Lesson
8th Grade Math – Coordinate Geometry, Logical Reasoning, Justification and Proof
Clip 5/11: Coordinate Geometry Lesson Part 5
Overview
Antoinette Villarin gathers her eighth-grade geometry students back together after their small-group work, praising the students’ strategies, problem solving, and collaboration. She asks them to share the strategies they used, then return to their task to “fix your work,” justifying and proving their approach.
Antoinette reminds her students that “If it’s hard to understand your thinking verbally, we’ll want to see your paper.” One student describes his thinking at the document camera; the student shares how he used the Pythagorean Theorem. Antoinette challenges him to include the quantities and the equation in his visual representation.
Antoinette asks how many others used the same strategy. As the group shares, one student catches a mistake in his thinking and uses a calculator to check his thinking.
Antoinette probes students’ thinking and precision as they share: “When you got 8.05, what unit were you using to measure?” and “How did you convert your unit?”
Teacher Commentary
Teacher Commentary
In my classroom I have a poster that says, "We celebrate mistakes." And I loved today when Grendel felt like he made a mistake, and he was doing Pythagorean Theorem. He said, “Oh, well, no, I made a mistake.” I loved that it was in front of the class and we were able to work through it.
Another poster says, "We celebrate mistakes as opportunities to learn.” Another says, "We will share and justify our solutions. We'll explain our thinking, and make sense of other's." That’s the culture of the classroom that I want to create — I'm hoping to bring with me.
But being at a new school, it's different at every new school. So, like, for me, coming into a geometry class, I was really excited to see how deeply they were going to justify their work, and I noticed that we were lacking in that. I feel like this is the year where I want to build it up with this group.