The tasks, discussion, and assignments for this week revolved largely around cooperative learning and reinforcing effort. Starting with cooperative learning, I believe the purpose is to enhance student comprehension, while at the same time learning how to productively interact with others. I can recall an instant when I paired seventh graders together to work on a regular homework assignment. The students were paired together (seemingly at random, as far as they were concerned) based on ability, with the mathematically apt students working with a struggling student. I believe this worked well because it made the more gifted students teach (a higher form of comprehension); and the struggling students got a chance to experience the confidence of getting questions right, along with hearing the content explained from a different source. I can also think of a time when I let my seventh graders select their own groups for an assignment, and consequently how poorly it went. Essentially, the students selected their friends, and very little was accomplished. I think this went so poorly due to the fact that friends often don't like to boss other friends around; not to mention the fact that getting the assignment accomplished is rarely the topic of conversation. Some technological resources that can be used to incorporate student cooperative learning include San Diego State University's WebQuest, WebQuest Taskonomy, Teacher WebQuest Generator, and Instant Projects. My main question regarding these resources would be which one is the most conducive to cooperative learning in a mathematical setting?
Along similar lines, we were to watch several presentations by the very intelligible Clay Shirky. He had many intellectually sound comments regarding the difference between institutions and collaboration in the first speech that I viewed. I particularly liked the way he referenced that institutions, albeit effective, stifle creativity. Now, this is a period of history where volunteer global collaboration has never been easier. This allows for like-minded individuals to collaborate effectively on their own terms, not in the "cookie-cutter" setting of the corporate world (YouTube musicians versus a record label). I find it very intriguing to think that with such a technological revolution on our hands, sole possession of ideas and services will gradually become less. As collaboration can now be done cheap and effectively, institutions are becoming more of an obstacle than a solution.
The other topic of conversation was how to reinforce effort. I believe the purpose of reinforcing a student's effort is to give a sense of accomplishment that can inspire productivity and self-worth. I can recall when I told one of my advanced math students that I thought she was mathematically gifted, and that she shouldn't shy away from math courses in college. This particular student may not have went on to major in mathematics, but I know that she's still in college, taking math classes beyond the minimal school requirement. I think my comment worked well because it let her know that she had potential, and as scary as the next level of academia may be, she could do it. I also can recall a time when a student in Algebra II simplified an "nth root" radical expression incorrectly, and I wasn't nearly as supportive as I could have been. Instead of reinforcing effort, I more or less referenced the fact that they should have done a better job of using their notes and textbook. I think this went poorly because instead of making the student feel welcome to come and ask questions, I made him feel like it was not okay, and that I was not supportive. I then spent weeks trying to earn back that particular students trust, and it certainly wasn't easy. Some technological ways to enhance reinforcing effort include GoogleDoc comments, positive emails, and spreadsheet documentation. The latter really peaks my interest, as our textbook explained how a teacher proved to his students that there is a correlation between effort and success. My question would be how to accurately implement this, and for what particular age groups?
I too will pair students together for assignments at times. I think it's good for them to collaborate with students below or above there ability level. However, when I do this, I monitor it closely because I do not want the student with the higher ability doing all of the work. I will sometimes have each of the students have something they are in charge of teaching the other student, then each student shares with each other.
ReplyDeleteI also agree about what you said about your simple comment that led your student to continue higher level math. Though I don't work with gifted students on a regular basis, I do encourage my lower level students that they can do more than they think they are capable when I see something they are doing very well. It's amazing what a simple comment can do for the motivation of someone.
Although people don't like grouping based on ability levels, I think it can work when done right. It seems to me that you used that grouping in the correct way - group students based on their strengths and weaknesses that support one another. Unfortunately, when I too allow students to choose their groups I either don't get the end product, or the quality of work is very poor. I work with middle school students. I think part of the problem is that they aren't mature enough. Based on your experience, do ever let students choose their own groups with more guidelines? Or do you do the pairing?
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