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.