Definite Integral Automatic Analysis Mechanism Research and Development Using the “Find the Area by Integration” Unit as an Example

Mu Yu Ting

doi:10.12973/eurasia.2017.00724a

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Mu Yu Ting ¹ ^*

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¹ National Formosa University, Taiwan^* Corresponding Author

Abstract

This approach was particularly applied to solve problems with the definite integral in university-level calculus courses Assessment of Content Analysis Expert Knowledge Structure Participators Error Type Analysis Research Tools The results show that the overall recognition rate of the BN (Model 2) is better than that of Model 1, which has only the multiple choice items. This research focuses on definite integral diagnostic tests and automated analysis mechanisms. Future studies may focus on remedial teaching.

Keywords

Bayesian network
DINA model
error type
expert knowledge structure
Q matrix

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2017, Volume 13, Issue 7, 2883-2896

https://doi.org/10.12973/eurasia.2017.00724a

Publication date: 15 Jun 2017

Article Views: 1947

Article Downloads: 1926

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References

Artigue, M., Batanero, C., & Kent, P. (2007). Mathematics thinking and learning at post-secondary level. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1011-1049). Greenwich, CT: Information Age Publishing, Inc.
Bunderson, C. V., Inouye, D. K., & Olsen, J. B. (1988). The four generations of computerized educational measurement. In R. L. Linn (Ed.), Educational measurement (pp. 367-407). New York, NY: Macmillan.
Caffrey, E., Fuchs, D., & Fuchs, L. S. (2008). The predictive validity of dynamic assessment: A review. Journal of Special Education, 41(4), 254-270. doi:10.1177/0022466907310366.
Chatzopoulou, D. I., & Economides, A. A. (2010). Adaptive assessment of student’s knowledge in programming courses. Journal of Computer Assisted Learning, 26(4), 258-269. doi:10.1111/j.1365-2729.2010.00363.x.
de la Torre, J. (2009). DINA model and parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34 , 115-130.
Doignon, J. P., & Falmagne, J. C. (1999). Knowledge spaces. Berlin, Germany: Springer-Verlag.
Fernando, B. M., & Aarón, R. R. (2013). Cognitive processes developed by students when solving mathematical problems within technological environments. Mathematics Enthusiast, 10(1/2), 109-136.
Friedman, N., Goldszmidt, M., Heckerman, D., & Russell, S. (1997). Where is the impact of Bayesian Networks in learning? In International Joint Conference on Artificial Intelligence.
Ghazizadeh-Ahsaee, M., Naghibzadeh, M., & Gildeh, B. S. (2014). Learning parameters of fuzzy Bayesian Network based on imprecise observations. International Journal of Knowledge-Based and Intelligent Engineering Systems, 18(3), 167-180. doi:10.3233/KES-140296.
Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner, & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 60–86). Reston, VA: National Council of Teachers of Mathematics.
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York, NY: Macmillan.
Irad, B. G. (2007). Bayesian networks. In F. Ruggeri, F. Faltin, & R. Kenett (Eds.), Encyclopedia of statistics in quality & reliability. Chichester, UK: Wiley & Sons.
Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 12, 55-73. doi:10.1177/01466210122032064.
Larson, C., Harel, G., Oehrtman, M., Zandieh, M., Rasmussen, C., Speiser, R., & Walter, C. (2010). Modeling perspectives in math education research. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 61-71). New York, NY: Springer US.
London Mathematical Society. (1992). The future for honours degree courses in mathematics and statistics: Final report of a group working under the auspices of the London Mathematical Society. London, UK: Council of the London Mathematical Society.
Mallet, D. G. (2013). An example of cognitive obstacles in advanced integration: The case of scalar line integrals. International Journal of Mathematical Education in Science and Technology, 44(1), 152-157. doi:10.1080/0020739X.2012.678897.
Marchis, I. (2013). Future primary and preschool pedagogy specialization students’ mathematical problem solving competency. Acta Didactica Napocensia, 6(2), 33-38.
Moise, E. E. (1948). An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua. Transactions of the American Mathematical Society, 63(3), 581-594. doi:10.1090/S0002-9947-1948-0025733-4.
Rosch, E. H. (1975). Cognitive representations of semantic categories. Journal of Experimental Psychology: General, 104, 192-233.
Schroeder, A., Minocha, S., & Schneider, C. (2010). The strengths, weaknesses, opportunities and threats of using social software in higher and further education teaching and learning. Journal of Computer Assisted Learning, 26(3), 159-174. doi:10.1111/j.1365-2729.2010.00347.x.
Schwarzenberger, R. L. E. (1984). The importance of mistakes: The 1984 presidential address. Mathematical Gazette, 68(445), 159–172.
Serdina Parrot, M. A., & Eu, L. K. (2014). Teaching and learning calculus in secondary schools with the TI-Nspire. Malaysian Online Journal of Educational Science, 2(1), 27-33.
Tall, D. (1993). Students’ difficulties in calculus. In Proceedings of Working Group 3 on Students’ Difficulties in Calculus, ICME-7 1992 (pp. 13-28). Québec, Canada: ICME.
Tall, D. (2004). “Thinking through three worlds of mathematics.” In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4; pp. 281–288). Cape Town, South Africa: International Group for the Psychology of Mathematics Education.
Tao, Y. H., Wu, Y. L., & Chang, H. Y. (2008). A practical computer adaptive testing model for small-scale scenarios. Educational Technology & Society, 11(3), 259–274.
Tapare, U. S. (2013). Conceptual understanding of undergraduate students of calculus in cooperative learning using calculus education software (CES). Retrieved from http://linc.mit.edu/linc2013/proceedings/Session5/Session5Tapare.pdf.
Tarmizi, R. A. (2010). Visualizing student’s difficulties in learning calculus. Procedia Social and Behavioral Sciences, 8, 377–383. doi:10.1016/j.sbspro.2010.12.053.
Tatsuoka, K. (1985). A probabilistic model for diagnosing misconceptions in the pattern classification approach. Journal of Educational Statistics 12, 55–73. doi:10.3102/10769986010001055.
Tatsuoka, K. K. (1995). Structure of knowledge states for NAEP science tasks: An application of the rule model. Paper presented at the Meeting of the National Council of Measurement in Education, San Francisco, CA.
Wauters, K., Desmet, P., & van den Noortgate, W. (2010). Adaptive item-based learning environments based on the item response theory: Possibilities and challenges. Journal of Computer Assisted Learning, 26(3), 549-562. doi:10.1111/j.1365-2729.2010.00368.x.
Wu, H.-M., Kuo, B. C., & Yang, J. M. (2012). Evaluating knowledge structure-based adaptive testing algorithms and system development. Educational Technology & Society, 15(2), 73–88.
Zerr, R. J. (2010). Promoting students’ ability to think conceptually in calculus. Primus, 20(1), 1–20. doi:10.1080/10511970701668365.

