I think both the introduction and the article give great insight into the expectations of this class, and I think as presumably all of us are or will be teachers it's definitely an appropriate goal. I agree with Martinez's assertions about the importance of problem solving and I feel as educators in order to find the best way to teach our students problem solving we just may need to go through the process of learning to problem solve ourselves. That's not to say we don't all already problem solve as Martinez stated, but there is definitely a difference between our natural problem solving skills and this explicit teaching of problem solving.
While I agree with Martinez that problem solving does need to be a greater focus in schools, I know from my own experience that not all schools focus simply on "the cognitive resource of knowledge" and many do also teach problem solving. This past year I worked with a group of third grade teachers, most of whom had been teaching for quite a while, who introduced me to a diagram of problem solving steps. At the bottom of the stairs was step one-reading the question and finding out what information is known, then on step two-reading the question again and distinguishing what information you are trying to figure out, next on step three-choose a strategy to solve the problem, and finally on step four-use your strategy to find the solution and check your answer. While this was an effective tool to teach students the process of problem solving and I felt it was completely adequate during the year, after reading this article I can clearly see some of it's limitations (that's not to say however that I don't think it's at least a 'step' in the right direction). First of all these problem-solving steps were limited to use in the mathematics area, which didn't help students to understand the process of problem-solving as a generalized idea that could be applied in all areas where uncertainty was encountered. Additionally, while students were encouraged to use different strategies to solve problems the types of strategies used and discussed were far more often specific heuristics and not general heuristics, which could be applied to a far greater array of situations. On the positive side, when problem solving, students were required to show all work and at the end present not just their response, but to talk the class through their problem-solving process so others could learn from their strategies and see that sometimes mistakes eventually led to the right answers and sometimes even though incorrect solutions were made due to computational errors, correct strategies were used. In both of these situations students received partial credit, hopefully learning that not only correct answers are valued.
What struck me most about Martinez's article however was that in all of my years of being educated and educating others I've never before heard or seen the term heuristics or had the process of problem-solving explicitly explained to me in that way. I think students could benefit immensely by seeing problem solving represented in this way using age-appropriate terms. I think if using more simplistic terms I had explicitly taught my third graders means-ends analysis or successive approximations they would have understood their own processes in problem-solving much better and therefore been able to engage in metacognitive skills and had more success in problem-solving.
I seem to be developing a pattern of pessimism at the end however and have to question one small comment in the article. Martinez discusses the detrimental effect of anxiety on problem-solving. I agree with his assertion that "Anxiety is a spoiler in the problem-solving process." However, I don't necessarily agree with his comment that "Those who cannot bear situations in which it is impossible to see the way clearly to the end are emotionally ill-prepared to solve problems." I think children can be taught to work through their anxiety and problem-solve despite this. However if we do choose to believe that Martinez's comments are true then what happens to the children who do have anxiety disorders or other disabilities and are therefore incapable of seeing the way clearly to the end without uncertainty clouding the way? Is he implying that these students are inherently incapable of developing problem-solving skills?
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4 comments:
Kimberly ... loved the fact that you are relating this article to your own personal experience.
In the final analysis... it's all a process. Obviously we would need to 'problem-solve' strategies for children with anxiety disorders. I think we would agree, however, the article is a big first step to thinking constructively about nurturing 'the art of problem-solving' Carol
Hey Kim!
Like Carol, I loved the fact that you incoporated stories of your class into your blog in relation to the problem solving article. For as many times as we read things in books and online it, an example like yours solidifes those concepts so much more and makes everything both more understandable and meaningful. I also really liked what you said about problem solving ourselves before we teach our students how to. How can we teach them if we don't fully understand it ourselves!?! Very insightful!- I look forward to seeing what you have to say next!
Hmmmmm . . . I really enjoy reading you posts Kim. Thank you for your thoughts.
Carol, are you trying to be punny . . . "thinking constructively" . . . is that a constructivist reference or merely coincidence?
Anyway, back to you Kim . . . I'm not sure I agree w/ your interpretation of Mr. Martinez comment re: individuals being "emotionally ill-prepared to solve problems." I don’t feel he is trying to say that an individual w/ LD, ED, etc. doomed. I stead I feel you are both saying the same thing. The individual simply must be taught how to deal with and overcome that anxiety. I guess for me, this goes back to chapter 2 of "How People Learn" . . . as you pointed out so well, it is at precisely this moment (when a child, adult, student, etc. experience anxiety, frustration, tension, and negativism when attempting to solve a problem) when you and I as teachers can do the most good! We may not be able to teach our students how to be an expert mathematician however, I do hope we can teach each of them to be an expert learner. Tall order I know but one can dream, right?
Joe
Kimberly: I took a workshop in problem-solving (back in the depths of time when I was in graduate school) which covered a lot of strategies. What I liked most about the workshop, though, was it's emphasis on all the stages that go before the solution. Problem IDENTIFICATION and ANALYSIS need to be a separate steps; it's often a mistake to assume that the problem, as stated, is the REAL problem. The problem "How can we get Bobby to sit down and behave himself in class?", is going to be hard to solve until we figure out: what exactly we mean by "behave himself"; who is bothered by his standing up?; how does his standing negatively affect others?; and WHY does he stand in the first place? and so on.
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