I was sure that they needed to get in the math pool in order to learn math. I told them that I knew that some of them came to class and didn’t get in the math pool. I could tell because they had out a device that you can’t take in the pool. “Our cell phones?” one of the students replied. “Exactly!” I said. I went on to explain that just like in learning to swim there were going to be times when they felt like they were drowning, but that if they kept on working and asked questions that eventually they would learn the tasks.
After that day many more students submitted homework regularly, and very few had their cell phones out during class. The whole level of commitment to the class, both during class and doing outside of class work seemed to rise. I even heard students occasionally say to another student with a phone out during group time, “hey you can’t have that in the pool.”
This particular tale seemed to work so well that I use it anytime I have a class with a significant number of students that don’t seem to be putting in the time and effort that it will take for them to be successful. I find that it’s not just a good analogy for my students, but good analogy for me as well. I need to make sure that I provide a structure for my students so they’re willing to try thing out that they’re not sure about, that give them that feeling of drowning. But I also need to create a space that makes them feel safe enough to do that. The activities need to be well designed and I need to be sure to identify the good thinking that lead to the wrong answers.
One quarter, Fall 2013, I had a exceptional Math 105 class. They were already sitting together in groups talking about math before I walked into the room. Their attendance rates and homework submission rates were the highest I’ve ever seen. That class created a math pool, even before I got a chance to tell them the story. I’m not sure exactly how it happened, but I think it started the second day of class, when a brave student went to the front of the class to do a problem. About half way through he stopped and looked at me and said he was stuck. I asked the rest of the class if anyone had a suggestion to help him move on. Several gave suggestions, then the class narrowed in on a strategy. I took a step back and they finished the problem together. About half way through the quarter, I still ended up telling this class the story of my daughter not getting in the pool, however in this case I wanted them to know how excited I was that they’d created a math pool all on their own.