Mid Sweden University

We present a research project on students’ mathematical reasoning and how beliefsare indicated in their arguments. Preliminary results show that students expressbeliefs that task solving does not include reflection or much struggle. The resultsunderpin earlier studies stressing expectations as a theme of belief.It has been shown that students working with textbook tasks of a routine characterexpress beliefs of safety, expectations and motivation used as arguments for centraldecision making (Sumpter, 2013). These types of tasks are often tackled by thestudents by using known algorithms (Boesen, Lithner & Palm, 2010). This is one of theexpectations students have on textbook tasks. Do arguments and the expressed beliefschange and if so, how when students get the chance to work on tasks of non-routinecharacter? Non-routine tasks are essential in developing the competence ofmathematical reasoning. This ongoing study explores how beliefs could work asarguments for the central decision making in students’ reasoning while solvingnon-routine tasks, as a support in their learning process. We apply the framework andthe notion of Beliefs Indications used by Sumpter (2013). By categorizing tasks inrelation to the reasoning demands, non-routine tasks have been selected (Jäder, Lithner& Sidenvall, 2014). Data is collected by video recording task solving sessions andinterviews.Preliminary results show that students express beliefs not to include reflection or muchstruggle in task solving. Beliefs of expectations are used as arguments for centraldecision making.ReferencesBoesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks andthe mathematical reasoning students use. Educational Studies in Mathematics, 75(1),89-105.Jäder, J., Lithner, J., Sidenvall, J. (2014). A cross-national textbook analysis with a focus onmathematical reasoning – The opportunities to learn. (Manuscript in preparation.)Sumpter, L. (2013). Themes and interplay of beliefs in mathematical reasoning. InternationalJournal of Science and Mathematics Education, 11(5), 1115-1135.