Assessment of university students’ understanding of abstract binary operations
Timo Ehmke, Martti E. Pesonen and Lenni Haapasalo
This paper presents the results of a study on the use of interactive online tasks to assess students’ conceptual understanding of abstract binary operations in a first-year linear algebra course. The assessment consists of recognition, identification and production tasks and uses verbal, graphic and symbolic representations of binary operations in numerous point set contexts. The aim of the study is to directly assess the students’ understanding of binary operations and – more indirectly – to identify different profiles for the students’ procedural and conceptual knowledge levels. A latent class analysis revealed different levels in students’ conceptual understanding. Implications will be drawn for teaching abstract binary operations – and other similar concepts. Finally, some suggestions about conceptual qualifications for mathematics teacher education will be discussed.
Timo Ehmke, Dr. habil., works as a research scientist at the Leibniz Institute for Science Education (IPN) in Kiel, Germany. He studied Mathematics, Technology and Education at the Universities of Kiel and Flensburg in Germany. He received the state examination in Mathematics and Technology Education in 1997 and a Ph.D. in Education in 2001. Since 2001 he has been working at the Department of Education at the IPN Kiel in the field of Educational Research. In 2007, he finished his habilitation (postdoctoral lecture qualification) in Educational Research at the University of Kiel.
Martti E. Pesonens
Martti E. Pesonen, Ph.D., acts as senior lecturer at the University of Eastern Finland (Joensuu campus). He studied mathematics and physics in Joensuu and Paris and got the doctor’s degree in mathematics in 1986. He achieved the pedagogical competence of mathematics and physics subject teacher in 1997. He teaches mostly the first year university mathematics courses including basic relational concepts, discrete mathematics and axiomatic approach to linear algebra.
Prof. Dr. Lenni Haapasalo worked at the University of Jyväskylä, at first 9 years as mathematician, and after that18 years as Senior Lecturer/Associate Professor in Mathematics Education. Since 1999 he is full-time Professor of Education at the University of Eastern Finland. His research interest is to develop practical theories based on modern socio-constructivist views, emphasizing technology-based self-determined learning environments, links between conceptual and procedural knowledge, and the genesis of sustainable heuristic processes.