Abstract
This paper reports a formative analysis of a Math Modeling Tool in the Algebra II Cognitive Tutor. This tutor is designed to support algebraic reasoning about real world problems. This study focuses on reasoning about situations that can be modeled with general linear form expressions (c = ax + by). Formative evaluations of an early general linear form lesson showed that it helped students comprehend the underlying problem situations, but was less successful in helping students construct symbolic models of the situations. These evaluations guided design of a new tool to scaffold students’ understanding of the componential structure of these symbolic models and the mapping of model components to the problem situation. An empirical evaluation shows that the new tool successfully helps students understand the structure of these mathematical models and learn to construct them.
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, J.R.: Rules of the mind. Lawrence Erlbaum, Hillsdale, NJ (1993)
Anderson, J.R., Corbett, A.T., Koedinger K.R., Pelletier, R.: Cognitive tutors: Lessons learned. Journal of the Learning Sciences, (1995), 4, 167–207
Corbett, A.T., Trask, H.J., Scarpinatto, K.C., Hadley, W.S. A Formative Evaluation of the PACT Algebra II Tutor: Support for Simple Hierarchical Reasoning. In B. Goettl, H. Halff, C. Redfield and V. Shute (Eds.) Intelligent Tutoring Systems: 4th International Conference, ITS’ 98. Springer, New York (1998).
Koedinger, K.R., Anderson, J.R., Hadley, W.H., Mark, M.A.: Intelligent tutoring goes to school in the big city. Artificial Intelligence and Education, 1995: The Proceedings of AIED 95. AACE, Charlottesville, VA (1995)
National Council of Teachers of Mathematics: Curriculum and Evaluation Standards for School Mathematics. The Council, Reston, VA (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Corbett, A., McLaughlin, M., Scarpinatto, K.C., Hadley, W. (2000). Analyzing and Generating Mathematical Models: An Algebra II Cognitive Tutor Design Study. In: Gauthier, G., Frasson, C., VanLehn, K. (eds) Intelligent Tutoring Systems. ITS 2000. Lecture Notes in Computer Science, vol 1839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45108-0_35
Download citation
DOI: https://doi.org/10.1007/3-540-45108-0_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67655-3
Online ISBN: 978-3-540-45108-2
eBook Packages: Springer Book Archive