Strategies and Skills Used by Middle School Students During the Solving of Non-routine Mathematics Problems

This study was conducted to determine the processes and strategies selected middle school students use during the solving of non-routine mathematics problems. Qualitative research methods were used to identify the cognitive and metacognitive skills and processes used in problem solving and to determine the affective influences on the problem solving process.

Six middle grade students were selected to participate in the study. Each student was interviewed four times. The first interview was conducted in order to develop student profiles by obtaining information about each student's family, school, and mathematics background. The second and third interviews consisted of two phases. First, students solved problems for twenty minutes and verbally explained their thoughts and work. Afterwards, a follow-up interview was conducted in order to clarify and enhance information collected during the twenty minute problem solving session. The fourth and final interview was conducted using a grid technique in order to determine student perceptions of the problem solving process.

The interviews were audiotaped, and the problem solving sessions were videotaped. The transcriptions were analyzed using a constant comparative method. Themes emerged from the data analysis, and findings were identified. The themes and findings led the researcher to the following conclusions.

1. Students are not aware of the various alternatives available to help them understand a non-routine mathematics problem when they first read it.

2. The only skills which students perceive as mathematics skills are the basic computations of addition, subtractions, multiplications, and division.

3. Students are unwilling to take risks when presented with a problem solving situation. They are hesitant to try a strategy unless they have seen a teacher use that particular strategy.

4. Students have been told that various heuristics exist to help them solve problems. Even though they have been instructed to use them, they have not been adequately informed concerning how and when to use the heuristics.

5. Students model the problem solving strategies and behaviors of their teachers.

The study demonstrates that teachers need to concentrate on fostering students' self-esteem and positive attitudes toward problem solving in mathematics. Non-routine problems should become a regular part of the mathematics which students are exposed to in school, and teachers should focus on modeling their successful problems solving behaviors.