How to cite this article

APA

Ting, M. Y. (2017). Definite Integral Automatic Analysis Mechanism Research and Development Using the “Find the Area by Integration” Unit as an Example. Eurasia Journal of Mathematics, Science and Technology Education, 13(7), 2883-2896. https://doi.org/10.12973/eurasia.2017.00724a

Vancouver

Ting MY. Definite Integral Automatic Analysis Mechanism Research and Development Using the “Find the Area by Integration” Unit as an Example. EURASIA J Math Sci Tech Ed. 2017;13(7):2883-96. https://doi.org/10.12973/eurasia.2017.00724a

AMA

Ting MY. Definite Integral Automatic Analysis Mechanism Research and Development Using the “Find the Area by Integration” Unit as an Example. EURASIA J Math Sci Tech Ed. 2017;13(7), 2883-2896. https://doi.org/10.12973/eurasia.2017.00724a

Chicago

Ting, Mu Yu. "Definite Integral Automatic Analysis Mechanism Research and Development Using the “Find the Area by Integration” Unit as an Example". Eurasia Journal of Mathematics, Science and Technology Education 2017 13 no. 7 (2017): 2883-2896. https://doi.org/10.12973/eurasia.2017.00724a

Harvard

Ting, M. Y. (2017). Definite Integral Automatic Analysis Mechanism Research and Development Using the “Find the Area by Integration” Unit as an Example. Eurasia Journal of Mathematics, Science and Technology Education, 13(7), pp. 2883-2896. https://doi.org/10.12973/eurasia.2017.00724a

MLA

Ting, Mu Yu "Definite Integral Automatic Analysis Mechanism Research and Development Using the “Find the Area by Integration” Unit as an Example". Eurasia Journal of Mathematics, Science and Technology Education, vol. 13, no. 7, 2017, pp. 2883-2896. https://doi.org/10.12973/eurasia.2017.00724a