MIMAPS - Measuring and Improving Mathematical Argumentation & Proof Skills

Responsible

•  Daniel Sommerhoff
•  Stefan Ufer

Project description

Mathematics is a proving science. Accordingly, the development of individual argumentation and proof competences is a major goal of mathematics and related degree programs. Although proof and individual proof attempts by the learners take up a great part of the schooling time, there are many students, especially in the first semesters, who fail to develop adequate argumentation and proof competences (Rach & Heinze, 2013). This can also be observed in the high drop-out rates of math students (Törner & Dieter, 2012).

Mathematical argumentation & proof comprise a complex skill which requires the coordination of various prerequisites (Ufer & Reiss, 2009). But how these prerequisites relate to each other and to mathematical argumentation and proof competence has not yet been covered by quantitative research extensively (Sommerhoff, Ufer & Kollar, 2015). Accordingly, the goal of the project is to gain a sound understanding of how the different individual prerequisites interact in the construction of mathematical argumentation and proof.
Therefore, assessment instruments for the various predictors (content area analysis) were created and successfully piloted within the program. These will be used in further studies to gain a theoretically grounded insight into the connections between mathematical argumentation and proof and its predictors, as well as to empirically validate these insights. A goal of the project is to make these insights useable for supporting students in proving, as well as for improving the mathematical education within the first semesters. Hence two different approaches to foster mathematical argumentation and proof competency will be implemented and empirically evaluated within the project.

Conference articles and Conference contributions

• Sommerhoff, D., Ufer, S., Kollar, I. (2017). The impact of cognitive resources on students' performance in mathematical proof construction. 17th Biennial Conference der European Association for Research on Learning and Instruction (EARLI) Tampere, Finnland: EARLI
• Sommerhoff, D., Ufer, S., Kollar, I. (2016). Mathematical Argumentation and Proof - Supporting a Complex Cognitive Skill. In: Looi, C. K., Polman, J. L., Cress, U., and Reimann, P. (Eds.). Transforming Learning, Empowering Learners: The International Conference of the Learning Sciences (ICLS) 2016, Volume 2 (pp. 811-814). Singapore: International Society of the Learning Sciences.
• Sommerhoff, D., Ufer, S., Kollar, I. (in press). Research on mathematical argumentation: A descriptive review of PME proceedings. Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education, (Research Report).
• Sommerhoff, D., Ufer, S., Kollar, I. (2015). Forschung zum Mathematischen Argumentieren - Ein deskriptiver Review von PME-Beiträgen. Beiträge zum Mathematikunterricht 2015.