Case two: “This is a triangle because it just looks right.”
For this case study students were paired up into groups and had to categorize geometric shapes. They were working with triangles and one of the groups put all of the equilateral triangles into a pile with all of the obtuse and scalene triangles into an ‘other’ pile. The teacher came around and started engaging in discussion. From this discussion she learned, through student talk, that students thought triangles were only triangles if all of the sides are the same. They had a cookie cutter concept of triangles and couldn’t analyze that any shape with three straight sides and three corners was in fact a triangle. The teacher did not, however, correct them immediately but brought this up in another lesson with another activity.
For the second activity, she had students make triangles of all different sizes and then the talk was directed once again towards what makes up a triangle. After putting together different sized triangles using strips of paper and brads students were questioning the same idea: what makes up a triangle? She got students to the place where they have observed and encountered and now they were ready for explanation. Through talk she was able to discover students misconceptions and further develop their reasoning through their own thinking.
After reflecting on this I noticed that the teacher allowed students to sleep on a concept without correcting them immediately. As a teacher I often want to correct students right away, but by incorporating another activity and engaging students in another classroom discussion, students will understand the concept more fully as opposed to receiving a quick correction. This was an enlightening case study, which I will try and incorporate into my own teaching. I need to learn to give more wait time and allow students to sleep on their ideas.
Sarah, I chose to read the first case study involving third graders so I did not read this one. It seems to have been very insightful and I appreciate the detail you have provided.
ReplyDeleteI find it very hard myself not to give children the correct answer after so long. However, as proven in the countless articles we have read throughout out career at Michigan State along with this case study, children take away so much more when they discover the answer themselves rather than having it be simply handed to them. I believe that after years of teaching, this concept will become much easier for us to grasp. I do believe that my biggest downfall when it comes to this, is that I simply to not think that a first grader would be able to figure out what makes a triangle, a triangle. I know that I need to have more faith in my students and I also need to provide numerous activities and have countless discussions to aid my students thinking. Through time, I believe that I will be able to let my students' though stew for a day or two as I let them be the leader of their learning.
Thank you for your thoughts. I thought that they were very insightful.
I agree with both of your postings! I feel the same way that you do in how the teacher allowed the students to sleep on a concept before she corrected them. I think that this allows students to develop a habit of how they will handle and think about their math and their math homework. Sleeping on a concept is super helpful in learning more about it and allowing the brain to think deeper about it. For the students who do not understand the concept or think about the concept in a different way than it should be- those students will have a deeper understanding of it and therefore see when they are presented with the material again that they were incorrect. This makes a lot of sense in this case study, good post!
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