A Small Scale Study: The Metacognitive Scaffoldings in Mathematics Problem Solving for Senior High Students with High Mathematics Ability

To describe the kinds of metacognitive scaffolding which are necessary given, we carried out a test in the topic of three dimensional space to three senior high school students with high mathematics ability. The metacognitive scaffolding was given when they worked with the problems of which they refer to the four steps of Polya. An interview was also conducted to the students for the data triangulation. The findings suggest that, although the three respondents basically understand the problems, they have difficulties in setting a plan for problem solving as they are unaccustomed. In contrast, they relatively have no difficulties in applying the third step of Polya, i.e. applying the plan of problem solving as well as the fouth step because there was no MS given to them. Concerning the kinds of the given MS, monitoring is the most used, followed by planning, and evaluating. Moreover, based on the Polya's steps of which the MS given, the most frequently used MS is the second step, followed by consecutively the first step, the fourth step, and the third step.