| Summary: | The participants in this study were twelve undergraduate students majoring in mathematics education at the university level in Iceland. The purpose of the study was to evaluate whether their pre-service training was sufficiently oriented towards strengthening the students’ conceptual understanding in mathematics as well as their problem solving ability and analytical skills. The study was aimed at answering the question whether the students’ preparation in mathematics was solid enough to enhance their competence to work as professional schoolteachers in the spirit of constructivism. A short overview of constructivism in mathematics teaching is provided and, in order to show the constantly growing emphasis that this theory has been given in the Icelandic educational system, a brief overview is included of the curricular changes in mathematics for the past few decades in Iceland. It is pointed out that both the 1999 and the 2007 official curricula explicitly state the importance of problem solving and present a discussion on what it means to understand a mathematical concept. The growing emphasis on constructivism in mathematics teaching is also clearly witnessed in recently published mathematics textbooks for Icelandic primary schools. The paper contains a short discussion on the importance of problem solving in connection with constructivism in mathematics teaching. In the second half of the 20th century problem solving was one of the key issues of mathematics as a field of study. In the skill of problem solving as well as in the theory of constructivism the questioning mind of the student is paramount. The evaluation of the students’ preparation was based on observations of their tackling five given mathematical problems, interviews with the students about the problems and the students’ written solutions. The evaluation was based on the following research questions put forward in the study: 1) Do the students understand the problem well enough to realize how they should solve it? 2) Do the students use ...
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