Developing reasoning competence in inquiry-based mathematics teaching

Learning to reason in mathematics education is often considered to be one of the most important competencies in mathematics education, but nevertheless it is also considered challenging, and how to get students to go from arguing empirically to arguing more mathematical deductivelyit is often problematised (EMS, 2011). The purpose of this thesis is to investigate how an inquiry-based teaching approach affects students' development of reasoning competence in primary school mathematics teaching. Furthermore, there is a focus on how to study students' development of reasoning competence and whether it is possible to develop a test that can measure this development.The thesis is closely linked to the development and research project named Quality in Danishand Mathematics (KiDM), which is aimed at developing and studying inquiry-based teaching in mathematics teaching in 4th and 5th grade in a randomised controlled experiment over three experimental trials.The thesis is designed as a mixed methods study, which uses both data from qualitative video observations from several KiDM classes, and data from quantitative teacher and student surveys. In addition, a competence test was developed and used in the KiDM experiment from which both quantitative and qualitative data are drawn. The result of the thesis is that an inquiry-based teaching approach affects students' developmentof reasoning competence in several ways: By analysing video observations from the KiDM intervention with a model developed byLatour (1999), the findings indicate that the students, through different representations, go in small steps, stage by stage, from arguing from the complexity of everyday objects to arguing based on more general and formal mathematical approaches, so the students’ representations insmall steps lose locality, particularity, materiality and multiplicity. In general, Latour’s (1999) model can be said to have the potential to focus on and clarify the students' work processes and reasoning (Paper I).In another analysis, the findings indicate that overall the difference between the students’ reasoning activities depends on which inquiry-based activity is in focus, and that this may have implications for how a teacher will grasp the class discussion (Paper II). Finally, analyses from the qualitative observations also provide evidence that cognitiveconflicts can drive the students reasoning process and that the environment has an important role of retaining the conflicting positioning by making them available for discussion and scrutiny. The process of resolving cognitive conflicts is a process stretched over time that involved taking different routes and exploring approached and understandings (Paper III).The quantitative data from the student survey indicates that students who were part of the KiDM experiment in mathematics experienced that they were generally more often focused on dialogues and more often discussed the students’ different solutions. The developed competencies test is described as both reliable and valid (Paper IV), and in someway aligned to the KiDM classroom teaching, although not in all aspects (Paper V), but the test does nevertheless not produce a significant total result for students' development of mathematical competencies after the three trials in the KiDM project.The findings from the thesis indicate that an inquiry-based teaching approach in general can have a positive effect on the students' development of reasoning competence; however, the teacher's approach to the activities and the designs of the tasks have a major influence on this effect.