Abstract
Previous research demonstrates that multiple representations can enhance students’ learning. However, learning with multiple representations is hard. Students need to acquire representational fluency with each of the representations and they need to be able to make connections between the representations. It is yet unclear how to balance these two aspects of learning with multiple representations. In the present study, we focus on a key aspect of this question, namely the temporal sequencing of representations when students work with multiple representations one-at-a-time. Specifically, we investigated the effects of blocking versus interleaving multiple representations of fractions in an intelligent tutoring system. We conducted an in vivo experiment with 296 5th- and 6th-grade students. The results show an advantage for blocking representations and for moving from a blocked to an interleaved sequence. This effect is especially pronounced for students with low prior knowledge.
This is a preview of subscription content, log in via an institution to check access.
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
Moss, J., Case, R.: Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education 30, 122–147 (1999)
National Mathematics Advisory Board Panel. Foundations for Success: Report of the National Mathematics Advisory Board Panel, U.S. Government Printing Office (2008)
Kaminski, E.: Promoting Mathematical Understanding: Number Sense in Action. Mathematics Education Research Journal 14, 133–149 (2002)
Rau, M.A., et al.: Intelligent tutoring systems with multiple representations and selfexplanation prompts support learning of fractions. In: 14th International Conference on Artificial Intelligence in Education Brighton, UK (2009)
Ainsworth, S.E., et al.: Analysing the Costs and Benefits of Multi-Representational Learning Environments. In: van Someren, M.W., et al. (eds.) Learning with Multiple Representations. Pergamon, Oxford (1998)
Schnotz, W., Bannert, M.: Construction and interference in learning from multiple representation. Learning and Instruction 13, 141–156 (2003)
Ainsworth, S.: Designing effective multi-representational learning environments. In: ESRC Centre for Research in Development, Instruction & Training Department of Psychology, Nottingham, vol. 58 (1999)
Ainsworth, S.: DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction 16, 183–198 (2006)
de Jong, T., et al.: Acquiring knowledge in science and mathematics: The use of multiple representations in technology-based learning environments. In: Van Someren, M.W., et al. (eds.) Learning with Multiple Representations, Oxford (1998)
Spiro, R.J., Jehng, J.C.: Cognitive flexibility and hypertext: Theory and technology for the nonlinear and multidimensional traversal of complex subject matter. In: Nix, D., Spiro, R.J. (eds.) Cognition, education and multimedia: Exploring ideas in high technology, pp. 163–205. Lawrence Erlbaum Associates, Hillsdale (1990)
Schmidt, R.A., Bjork, R.A.: New conceptualizations of practice: Common principles in three paradigms suggest new concepts for training. Psychological Science 3, 207–217 (1992)
de Croock, M.B.M., Van Merrienboer, J.J.G.: High versus low contextual interference in simulation-based training of troubleshooting skills: Effects on transfer performance and invested mental effort. Computers in Human Behavior 14, 249–267 (1998)
Koedinger, K.R., Corbett, A.: Cognitive Tutors: Technology Bringing Learning Sciences to the Classroom. In: Sawyer, R.K. (ed.) The Cambridge handbook of: The learning sciences, New York, NY, US, pp. 61–77. Cambridge University Press, Cambridge (2006)
Aleven, V., et al.: Example-tracing tutors: A new paradigm for intelligent tutoring systems. Document submitted for publication (under review)
Charalambous, C.Y., Pitta-Pantazi, D.: Drawing on a Theoretical Model to Study Students’ Understandings of Fractions. Educational Studies in Mathematics 64, 293–316 (2007)
Aleven, V., Koedinger, K.R.: The need for tutor dialog to support self-explanation. In: Rose, C.P., Freedman, R. (eds.) Building Dialogue Sstems for Tutorial Applications. Papers from the 2000 AAAI Fall Symposium, pp. 65–73. AAAI Press, Menlo Park (2000)
Raudenbush, S.W., Bryk, A.S.: Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd edn. Sage Publications, Newbury Park (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rau, M.A., Aleven, V., Rummel, N. (2010). Blocked versus Interleaved Practice with Multiple Representations in an Intelligent Tutoring System for Fractions. In: Aleven, V., Kay, J., Mostow, J. (eds) Intelligent Tutoring Systems. ITS 2010. Lecture Notes in Computer Science, vol 6094. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13388-6_45
Download citation
DOI: https://doi.org/10.1007/978-3-642-13388-6_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13387-9
Online ISBN: 978-3-642-13388-6
eBook Packages: Computer ScienceComputer Science (R0)