Student Work- Robb

This week my students worked on measuring skyscrapers, which they constructed from paper. This was not part of my own unit but part of the Math Trailblazers series. Because my students had had experience measuring with non-standard units during my unit, I was interested in seeing how the students would fair with this activity.

I took down several notes when conversing with students about their procedures for measuring and their thinking, sort of like an informal post-assessment. The following are quotes that I found the most inspiring.

I went to one of my students who is generally not that strong in Math, first. I wanted to see if this particular student had a good understanding of how to measure with non-standard units because he did struggle during my unit.
"Can you tell me how you measured?", I said.

 "Yeah. Ummm, like, well you have to start at zero? Right?" the student said.

"I think so, but can you show me?"

"Well, I was thinking *this* is zero, like the bottom." he said this as he pointed to the bottom of his skyscraper.

"Good!" I said. "So then what do you do?"

"Then I go, 1-2-3-4-5 and I make the links go next to the tower." He placed the links end-to-end, right up next to the tower.

"So then, how tall is it?" I asked.

"It's 5, 5 things tall." He said smiliing.

This student placed his links end-to-end, he did not connect them. Another student I worked withhad a different approach.

When working with one of my female ELL students, I asked her to go through the process of measuring with "links" from step one. She began by saying, "First, you get your links. And then you can put them together if you want."

"You should make the links taller than your skyscraper", she said as she built a link chain quite tall. She then moved the bottom of the chain to line up with the bottom of her paper. "It should go here, if you don't put it here you aren't looking at the right spot." Then, looking at her full length chain, she took off the excess chain at the spot where her building ended.

"What do you do next?" I asked.

"I taked it away here because this is how big it is. Then I count the links and I get 6."

I think this is an essential thing to do, you have to let your students think about their thinking and you have to accept their answers, no matter what variations they come in. If I had told either student that they were "wrong" or told them to measure any other way, I would have defeated them. I would have shot their confidence. I did not see how connecting or, not connecting, the links made either answer more or less valid. Students working from their own ideas are students who are exploring and making the connections that build true mathematical thinkers. When we tell our students to only do things one way, we aren't truly doing our students, or mathematics as a field of study, any justice.