Analyzing Computer-Based Fraction Tasks on the Basis of a Two-Dimensional View of Mathematics Competences

Anja Eichelmann, Susanne Narciss, Arndt Faulhaber, Erica Melis

In: J. Zumbach , N. Schwartz , T. Seufert , L. Lester (editor). Beyond Knowledge: The Legacy of Competence. Meaningfull Coumputer-Based Learning Environments. European Association for Research on Learning and Instruction SIG conferences (EARLI SIG-6 & 7) September 2-4 Salzburg Australia Pages 125-134 Springer Verlag 6/2008.


As the role of competences and educational standards is stressed in current approaches to education there exist a variety of descriptions, definitions or lists of competences, which should be addressed in instructional contexts. Even though in mathematics education the discussion and description of competences is more advanced than in other fields of knowledge, many of these descriptions do not provide enough detail for guiding the analysis and design of (computer-based) learning tasks. Therefore, the purposes of the present study are to (a) develop a two-dimensional conceptualization of fraction competences, and (b) evaluate the developed competence-framework through an empirical task analysis of a set of computer-based fraction tasks. The results of this task analysis revealed that for 76.3% of the 173 tasks a clear competence assignment was possible. Furthermore, we found that in this set of tasks the cognitive processes associated with mere algorithmic calculation and formula manipulation are much more frequently addressed, than complex cognitive processes (i.e., communicate, model). Future research and practice in designing computer-based fraction tasks should thus focus on developing and investigating tasks addressing the complex processes. (doc, 56 KB )

German Research Center for Artificial Intelligence
Deutsches Forschungszentrum für Künstliche Intelligenz