Abstract
Countries are regularly upgrading K12 curricula. This is a major challenge, involving the knowledge and experience of experts on teaching and experts on the subject matters. But to teach a curriculum it is also critical to know the causal dependencies between contents during the learning process: how the students’ previous performance in each content influences their future performance in each one of them. This critical empirical information is not provided in the curriculum. However, nowadays with the massive online activity of teacher and students, patterns among contents can be detected. Applying machine learning algorithms on the trace of more than half a million mathematical exercises done by 805 fourth graders from 23 courses in Chile we have identified graphs with causal dependencies among contents. These graphs emerge from the collective activity of teachers and students. They implicitly take into account logical relations, teachers’ practices as they follow the curriculum, and students’ learning 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
Araya, R., Gigon, P.: Segmentation Trees: A New Help for Building Expert Systems and Neural Networks. In: COMPSTAT 1992, vol. 1, pp. 119–124 (1992)
Araya, R., Calfucura, P., Jiménez, A., Aguirre, C., Palavicino, M., Lacourly, N., Soto-Andrade, J., Dartnell, P.: The Effect of Analogies on Learning to Solve Algebraic Equations. Pedagogies: An International Journal. Special Issue The teaching of Algebra 5(3) (2010)
Araya, R., Van der Molen, J.: A mayor ejercitación en línea en matemáticas más aumenta el SIMCE. Revista Chilena de Educación Matemática RECHIEM (2010)
Araya, R.: Introducing Mathematical Modeling Skills in the Curriculum. In: Mathematical Modeling Course in Mathematics Curriculum: Some Best Practices in APEC Economies (2012), http://publications.apec.org/publication-detail.php?pub_id=1362 (retrieved)
Bouckaert, R., Frank, E., Hall, M., Kirkby, R., Reutemann, P., Seewald, A., et al.: WEKA manual for version 3-6-0, pp. 3–6. University of Waikato, Hamilton (2008)
Common Core State Standards Initiative: Common Core State Standards for Mathematics (2011), http://www.corestandards.org/the-standards/mathematics (retrieved)
Consortium for Policy Research in Education: School Improvement by Design: Lessons from a Study of Comprehensive School Reform Programs (August 2009)
Friedman, J.H.: A recursive partitioning Decision Rule for Nonparametric Classification. IEEE Transactions on Computers 26(4), 404–408 (1977)
Geary, D.: Educating the evolved mind: Conceptual foundations for an evolutionary educational psychology. Information Age Publishing, Charlotte (2007)
Gigerenzer, G.: Adaptive thinking: Rationality in the real world. Oxford University Press, Oxford (2000)
Hadamard, J.: The Mathematician’s Mind. Princeton University Press, New Jersey (1945)
Koedinger, K.R., McLaughlin, E.A., Stamper, J.C.: Automated student model improvement. In: Proceedings of the Fifth International Conference on Educational Data Mining (2012)
McKinsey Global Institute: Big data: The next frontier for innovation, competition, and productivity (2011)
Michie, D., Spiegelhalter, D., Taylor, C.: Machine Learning, Neural and Statistical Classification. Ellis Horwood (1994)
Mingers, J.: An Empirical Comparison of Selection Measures for Decision Tree Induction. Machine Learning 3 (1989)
National Mathematics Advisory Panel, Report of the Task Group on Instructional Practices (2008)
OECD: The PISA 2003 – Assessment Framework (2003)
The National Academies: Knowing What Students Know: The Science and Design of Educational Assessment (2001)
Richland, L.E., Zur, O., Holyoak, K.J.: Cognitive supports for analogies in the mathematics classroom. Science 316(5828), 1128–1129 (2007)
Siegler, R.: Children’s thinking. Prentice Hall, Upper Saddle River (1998)
Siegler, R., Araya, R.: A computational model of conscious and unconscious strategy discovery. In: Kail, R.V. (ed.) Advances in Child Development and Behavior, pp. 1–42. Elsevier, Oxford (2005)
Thai-Nghe, N., Drumond, L., Horváth, T., Schmidt-Thieme, L.: Using Factorization Machines for Student Modeling (2012), http://www.ismll.uni-hildesheim.de/pub/pdfs/Nguyen_factmod_2012.pdf (retrieved)
The American Statistical Association: Using Statistics Effectively in Mathematics Education Research (2007)
U.S. Department of Education: Improving Mathematical Problem Solving in Grades 4 Through 8 (2012)
U.S. Department of Education: Enhancing Teaching and Learning Through Educational Data Mining and Learning Analytics. (draft for public comment) Office of Educational Technology (2012)
Lehn, V.: Mind Bugs: the Origins of Procedural Misconceptions. MIT Press (1990)
Yang, F., Li, F.W.B., Lau, R.W.H.: Fuzzy Cognitive Map Based Student Progress Indicators. In: Leung, H., Popescu, E., Cao, Y., Lau, R.W.H., Nejdl, W. (eds.) ICWL 2011. LNCS, vol. 7048, pp. 174–187. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Araya, R., Van der Molen, J. (2013). Causal Dependence among Contents Emerges from the Collective Online Learning of Students. In: Bǎdicǎ, C., Nguyen, N.T., Brezovan, M. (eds) Computational Collective Intelligence. Technologies and Applications. ICCCI 2013. Lecture Notes in Computer Science(), vol 8083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40495-5_64
Download citation
DOI: https://doi.org/10.1007/978-3-642-40495-5_64
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40494-8
Online ISBN: 978-3-642-40495-5
eBook Packages: Computer ScienceComputer Science (R0)