A Subtle View to Metacognitive Aspect of Mathematical Problems Solving

AbstractThis research has focused on the study of meta-cognitive behaviors as one of the important and effective behaviors in mathematical problem solving. The main purpose of this study was to assess the role of meta-cognitive skills in mathematical problems solving (example of combinatorics). Wherefore complexity nature of meta-cognition, there is broad consensus among researchers that all methodologies applied in this area of research are fallible, have strengths and weaknesses, and feel that the strengths of one single methodology can complement the weaknesses of another methodology. Thus, in this study, we used mixed methodology (writing and self-questionnaire) that do not share the same source of error to provide a more reliable picture of the phenomena under investigation. Another aims were, identity of prevalent errors and student's difficulties in combinatorics problems solving, and to assess the role of meta-cognition on routine and non-routine problems. A group of thirty four college students enrolled in discrete mathematics participated in this study. In this research the students were asked to write their total mental processes during solving two problems. Immediately after solving the problems, the students were given a questionnaire to answer the questions accordingly to their mental processes during solving the second problem. The Problem solving protocols were initially analyzed using Foong's model. The results showed, first, the mean difference of successful student's meta-cognitive behaviors was significant in solving both problems compare to unsuccessful students at the 0.05 level, (F[2,31]=34.015, p<0.05), (F [2,31]=65.764, p