Abstract
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 these complex processes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, L.W., Krathwohl, D.R., Airasian, P.W., Cruikshank, K.A., Mayer, R.E., Pintrich, P.R., Raths, J. & Wittrock, M.C. (2001). A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives. New York, NY: Longman.
Blum, W., Drueke-Noe, C., Hartung, R. & Koeller, O. (2006). Bildungsstandards Mathematik: konkret – Sekundarstufe I: Aufgabenbeispiele, Gestaltungsanregungen, Fortbildungsideen. Berlin: Cornelsen Verlag.
Brown, G. & Quinn, R.J. (2006). Algebra students’ difficulty with fractions: an error analysis. amt, 64(2), 28-40.
Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 10, 37-46.
Melis, E., Büdenbender, J., Andres, E., Frischauf, A., Goguadze, G., Libbrecht, P., Pollet, M., & Ullricht, C. (2001). ActiveMath: A generic and adaptive web-based learning environment. International Journal of Artificial Intelligence in Education, 12, 385-407.
Narciss, S., Proske, A. & Körndle, H. (2004). Interaktive Aufgaben für das computergestützte Lernen. Vom ersten Entwurf bis zur technischen Realisierung. In U. Schmitz (Hrsg.), Linguistik lernen im Internet. Das Lehr-/Lernportal PortaLingua (S. 193-206). Tübingen: G. Narr.
National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston: NCTM.
Neubrand, M., Biehler, R., Blum, W., Cohors-Fresenborg, E., Flade, L., Knoche, N., Lind, D., Löding, W., Möller, G. & Wynands, A. (2001). Grundlagen der Ergänzung des internationalen OECD/PISA-Mathematik-Tests in der deutschen Zusatzerhebung, Zentralblatt für Didaktik der Mathematik, 33(2), 33-45.
Organization for Economic Cooperation and Development (2004). Learning for Tomorrow’s World – First Results from PISA 2003. Paris: OECD.
Wartha, S. & vom Hofe, R. (2005). Probleme bei Anwendungsaufgaben in der Bruchrechnung. mathematik lehren, 128, 10-15.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media B.V.
About this paper
Cite this paper
Eichelmann, A., Narciss, S., Faulhaber, A., Melis, E. (2008). Analyzing Computer-Based Fraction Tasks on the Basis of a Two-Dimensional View of Mathematics Competences. In: Zumbach, J., Schwartz, N., Seufert, T., Kester, L. (eds) Beyond Knowledge: The Legacy of Competence. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8827-8_19
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8827-8_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8826-1
Online ISBN: 978-1-4020-8827-8
eBook Packages: Humanities, Social Sciences and LawEducation (R0)