Response to a Research Paper
The aspect the paper tries to describe is the use of problem solving methods and proofing among undergraduate and graduate students as an approach to theorems in thesis and dissertations. In addition, a comprehensive description of these methods of problem solving, which include a continuum of tasks from very routine to very non-routine, tentative solution and use of proofs is given. These methods also provide some of the techniques employed in problem solving. For instance, the very routine to the very non-routine provides three ways that may be used in problem solving which include identification of similarities, local plausible reasoning and global plausible reasoning.
The paper uses a number of technical words, but clearly elaborates their meaning. Information presented is clear and to the point. No vagueness is encountered. Examples are well used to illustrate some of the methods used in problem solving. A number of these examples can be seen especially where behavioral schema is described. A new concept in problem solving that the paper brings to light is the use of behavioral schema.
The paper is written based on research done by other authors who have taken time to study how students solve mathematics problems. In addition, the paper provides some areas such as conversion of informal arguments into accepatable forms where further research may be required. Furthermore, more knowledge is required concerning the emotion and beliefs during problem solving.
The paper describes behavioral schema as the ability to discern similarities between various situations and in the process being able to draw up answers. In addition, the paper provides a brief description of properties of behavioral schema that may be encountered during problem solving. In analyzing behavioral schema among students, positive traits of behavioral schema may be encouraged to foster understanding of mathematical problems.
