Abstract:

Project CODI (COnceptual DIfficulties of functional relationships) by Nitsch (2015) investigated typical learning difficulties in the field of linear and quadratic functions, especially with the transformation from graphical to situational descriptions. Nine systematic errors were found within more than 10% of the learners. Systematic errors are relatively stable and occur at every different task of the same type of question. The graph-as-picture-error, as an example for the mentioned transformation, occured again six month later at 43.3% of all students with this diagnosed misconception in the pretest (Nitsch & Johlke, 2016).

Intuitive images seem to affect initial solutions and interfere with mathematical ideas and patterns of mathematical acts. They so lead to stable misconceptions. To overcome this situation, Conceptual-Change-processes (Vosniadou, 2008)) are going to be initiated by a digital feedback. That is one part of a digital given task with a special design: the DDTA (Digital Diagnostic TAsk).

Project EOM (E-Feedback to Overcome Misconceptions) is connected to the running project of the DDTA (Kallweit et al., 2017) and researches the possibilities to design computer-based feedback by the use of digital instruments to activate Conceptual-Change-processes.
This E-Feedback has to be fitted to the learner individually, it will appear automatically, uses different kinds of multimedia options and it should be able to activate Conceptual-Change-processes in the learner’s mind.

The long-dated aim of the project is an independent online-tool, which can be used by teachers for mathematical diagnosis but simultaneously stimulates the learning processes of the students. A proposal for an E-Feedback with the use of a video-tutorial will be presented.

References:
[1] Kallweit, M., Schaub, M., Feld-Caesar, N., Bruder, R., Krusekamp, S., Neugebauer, C., & Winter, K. (2017). Digitale Diagnostische Testaufgaben - Theoretisches Design und interaktives Beispiel. In Institut für Mathematik der Universität Potsdam (Ed.): Beiträge zum Mathematikunterricht, Beiträge zum Mathematikunterricht 2017. Münster: WTM-Verlag.
[2] Nitsch, R. (2015). Diagnose von Lernschwierigkeiten im Bereich funktionaler Zusammenhänge: Eine Studie zu typischen Fehlermustern bei Darstellungswechseln. Wiesbaden: Springer Spektrum.
[3] Nitsch, R., & Johlke, F. (2016). Stabilität von Fehlermustern bei funktionalen Zusammenhängen. In Institut für Mathematik und Informatik Heidelberg (Ed.): Beiträge zum Mathematikunterricht, Beiträge zum Mathematikunterricht 2016. Münster: WTM-Verlag.
[4] Vosniadou, S. (Ed.). (2008). Educational psychology handbook series. International handbook of research on conceptual change. New York: Routledge.

Keywords:

Misconceptions, learning difficulties, Conceptual-Change, digital media, video.