SHARING REFLECTIONS ON TEACHING AND LEARNING AT CATE SCHOOL
By Annalee Salcedo
I had the pleasure of formally observing two PBL classes recently. As a window into what our Integrated Problem Solving courses look like, I share here excerpts of my observation write-ups of these two classes.
IPS 2: C Block, Teacher: Taylor W.
This class, as expected had a high ratio of student to teacher voice. Students were constantly talking to each other about math. Sitting in a circle, students were leaning over to neighbors, and talking across the circle to discuss with their peers the tests that they had just gotten back. Taylor seemed just another member of the circle, talking about math with a neighbor. Her input was not solicited any more than any other active student, and her neighbors easily turned the other way to talk to a peer when they were done talking with Taylor.
What the students were saying as they reviewed their work and their mistakes on the test was also a model for what I'd hope students in all our classes are saying: "I struggled through it then I got it." "It made me so happy." "That was hard!" "That makes sense" "Wait, I need to think." "I enjoyed this problem."
When discussing homework problems, and recognizing the opportunity to apply various methods they've seen before, I heard students say: "I like the Shion method." or "I like the Yuki method." The students themselves are clearly sources of knowledge and techniques for each other, rather than the teacher or the textbook. The students associate problem solving strategies that they can use with the work that other students have shown them.
Taylor spoke more during the discussion of the HW problems. But her comments were about bringing attention to key points: emphasizing the introduction of notation, asking students to generalize an outcome of a problem. After the Midline Theorem problem, for example, no fewer than five students chimed in to try to articulate what the problem showed them. They built on each other's comments and finally arrived at a clear theorem they could put in their "What we know about Geometry" document. A 6th student noted that the theorem was "pretty rad."
IPS 2: A Block; Teacher - Rachel VW.
Rachel sets a clear expectation that math can be / is enjoyable. Her opening questions about the homework were "Did we have any favorites?" and "What are we most looking forward to?"
After those opening questions, most of the comments/discussion featured student voices. Students are clearly used to the culture of responding to each other's work, raising questions, showing different ways of approaching the problem, and even thanking each other for pointing out mistakes! One student who presented knew to check for understanding from his peers, stopping at a point in his presentation to say, "Sound good?" or “Do we all agree?” Another student started her presentation by listing what she noticed about the problem. A different student took the results of one problem and asked the group if they thought it generalized to all right triangles. Another student noted that it generalized to all triangles, not just right triangles. On a different problem, one student was able to identify an assumption he made that led him astray. A different student recognized he was about to make the same mistake as a classmate did, and noted that he remembered discussing her mistake and that helped him avoid it. There's clearly a culture of learning from mistakes and seeing them as valuable, and probably in part a result of Rachel’s explicit valuing of mistakes: "I saw some great mistakes."
Overall, two great classes to observe because the students were so active and vocal. It wasn't so much teaching I got to see, but the process by which students were learning themselves. But of course, the environment is set by the teacher, and I appreciate the thoughtfulness, purpose, skill behind Taylor’s and Rachel’s moves that make such a learning environment possible for their students.