After reading Mathematical Tasks as a Framework for Reflection, I re-evaluated the elementary tasks as follow:
Memorization: E, L
Procedures: A, B, D, G, I, M, O
Procedures with Connections: C, F, H, K
Doing Mathematics: J, N, P
Based on the answer key, I got B, C, H, I, M, P wrong! I do not agree with Task B being "doing mathematics". I see students continuing the pattern by multiplying by 2 and students can easily recognize that 375 is not divisible by 2. I looked at Task C as making connections. How did you all see it? I was unsure about Task H, however, I think the teacher should set up the problem so that students create real-life situations for the graphs they did not select.
In Task I, I feel the teacher provided students with too much information. This task is similar to the Ron case in the article. Ron provided his students with answers to entry points on how to solve the problem, thus removing productive struggle and student thinking. Teachers must be mindful of how they probe and engineer discussions around mathematical problems. It is very easy to shift the emphasis to correct or complete answers or not providing ample wait time for student responses. As the article stated, students are conditioned to know that teachers will quickly show them how to do a problem, thus taking away the opportunity for ownership of their learning . Teachers would need to practice how to provide feedback or answer questions that move learning forward.
I need more practice with "procedures with connections" and "doing mathematics". In Procedures with Connections, students would build connections to mathematical meanings and/or make connections among various representations of a concept. In Doing Mathematics, students are afforded the opportunity to explore relationships and present different strategies or ways to approach a problem as well.
Hello Shannon.
ReplyDeleteI wanted to let you know that I will be creating a new blog for each module. I am hoping it will make things easier to find on my blog page. I have already blogged about the first two articles in module two. Please let me know if you have trouble finding or accessing anything. Thanks.
Hello Shannon. I took a different approach to re-evaluating. I labeled memorization and procedures without connections as LOW. I labeled procedures with connections and doing mathematics as HIGH. Then I looked to see how I had originally labeled the tasks. When I compared my labeling to the appendix, I found that only tasks I and M were not placed appropriately. Re-evaluating task I, I had not previously considered the requirement of an explanation. However, if a student is to use prior information and rules to arrive at another answer, then they would have to be able to explain (at least to themselves) how to arrive at the second answer. Task M is another that was a struggle for me. After the reading, I see task M as being a visual approach to finding an average. This is similar to the example in the reading with the fractions and the use of the rectangles. Having to move pieces of the bars makes this problem a high cognitive one. It requires the students to establish balance in each column. Very good assignment.
Delete