After reading the NCTM article, “3 Strategies for PromotingMath Disagreements” written by Angela Barlow and Michael McCrory, I decided to watch for opportunities to try these strategies in my third grade classroom. The article encourages teachers to watch for differing opinions during classroom discussions and use this time as an opportunity for students to debate, prove, and deepen their thinking about a mathematical concept. This is the perfect atmosphere for MP3 Construct viable arguments and critique the reasoning of others.
A few days later, my students were discussing why fractions have equal parts. I quickly realized that several were confused about how to turn our “Crusty the Clown” pattern block model into equal parts. The textbook and student workbook pages always neatly did this for the children, so they never had to think about forming equal parts of an irregular shape on their own.
As stated in the NCTM article, I asked students to choose a side of the classroom that represented their viewpoint. Immediately, two of my sharpest students went to the wrong side, declaring that Crusty had 5 equal parts. Jeffrey and Jorge were correct that part of Crusty was made up of 5 equal blocks, but they were not looking at the whole clown shape. Others who were unsure or undecided trusted the boys and stayed with them—even after much proof and evidence was offered by students on the other side of the room that Crusty had 14 equal parts. The children were delighted to debate and state their views with a microphone in hand. Emotions surged and intensified on both sides of the discussion; however, I stayed neutral and continued to encourage them to listen to each other and clearly state their opinions.
|14 equal parts of Crusty the Clown|
The next day, we used snap cubes to show “5 of 6 equal parts of 18,” and I noticed that the children were immediately engaged and knew how to do it. Several enjoyed making the connection back to dividing our pattern block Crusty into equal parts as well. Success! I now have them beginning to listen to each other and starting to support their views with concrete evidence and simple proofs.
Source of the Math Disagreements article: Teaching Children Mathematics, v17 n9 p530-539 May 2011, NCTM
|4 equal parts--but is the whole complete?|
|6 equal parts--what happened to Crusty's hat?|
|5 equal parts--but is it still Crusty the Clown?|