In class, we’re just finishing off our math unit on area and perimeter. I started today’s math class asking the students to create irregular shapes using any tools that they wanted in the classroom. I gave some examples of tools, including, geoboards, tanagrams, pattern blocks, computer programs, and graph paper, but I left the choice up to them. Students had to create the irregular shape, calculate the area of this shape, and explain their calculations. This was a very open-ended math activity that had students sharing their knowledge and understanding of area, but definitely included an application and communication component as well.
As the students started working, I went over to work with a group of students that are struggling with the calculations as well as communicating their thinking. I noticed that this small group of students was working together, drawing the irregular shapes on the whiteboard. I went up to them and asked, how are you going to figure out the area of these shapes? I was thrilled when one of the students said to me, “I’m going to draw the little squares just like this, and count them out.” He then started to draw small squares in the middle of his irregular shape.
Okay, so he understood the need to use a grid. Did he understand that the squares in the grid all needed the same measurements? There was only one way to find out. I asked him, “Are all of the squares the same size? Does this matter?” He stopped for a minute and looked at me. Then this student responded, “I don’t think they are all the same size. Maybe I need to use grid paper.”
Instead of agreeing that this was a good choice, I instead asked, “Why would you use grid paper?” He replied, “Because then all of the squares will be the same size. I can draw my shape, count up the squares, and then know the area.” Excellent! By asking him questions, this student was able to show me his understanding of area, and actually work through this problem on his own instead of with my direction. The other students in the group heard this discussion, and quickly agreed that using grid paper would be the best option. All of the students then grabbed grid paper, and started creating their shapes.
This short conversation today really made me rethink my interaction with students during math. How many times do I tell them what to do instead of letting them explore on their own? How many times do I jump in with solutions when problems arise, instead of letting the students work out the solutions together? Instead of answering questions today, I was asking them, and this small difference was big when it came to communication in math.
How do you use questions to facilitate problem solving in math? What kinds of open-ended questions do you ask to help students figure out difficult concepts on their own?
Aviva Dunsiger taught Junior Kindergarten to Grade 2 for 11 years before moving to Grade 6 this year. She’s passionate about using technology in the classroom to support student learning, and she’s presented on this topic numerous times both online and offline.
She enjoys maintaining her blog, Living Avivaloca: My Many Musings on Life and Learning. Aviva’s reflective writing about her professional practice inspires communication between educators, administrators and parents.
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