December 21st, 2011
In a traditional, teacher-centered algebra class, students sit passively while a teacher demonstrates strategies for solving various problems. Recently, Anne Collins—co-author with Linda Dacey of The Xs and Whys of Algebra—visited two classes where students were actively engaged in solving multi-step problems while teachers were using formative assessment techniques to understand their thinking and monitor their progress. Here’s Anne’s account of her visits:
On a recent visit to a middle school I had the opportunity to attend two different math classes. I walked into one eighth-grade algebra class and was overwhelmed by the buzz of excitement. Some students were working at the board, others were working on individual white boards, while still other heads were bent over the same problem with the students discussing the next steps.
It took me a moment to find the teacher in this busy classroom. I found her standing between two students at the board. She was asking clarifying questions of one student as she tried to understand what he was thinking at a particular point in the solution process. I came to discover that this teacher was using a round-robin exercise with part of her class as a means of determining how proficient her students were with solving multi-step equations. She had organized her class into groups of three and had given each student the numbers one, two, or three. She began by sending student two to the board to record the equation she announced. Student two recorded the equation and solved only the first step. Student three replaced student two at the board to complete the second step, followed by student one. This continued until the problem was solved. The teacher explained to me that by using this round- robin activity she is able to determine at a glance how well each student is able to enter into the solution process and whether or not any students display misconceptions about solving problems.
I asked some students what they thought about going to the board and was pleased to hear Luis say, “I really like going to the board and the fact that I can get help right away if I need it. I can even help my teammates. And B.J. shared his relief that they go to the board because, “I need the extra time practicing and when I work alone I don’t know if I am doing the math correctly but when I go to the board, I get all the help I need from my team mates or my teacher.”
Next I visited another eighth-grade class and found that in this class students were grouped into triads and were trying to solve the problem Is It a Function? Each student had two clues that they had to share orally within their group to answer one question. I listened to one student asking, “What do I need to know about perpendicular lines?” A teammate responded, “I think there is something about the slopes of perpendicular lines but I don’t remember what it is. Why don’t we draw two lines that make a right angle and see what we get.” I was thrilled to hear the questions and see the strategy that this group used to make sense of the problem. Still another group was working on finding the slope of the line they had identified. They had graphed the ordered pairs given in the clues and were working on the equation. I also observed the teacher walking around listening to the groups, stopping to ask questions as she deemed necessary.
These interactive algebra classes are the polar opposites of how traditional algebra classes are run where the teacher shows and explains to students how to manipulate symbols. The students in the classes I visited actually knew what questions they need to ask to deepen their understanding. In both of these classes I was delighted to see students trying to make sense of the algebra on which they were working. These two teachers engage their students in solving rich problems. The collaborative nature of these classes illustrates just how much students can achieve when they are given the opportunities to solve interesting problems which require them to apply the procedural skills they have learned. And the teachers I observed model the positive impact effective formative assessment has on student learning.
Entry Filed under: math