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Probability Reasoning Internet Assessment System with Rule Usage Structures and Similarity Comparisons

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Book cover Opportunities and Challenges for Next-Generation Applied Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 214))

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Abstract

The purpose of this study is to implement an Internet assessment on probability reasoning which provides graphs of rule usage and similarity coefficient in comparison with expert. Ordering theory (OT) combined with interpretive structural modeling (ISM) is the method to construct structural graphs of rule usage on probability reasoning. Set operation is adopted to calculate the similarity coefficient for graphs of rule usage. An empirical study for pupils shows that rule usage varies with the total score and there is significant difference on similarity coefficient based on age, gender and interaction. Finally, some recommendations and suggestions for future research are discussed.

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References

  1. Piaget, J., Inhelder, B.: The Origin of the Idea of Chance in Children. Routledge and Kegan Paul (1975)

    Google Scholar 

  2. Konold, C.: Informal concepts of probability. Cognition and Instruction 6, 59–98 (1989)

    Article  Google Scholar 

  3. Siegler, R.S.: Developmental of sequences within and between concepts. Society for Research in Child Development Monographs 46, Whole No. 189 (1981)

    Google Scholar 

  4. Siegler, R.S.: The rule-assessment approach and education. Contemporary Educational Psychology 7, 272–288 (1982)

    Article  Google Scholar 

  5. Warfield, J.N.: Interpretive structural modeling (ISM). In: Olsen, S.A.W.E., Walter, W.V., Lehner, W. (eds.) Group Planning & Problem Solving Methods in Engineering, pp. 115–201. Wiley, New York (1982)

    Google Scholar 

  6. Bart, W.M., Krus, D.J.: An ordering-theoretic method to determine hierarchies among items. Educational and Psychological Measurement 33, 291–300 (1973)

    Article  Google Scholar 

  7. Bart, W.M., Williams-Morris, R.: A refined item diagraph analysis of proportional reasoning test. Applied Measurement in Education 3, 143–165 (1990)

    Article  Google Scholar 

  8. Bart, W.M., Post, T., Behr, M., Lesh, R.: A diagnostic analysis of a proportional reasoning test item: An introduction to the properties of a semi-dense item. Focus on Learning Problems in Mathematics 16, 1–11 (1994)

    Google Scholar 

  9. Jansen, B.R.J., Han van der Maas, M.L.J.: Statistical test of the rule assessment methodology. Developmental Review 17, 321–357 (1997)

    Article  Google Scholar 

  10. Lin, Y.H., Hung, W.L.: Robust clustering on rule usage of probability reasoning with raw rule score. In: The 4th International Conference on Fuzzy Systems and Knowledge Discovery, Haikou, China, pp. 251–255 (2007)

    Google Scholar 

  11. Cosmides, L., Tooby, J.: Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition 58, 1–73 (1996)

    Article  Google Scholar 

  12. Fischbein, E., Gazit, A.: Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics 15, 1–24 (1984)

    Article  Google Scholar 

  13. Tarr, J.E., Jones, G.A.: A framework for assessing middle school students’ thinking in conditional probability and independence. Mathematics Education Research Journal 9, 39–59 (1997)

    Google Scholar 

  14. Bart, W.M., Rothen, W., Read, S.: An ordering-analytic approach to the study of group differences in intelligence. Educational and Psychological Measurement 46, 799–812 (1986)

    Article  Google Scholar 

  15. Goldsmith, T.E., Johnson, P.J., Acton, W.H.: Assessing structural knowledge. Journal of Educational Psychology 83, 88–96 (1991)

    Article  Google Scholar 

  16. Warfield, J.N.: Crossing theory and hierarchy mapping. IEEE Transactions on System, Man, and Cybernetics 7, 505–523 (1977)

    Article  MATH  MathSciNet  Google Scholar 

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Lin, YH. (2009). Probability Reasoning Internet Assessment System with Rule Usage Structures and Similarity Comparisons. In: Chien, BC., Hong, TP. (eds) Opportunities and Challenges for Next-Generation Applied Intelligence. Studies in Computational Intelligence, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92814-0_31

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  • DOI: https://doi.org/10.1007/978-3-540-92814-0_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92813-3

  • Online ISBN: 978-3-540-92814-0

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