Browsing by Subject "avoin ongelmanratkaisutehtävä"

This thesis is part of a broad research project funded by Academy of Finland, in which the Finnish and Chilean mathematics teachers have given lessons focusing on problem solving for three years. The aim of the study is to describe, analyse and interpret the students' solutions to an open-ended problem and to find out what kinds of problem-solving strategies students use to reach the solution. In addition, the aim of this thesis is to analyse the students' problem-solving process under the guidance of the teacher. The theoretical frame of this study is based on defining mathematical problem solving and describing the problem-solving process. The theory also consists of the definition of problem-solving strategies based on LeBlanc's (1977) research. The research material of this study consists of the answer sheets of six Finnish classes and the videotapes of four of these classes' problem solving lessons. Firstly, the answer sheets were analysed using data-driven content analysis. Then, to find answers to the second research question, data was analysed using theory-driven content analysis. The videos were analysed using theory-driven content analysis. The pupils' solutions to the open-ended problem varied very much, especially the amount of rectangles students had drawn to find the solution. On the other hand, almost all the answer sheets included rectangles 10 cm x 5 cm and 1 cm x 14 cm. In addition, it is noteworthy that the right solution was found in just five answer sheets. Among the fifth-graders, there are big differences in what kind of problem-solving strategies they can use. The pupils used three different problem-solving strategies. Experimentation was clearly the most common, and systematic listing of possible solutions the second most common strategy. Only one class of students had tried to find patterns in the problem. The problem-solving process of the students was clearly affected by the problem-solving strategy they decided to use. The pupils' problem solving process was cyclical and the teacher influenced the process significantly the whole lesson.