Estimates from the Fishbowl

Immediately using ideas from a workshop helps me carry momentum forward. As I wrote in my last post, I spent the previous weekend discussing how to make learning more accessible for English language learners. Multiple strategies were modeled and I chose to use a fishbowl activity in my math class today. My goal revolved around increasing student conversations about mathematics. I wanted them to talk about their thoughts and for other students to observe how a problem can move forward through group discussion. With absences, a small class of seven students entered the room and each learner spent a round inside and on the outside of the fishbowl.

In terms of contents, I have had my eyes on Andrew Stadel’s great new Estimation 180 blog as a means to kick off regular estimation practice. Today, Mr. Stadel’s height was the first estimation with four students sitting around one whiteboard. Peering into the bowl, I eagerly joined the remaining students to observe and record the math processing.

“Do you know how tall you are?” One student was fairly confident that she measures 140 cm. A student grabbed a couple of meter sticks and stacked them end-to-end. “200 cm. Hmmm, that seems really tall. Maybe that is the upper number.”

My Mom is really tall and I’m up to her shoulders.”

“Really, well let’s see how tall you are.” I was happy to hear this check. Students made some measurements and decided that the boy’s mother was closer to 160 cm.

As group processing slowed, I asked each student to make his or her own estimate and provide reasoning.

The estimations ranged from 180 to 190 cm. Some reasoning included:

I think the fence must measure 100 cm. I then found out that the length from his toes to his belly is longer than from his belly to head so I doubled 100 cm and subtracted 10.

I believe that the bush (located in the photograph) does not come to his hips and that his hips (student measure height of her own) would be about 90 cm. So it is a little more than double.

After a debrief where the observers shared their thoughts and the “fish” shared what it was like to work on a problem while being watched, groups switched places for the second estimation: Ms. Stadel’s height. I again heard great conversations. The observation group picked up what they believed to be key math ideas: using ratios, number lines, making calculations and explaining why, using previous (Mr. Stadel’s height from the earlier estimation) answers, and halving fractions – halves, quarters, eighths… The actual height in this case was 165 cm and student estimations ranged from 163 to 166 cm.

To wrap up, I asked students what they learned about the process of math from this activity. Many students wrote that it was important for them to see that there are many different ways to solve problems. A few also commented on the need to respect the ideas of others and to allow people to share their ideas.

I usually bounce from group to group listening to snippets of math processing and rarely find the wonderful opportunity to observe students work through an entire idea. I enjoyed it and will look forward to more opportunities to join students on the outside of the fish bowl.