Friday, July 23, 2010

Problem Solving Article Review

I read the article “Teaching Students Math Problem-Solving Through Graphic Representations at the following website: Math Problem Solving. The premise of the article is that graphic representations can be used to teach students with learning disabilities to be effective problem-solvers. While the article focuses on students with learning disabilities, these techniques can be used for a more general student population.

The first phase of problem solving is for students to identify the problem type and then to organize and represent the key information in a graphical way using schematic diagrams. The second phase is to solve the problem by selecting and applying the appropriate mathematical operations based on the problem type. The article shows that using graphic representations to emphasize conceptual understanding can help children to solve problems. After the students have created their graphic representations, they put together a plan to solve the problem.based on the type of word problem being solved.

The article then goes on to advise teachers on how to evaluate students’ problem solving performance. Teachers are encouraged to examine students’ completed tests not only for correct solutions but also for strategy use. If students are consistently getting stuck at one point, more instruction should be provided.

The reported results of this problem solving method for students with disabilities in elementary and middle schools have been good. Students have shown dramatic improvements in problem-solving scores, have maintained their new skill set for up to four weeks, and have also had more positive attitudes toward strategy instruction. Teachers have also reported more effective problem-solving in their classes.

Again, though this article targets students with disabilities, I believe that these skills are more far reaching than just for students with disabilities in elementary or middle schools.

1 comment:

  1. Doug,

    Your blog site is much different in style than those offered by wordpress. I like the whimsical look and feel. I don't get much insight into what content has been posted or what replies have been made right away, though. One of my concerns with posts is their serial nature. One has to read the whole thread, most times, to make any context manifest. Finding context on your blog is a bit more difficult. I've got to "jump righ in", so to speak. Fun and intresting experience though.

    Anyway, back to the article you reviewed. I also found an article about visualization. It showed that visualization comes in two flavors: one that is pictorial and one that is schematic. As you mention schematic visualization, I wonder if that means your article only touched on that aspect.

    What is your experience with reviewing assessments of your students' work with respect to using schematic drawings? When I graded my sudents work, I gave half of the credit for showing the work, and one half of the credit for getting the correct answer. I believe it is much more important to know how to solve a problem than actually solving it correctly. That is why I set the balance at 50%-50%. I didn't think it would be a good idea to tip the scales more heavily toward showing work.

    Even though a student could pass without knowing very much, I found my students didn't bother to show their work. I pleaded, and some made moves in that direction.

    Finally, how did you instruct using schematic drawing when problem solving?