I have found that many of my students have trouble being able to start a problem. Once they are given a starting point they can usually work from there. I also have students that tend to get stuck in the middle of a problem and will give up. They lack the confidence and persistence to keep trying at that point. I think the four corners and a diamond organizer could help in both of these situations. I am not available, nor or other students, during an assessment or the EOG. The graphic organizer would help them to organize their thoughts, make connections, and identify missing information (Zollman, 2012). My favorite part about the graphic organizer is that it is not intended to be a linear activity. Our students do not see the different approaches that we may try when we first encounter a problem. They only see well thought out steps that appear to be easy for us because we are the teachers or maybe because they think we are smarter than them. If they are unable to solve problems with the same ease and linear fluidity they can become frustrated and even give up. The graphic organizer can help them move away from this mentality.
I plan to use the graphic organizer for my unit challenge problems at the end of each unit. There are 3 levels of problems each worth an assigned number of points based on the difficulty. It does not matter which problem that they choose as long as they have earned at least 5 points by the end of the quarter. I will be requiring them to submit the four corners and a diamond graphic organizer with each problem. This will help them to be more successful at solving the problems (especially the more difficult ones) and it will allow me to see their thought process.
Brown and Walter (2005) suggested a problem solving strategy that consisted of 4 levels; list the attributes of the given, give some alternative attributes using the "What If Not" strategy, pose questions, and analyze the results. Dr. Wiles used a version of this strategy while working on Fermat's Last Theorem. Since he knew that he could not possibly determine the number of elliptical curves, Dr. Wiles went a different route. He used level 2, the "What If Not" strategy, to try representing them as Galois representations instead.
I am the most impressed by the difficulty of the math involved in proving Fermat's Last Theorem. I could not even begin to comprehend the math that they were implementing. I am also impressed that Dr. Wiles worked so tirelessly on his own on the same problem before reaching out for help. I feel like I would have gone searching for a second a pair of eyes much sooner. I cannot imagine being that persistent.
Dear Renee,
ReplyDeleteI loved this idea from your Blog Posting # 3: "Our students do not see the different approaches that we may try when we first encounter a problem. They only see well thought out steps that appear to be easy for us. " This makes me think that, as teachers, it is perhaps an important part of the modelling process to try and solve problems in round about ways in front of them while thinking out loud, to demonstrate that such processes are a normal part of every-day problem solving.