What did I learn?
In class on October 27th, I learned that there are multiple ways to approach a problem. I was truly amazed at the number of ways that the members of our cohort came up with when we were given the task of determining which park location would have the largest blacktop area. I also learned how useful diagrams can be when solving these types of problems. After hearing about the two possible park locations on the video presented, I immediately set up a math formula to determine which one would have the largest blacktop area. It never occurred to me to draw a picture of the two options and then compare them visually. These pictures, however, brought clarity to the solution because, as it turned out, both locations ended up having the same area of blacktop. When I first looked at my answers, I thought I must have made a mistake. It took me a minute to realize that taking a smaller fraction (2/5) of a larger area (3/4) of Carroll Park was the same as taking a larger fraction (3/4) of a smaller area (2/5) of Flatbed Park, even though I knew the commutative property of multiplication.
What do I have questions about? To ensure the success of this type of problem solving session with our future students would it be wise to select groups based on math ability or possibly set up roles within the group to ensure that each member understands the various ways to approach the problem?
What are the implications for classroom practice?
I see the value of ordering the solutions that are presented to a class of various student groups during a problem-solving exercise. By doing this strategically, I can advance the students’ understanding of the mathematical ideas presented. As I teacher, I must take on the role of a facilitator. It’s important that I monitor the student groups, listen to their strategies and then decide which groups will share with the class and in which order.
Another important implication is the importance of having students solve real problems, ones that they will care about, similar to the one in the video, about two local parks. If this is done, the students will be more engaged in finding solutions.
I loved this particular class! It was amazing to see all the different ways people solved the problem. Some of the solutions were quite simple, whereas, other were somewhat hard to grasp at first. Being a person who loves math and math comes easy too, I went straight to the actual numbers and equations to solve the problem and then drew a picture. I think I drew the picture only because I felt like I needed to, not that it enhanced the "math" portion of the problem. I did not even realize that one could solve this type of problem without necessarily using numbers and equations. It was really cool to see all the different ways one could about solving this problem. I think it is important to incorporate this into our classrooms. As a teacher, you need to teach all the possible ways of solving math problems. But, at the same, time allow the students to be creative and tackle a problem in their own way. Having the students share their work gives students the opportunity to enhance their learning and further their thinking.
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