Talking helps us make sense of ideas.
Talking helps us synthesize our ideas.
Talking helps us communicate our ideas.
We want to get this kindergarten class talking — a lot — throughout our current unit: geometry.
But the students weren’t talking much…. yet.
After exploring student understandings about shape during our Same or Difference activity — see blog post from 1.4.19 — Jessica and I prepared for the Shape Hunt. It’s based off a task by Illustrative Mathematics (from the current website, not the forthcoming elementary curriculum).
I cut out six shapes — some familiar to the kindergartners, and some less so — which Jessica and I placed strategically around the classroom.
Once the students returned from music class, we gathered them at the class meeting area on the rug to launch the investigation.
I pinned shape number 1 — a rectangle — to the white board.
“What can you say about this shape?” I expected they would say things like “it’s long” (attending to an attribute) or “it’s a rectangle” (which most know intuitively at this point).
Instead, the first student, Savannah, said “we can add squares together to make it.” I recorded her words on the board.
“Tell us more about that.”
“I see it! It’s three squares!” Cedric burst out.
“Yeah,” Savannah said. “Three squares.”
“Where?” I pushed them for clarity.
Savannah stood up and approached the board. She gestured with her fingers: “Here.”
“Oh, in a stack?”
I added a caret clarifying the number of squares that fit into that rectangle.
From the third row on the rug, I could see Gianna scrunching her face.
“Gianna, do you want to add something?”
Gianna paused, and bit her lip. “I think it’s a square that’s all stretched out.”
“Yes, it does remind me of a square,” I murmured while recording Gianna’s thinking on the board. “What parts of this shape remind you of a square?”
“The shape,” Gianna responded. A dead end.
“Yesterday, we talked a little bit about the number of sides. Does that remind you of a square?”
“No. The shape.” Gianna was insistent.
I felt like I was fumbling. “How many sides are there?”
“A lot,” Gianna said quickly. We were spinning our wheels, and we wanted to launch the investigation. I took a few more responses before we moved on.
During the investigation, students, armed with clipboards and pencils, did their best to sketch the shapes around the room on their recording sheet. We encouraged the students to talk with one another about the shapes while they worked, but most were so focused on their own drawings that they didn’t talk much.
I wandered over to shape 2, a “tilted square,” to observe.
Bo’s drawing, shown at left, closely matched the shape.
Meanwhile, George had drawn the outline of a blue triangle (shown below).
“No, you’re missing a point!” Bo said indignantly.
“My shape is pointy!” George seemed defensive of his work. As I watched, I wish we had prepped them more for how to talk to one another.
“It’s missing a point here,” Bo explained, pointing to the bottom of the triangle. “Look.”
George considered the idea.
Sara overheard them. “It’s got points on both sides. It’s flipped.” I couldn’t tell if she was attending to the fact that this tilted square looked like two isosceles triangles, joined at the base, or what, but I decided to just listen.
George had already gotten out a regular pencil to revise his shape, which he then filled in with a red colored pencil.
I walked over to shape #3, shaped like an L. To me, it looks like two fused rectangles. Jessica saw it as composed of 3 mini-rectangles or squares. I wondered if any students would see it as a “square missing a chunk.”
This one seemed challenging for students to sketch. I wondered if it was because many students saw it as composed of other figures as opposed to one solid shape. None of the students were talking to one another.
Here’s Gianna’s sketch of shape #3. To us, it looks like she sees it as two figures, possibly two rectangles. It looks like she drew the lower one, and started to close the shape before veering back out to show the upper rectangle. Her lower rectangle features straight(ish) lines and sharp 90 degree(ish) angles. The upper one is anemic and curved.
Back at the carpet for the close, I tried to use a “Collect and Display” math language routine to capture and make visible students oral language. Unfortunately, many students were still feeling stuck in that Level 0 of Van Hiele. They were able to name familiar shapes, and felt uncomfortable with some of the others.
The students offered limited descriptions. I expected us to dwell in that remarkable, natural language of shapes — “pointy,” “glued,” “turned,” “flat,” etc. Instead, students were very cautious. They talked about the shapes they knew, and about how some sides seemed to have the “same measure.”
I was disappointed, but tried not to show it.
Students did wonder about the name for that tilted square. “If a shape is tilted, does it have a different name?” I recorded this on the board. “We should think more about this. It’s so puzzling, since they LOOK different but are also a lot the SAME. They have the same sides like a square.”
I asked a few students to share their drawings, but I had been so caught up in trying to listen to and capture the vocabulary students were using — even though it was spare — that I hadn’t been as deliberate as I would like about selecting and sequencing the share. Oops.
After the lesson, the teacher Jessica and I met in the back of her room to look at student work samples. Even though students hadn’t talked much about these shapes, Jessica and I had so much to say about what we saw! We used the question “what did this student think was important about the shape?”
Some students seemed to focus on the composition of the shape from other shapes, or the straightness of the lines, or the measure of the angles (how “pointy” they are), and making prominent points jut out at the expense of some of the lines. Some students seemed to equate pointiness with triangles, and smoothed that tilted square out to become a rectangle with a long base.
So even if the students weren’t talking as much as we wanted yet, at least the teachers were. Getting the teachers talking — anticipating, sharing, and analyzing — is an excellent first step. Talking about both the mathematics and the student work together gives us the same benefits of talk that students get — making sense of and synthesizing ideas, and communicating reasoning. We had a lot to think about for the next day.