Interference. A big word with many meanings. In this case, interference was causing my students to misunderstand what I anticipated to be a simple problem: "You have a bag with 5 marbles. Three of the marbles are blue. The rest are red. If you double the red marbles, what fraction of the marbles will be red?" I gave students a couple of minutes to start this problem individually. As I walked around observing their work, I jotted down their solutions. Most students were finding an answer of either 2/5 or 2/7. I posted these two possible solutions in the room and asked them to stand by the answer that best fit their thinking. As part of our routine during class debates, there is a section in the room for those "still thinking". Once students have made a choice, they are to talk with the people in their group about why they made this choice and work to convince others in the room why their choice is correct. For those at "still thinking", they are to think of a question that will help them come to a decision about the answer. After each group has time to share, students may revise their thinking and change groups. This particular episode fascinated me because only two students initially chose the correct answer. As I listened to their reasoning, I understood that many were thinking about what we had learned with fraction multiplication - that 2 x 2/5 would equal 4/5. Even with other students modeling the problem with blocks and drawing pictures, some of the students were firm in their belief that the correct solution must be 4/5. The debate lasted for approximately 25 minutes (although the video is condensed to about 7 minutes). At the end of the debate, many students still were at the incorrect solution so we waited until the following day to discuss the solution. After having the evening to think more about the problem and talk with others, all students came to agreement that the correct solution was 4/7. While this was a time-intensive activity, the time was well spent. Students did very well with the unit about ratios and had a clear understanding of when they might be able to use fraction operations and when they needed a different approach. To have given the solution to quickly would have cut off the students' opportunity for sense-making and reasoning about the mathematics.
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AuthorSharing what I'm learning from others. Collaborative experiences and communication are essential in building a shared understanding of mathematics! Archives
September 2018
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