The more that I focus on math problem solving in class, the more that I realize that it’s not just about improving math skills, but it’s also about improving thinking skills. Today was a great example of this! In class today, I posed the following question to the students:
Students worked in partners to solve this problem. Some students used the Livescribe Pen and various iPad apps to record their thinking, some students used whiteboards to write down their thoughts, and some students used a combination of the two.
(The photo quality here is not as clear, but it talks about the fact that the rectangle is the best choice because it has four sides and so does the square. It also said that the diamond is not the best choice because it would leave little spaces.)
This activity was really not about the answer. It was about the rationale for the answer. Just listening to the students discussing their answers were incredible. They were using math language, and in a really meaningful context too. Not only were they justifying their decisions, but they were also explaining why the other choices were not good ones. Students were being critical thinkers, and as teachers, isn’t this what we want most out of our students?
During the reflect and connect portion of the problem-solving process, students shared their great ideas too. Here’s a Livescribe pencast of their thinking:
brought to you by Livescribe
While most students shared that a rectangle would be the best choice, one student (Dana) said that she would pick a diamond. This is where I got stuck. This student had some great thinking, but I wanted her to see the importance of all shapes going in the same direction, as well as the value of not having gaps in between the shapes. I was trying to come up with the right questions to ask, but I felt like I was too leading.
What questions would you have asked? I’d love your thoughts here. If I’m encouraging my students to think then I want to be thinking too. As for this math problem, my students would love to hear what your students think the three Grade 1 teachers should do. What would they recommend and why? Hopefully we can all learn some math together!
I can’t tell from the video but it sounds like the students had the shapes on the smart board to try to move around to test their thinking. Did they have pattern blocks at the beginning? I think your students had really good thinking about why the rectangle was the most efficient choice. I wonder about Dana’s thinking. If you tiled a rectangle with the “diamond”, would the students be able to look at the empty spaces and see parts of the shape? Would some of the students see two half shapes and be able to put them together as a whole? That goes beyond the expectations of the lesson but would be an interesting investigation.
Thanks for posting this lesson.
Thanks for the comment! Yes, the students had shapes on the SMART Board to manipulate as well as pattern blocks. Your question has me thinking about a follow-up activity. I’m not sure what the students would do, but I’m curious to see. Thanks for always getting me thinking!