We make assumptions every minute of the day without thinking about them or making them explicit. We have to. We assume that we'll get up, go to work, and follow a certain routine. We assume that we can turn on the tap and get a glass of water, pick up the phone and call a loved one, turn on our computer and get hooked up to the universe. Of course, there are times (like September 11) when our assumptions are drastically shaken, but on a day-to-day basis we operate from certain givens. If we questioned all of these assumptions all the time we'd go nuts; we couldn't go about our daily business of work or fun.
When we teach we also make assumptions. We assume things about our students and about our teaching. Some of these unexamined assumptions can get in the way of successful teaching and learning. Part of good teaching means identifying our assumptions and questioning them from time to time.
The other day I was reminded of this need to question assumptions about teaching. I was working with my daughter on her second grade math homework. Their math group was studying the concept that you could get to the same answer in different ways. In this case, they were focusing on money. On their worksheets, they were asked to create a total of, say, 50 cents, by using combinations of various coins. So, two quarters, or five dimes, or two nickels and four dimes, or four nickels and three dimes, and so on. The next task asked them to identify different combinations of coins that would equal 75 cents, and so on. You get the picture.
My daughter completed her assignment with ease and speed. (And I was grateful that at this stage in her math schoolwork, I have the math skills to check her work!) But I was curious about what she learned. There wasn't any place on the math homework that described the purpose of the activity. It seemed obvious: you can make a total of X by using many different combinations of coins. But I wanted to hear what she thought. So I asked my daughter, "What do you think this math homework was trying to teach you?"
She paused for a minute and then said, "They were telling you that you should use the least number of coins you can. So, like, if you are going on the subway, use 2 quarters instead of all those nickels and dimes."
I was surprised at her answer, because I knew she was well aware that you could get to X by a variety or combinations. Starting in kindergarten, they practiced ways to write or illustrate the concept of 100 in as many ways as they possibly could. In first and second grade their investigation of numbers became more sophisticated to expand and reinforce this concept. And now they were applying the same principle to money.
"Oh," I said, "but what if you were saving your quarters for meters and wanted to use your other coins for the subway or bus?"
"I don't know," she said, "I guess that's OK."
"I think the homework was about the idea that you can get to the same total amount by using different combinations of coins," I said.
"Oh," she said. "I knew that, but I thought the homework was about something else."
Now, I don't know how the teacher framed the homework, or how she analyzed it with the kids afterward. But what this incident showed me is that sometimes we assume that because things seem so obvious to us, the same must be true of our students--that somehow they will make that leap and "get" the learning principle involved without the need for an explicit explanation of the principle. I think that if we neglect to name the principle explicitly, we are losing valuable opportunities to make the connection between something concrete and something abstract.
I remember lots of lost opportunities in my own teaching, and in my work as a staff development facilitator. I know I assigned many creative, engaging activities in class, but I wish I had learned earlier to stop after or before each of the activities and ask: Why do you think we are doing this? How can you apply this in your life (or to your teaching?) While some students will make that connection inductively, others will not; they need the teacher to make the connection between activity and principle clear.
For example, say you are working with students in a math class on ways to solve problems. In one class, you use a pie chart to help you frame a word problem visually. The students are able to solve the problem. You assume that because they solved that problem, they understand that the use of a visual like a pie chart or a graph is a good way to solve a similar problem. Can you always assume that students will make this connection? How can you make it explicit and reinforce it?
How much more powerful each lesson would be if we took a few minutes to check if and how students are "getting" what we are teaching rather than relying on our assumptions that they are understanding things the way we intend. Even if their understanding diverges from our intentions, how much we can learn from listening to their reflections. I wish now I had asked my daughter, for example, why she thought her homework was teaching her to use the least number of coins. It would have revealed something about her thinking.
Since I see her all the time, I can always go back and do that. But I can't go back and fill in the missed opportunities I had to question my assumptions about what students (or teachers) were "getting."
Lenore Balliro, the editor of Field Notes, has worked in adult basic education for about 18 years. She can be reached at <lballiro2000@yahoo.com>.