Monitoring and Guiding Pupils' Problem Solving

Abstract

This paper presents a discussion of the problem-solving approaches of primary and secondary school pupils in relation to the following issues: developing strategies, communicating, and receiving guidance. Guiding is the role of the teacher who should be sensitive enough to support pupils’ thinking, when necessary, but not direct it. A group of pupils (35 pupils between 10 and 19 years old) were given a geometrical problem that required them to define the number of parts created when a single plane was divided by straight lines. Each pupil tackled the problem individually, while prospective teachers from the Faculty of Education observed and guided them. After analysing the prospective teachers’ research reports on guiding pupils through the problem we came to the following conclusions: all the pupils needed guiding in order to make progress in problem solving towards general rule, most of the pupils need to learn about heuristics more systematically, prospective teachers got better inside view on thinking process for problem solving of different age groups of pupils. From the success at problem solving point of view we observed the following: until presented with a problem that required a geometrical approach, the differences among the age groups in terms of successful problem solving were not that noteworthy, the difference among age groups was observed in examples of more complex problem solving where a shift towards an arithmetical approach was needed.