Improving problem solving ability in mathematics by using a mathematical model: A computerized approach

摘要

The present study investigates the improvement of students' mathematical performance by using a mathematical model through a computerized approach. We had developed an intervention program and 11 years students worked independently on a mathematical model in order to improve their self-representation in mathematics, to self-regulate their performance and consequently to improve their problem solving ability. The emphasis of using the specific model was on dividing the problem solving procedure into stages, the concentration on the students' cognitive processes at each stage and the self-regulation of those cognitive processes in order to overcome cognitive obstacles. The use of the computer offered the opportunity to give students general comments, hints and feedback without the involvement of their teachers. Students had to communicate with a cartoon animation presenting a human being who faced difficulties and cognitive obstacles during problem solving procedure. Three tools were constructed for pre- and post-test (self-representation, mathematical performance and self-regulation). There were administered to 255 students (11 years old), who constituted the experimental and the control group. Results confirmed that providing students with the opportunity to self-reflect on their learning behavior when they encounter obstacles in problem solving is one possible way to enhance students' self-regulation and consequently their mathematical performance.