SHARING REFLECTIONS ON TEACHING AND LEARNING AT CATE SCHOOL

by Rachel Van Wickle What is it that creates a classroom environment where students feel supported and believed in, and safe enough to take risks without fear of failure? In past years, it has felt like some of my classes have had this “magic” while others have not. How can I break the magic down into tangible and repeatable steps? I’m thinking that constructing classroom values is one step in the right direction. In my Integrated Problem Solving II course this year, I experimented with the first three days to try to create a sense of safety and belonging. I did so by first presenting my values as teacher, then asking students to journal about their individual values, and finishing with a discussion of values for our class as a whole. Later in the term, we revisited our class values and reflected on what might be added or adjusted. Here is what it looked like: Day 1 – Teacher ValuesOn the first day of class, I presented my students with the following: We discussed why these values are important to me as a math teacher, and I explained how my grading and assessment policies align. To drive the message home, I asked the students to take about five minutes to journal a response to the prompt, “Why are mistakes important?” This idea came from Jo Boaler’s course, “How to Learn Math For Teachers.” Here are the main themes that I took from discussing mistakes with my students: - Mistakes change the way we think and learn how to change
- Mistakes give us insight into future problems
- Mistakes help us gain a deeper understanding
- Our brains are wired to remember bad experiences
- Best learning comes from making a mistake
- Sharing a mistake helps the whole class
- Failures are more useful than successes
Day 2 – Individual Values On the second day of class, I asked students to journal about their own values. This prompt came from math department member, Taylor Donovan Wyatt, and allowed students an opportunity to be specific about how they view themselves as a member of the class. Here is the exercise, followed by three student examples: A question I have after conducting this activity is whether or not to ask students to share these with each other. Do they gain the feeling of safety and belonging from this activity merely by me reading and responding to their journal entry? Would it be asking them to be too vulnerable to share out as a class? Or, would sharing them with each other create an even better sense of community? Below are three student examples that show the variety and scope of the exercise. Day 3 – Class ValuesOn the third day of school, I asked students to partner up and discuss what values we should set in place for our class so that our discussions for the rest of the year would be as successful as possible. After sharing out, we compiled the list shown at the right. I then posted this list on the main page of our LMS so that we could refer back to it as the year progressed. Because the students all agreed to this list on day 3, I was able to hold each student accountable so that everyone in the class would feel supported and encouraged. Day 40 – Revisiting ValuesOn the first day of the second term, I brought out the list of class values that we created on day 3. I asked students to reflect on which of these values was a strength for our class in the first trimester and which, if any, we could work on more. Students also used this exercise as an opportunity to add and revise our list since so much time had gone by since it was first created. I find it interesting that the student in the example below uses the word “we” to discuss the growth of our class as a whole. Then, she finished writing by detailing how the class dynamic affected her own individual experience. Here is what she wrote: All in all, I am excited to use this sequence at the beginning of next year, but I am definitely interested in adjusting it to better serve my students. Is this too touchy feely to start math class with? How do I encourage students to be authentic right at the start of the year? What else should be done as the year progresses to revisit the values and continue cultivating the sense of safety and belonging???
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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. |
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