Johan Häggström The same topic – Different opportunities to learn The same topic – Different opportunities to learn

The teaching and learning of mathematics involve intricate processes and many different factors may have impact on learning outcomes. The study reported in this paper, however, has a quite narrow focus on how the mathematical content is treated. It is part of a larger study and is based on the assumption that what students learn or don’t learn, in respect to a certain content, is dependent on what features of the content have been possible to experience by the students. Three lessons where the same mathematics is taught are compared and substantial differences are found. Comparative studies Most large international comparative studies in mathematics education involve comparing learning outcomes or student achievement. In the series of IEA-studies (FIMS, SIMS and TIMSS) more and more variables – mathematics curriculum, size of mathematics classes, grouping and streaming of students, amount of mathematics lessons and homework, teacher education, attitudes of students and teachers, etc. – have been included in the studies in order to understand and explain differences in achievement between countries (IEA, 2005). Subsequently, in the TIMSS-studies of 1995 and 1999 the ”teaching process ” was included through the video-recording of 8th grade mathematics lessons (Hiebert et al., 2003). One aim was to identify what is typical of teaching in high-achieving countries. An interesting result was that, despite a huge effort, it turned out to be hard to find any factors that could explain the differences in achievement. After having coded and examined more than 60 aspects of mathematics teaching in between 50 and 140 taped lessons from the seven countries the research group alleged, ”... we had difficulty finding lesson features that correlate with differences in achievement ” (Givvin, 2004, p. 208). A further analysis of how the mathematical content was dealt with, from a student perspective, was needed. What, then, do the higher-achieving countries have in common? The answer does not lie in the organisation of classrooms, the kinds of technologies used, or even the types of problems presented to students, but in the way which teachers and students work on problems as the lesson unfolds. (Stigler &amp