Since September 2011, Anna Lundberg is a part-time doctoral student in mathematics education at the Department of Pedagogical, Curricular and Professional Studies, Gothenburg University within the framework of the Center for Educational Science and Teacher Research (CUL). Alongside her PhD studies, she works, part-time as an upper secondary teacher in mathematics at Anders Ljungstedts Gymnasium, Linköping.
In her licentiate thesis, Lundberg investigated how the mathematical notion of proportionality is handled in the Swedish upper secondary school. A general problem connected to this aim is how the national curriculum is realised in textbooks and national examinations. To examine this, an analytical tool based on the theoretical framework of the ATD (Anthropological Theory of the Didactic)(Chevallard, 2007) was developed. Of interest here are relations between the different levels in the didactic transposition, concerned with how the national curriculum is realised in textbooks and national examinations.
The result of this study encouraged her to continue with a classroom study to find out how proportionality tasks are handled by the teachers and students. Lundberg is analysing data from the project VIDEOMAT where the lesson content is algebra, which is a natural context for handling proportionality, since proportionality is a special case of algebra. In Grade 6, proportionality is introduced for the first time after a change in the curriculum in the autumn 2011. This makes it intriguing to investigate how the teacher uses tasks with proportionality and proportional reasoning.
Lundberg, A. L. V., & Kilhamn, C. (accepted). Transposition of Knowledge: Encountering Proportionality in an Algebra Task. International Journal of Science and Mathematics Education. doi:10.1007/s10763-016-9781-3
Lundberg, A. L. V., & Hillman, T. (2013). Student-driven proportional reasoning approaches to an early algebra task. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th International Group for the Psychology of Mathematics Education (Vol. 5, pp. 112). Kiel, Germany: PME.
Lundberg, A. L. V., & Kilhamn, C. (2013). The lemon squash task. In A. Watson, M. Ohtani, J. Ainley, J. Bolite Frant, M. Doorman, C. Kieran, A. Leung, C. Margolinas, P. Sullivan, D. R. Thompson & Y. Yang (Eds.), ICMI study 22: Task Design in Mathematics Education (pp. 363-372). Department of Education, University of Oxford, UK.
Lundberg, A. L. V. (2011a). Proportion in mathematics textbooks in upper secondary school. In M. Pytlak, E. Svoboda & T. Rowlands (Eds.), Proceedings of the Seventh European Congress for Research in Mathematics Education (CERME 7) (pp. 336-345). Rzeszów,Poland: University of Rzeszów, Poland.
Lundberg, A. L. V. (2011b). Proportion in mathematics textbooks in upper secondary school. In Marianne Foss Mortensen & Carl Winslow (Eds.), The Anthropological Theory of the Didactical (ATD) Peer reviewed papers from a PhD course at the University of Copenhagen, 2010 (pp. 15-30). Copenhagen, Denmark: Department of Science Education University of Copenhagen.
Lundberg, A. L. V. (2011c). Proportionalitetsbegreppet i den svenska gymnasiematematiken - en studie om läromedel och nationella prov [The Concept of Proportionality in the Swedish Upper Secondary School Mathematics - a Study of Textbooks and National Examinations] Linköping, Sweden: Liu-tryck.