Analysis of Students’ Misconception Based on Rough Set Theory

Author(s)
Tian-Wei Sheu,
Tzu-Liang Chen,
Ching-Pin Tsai,
Jian-Wei Tzeng,
Cing-Ping Deng,
Masatake Nagai

Affiliation(s)

Graduate Institute of Educational Measurement and Statistics, National Taichung University of Education, Taichung, Chinese Taipei..

Graduate Institute of Educational Measurement and Statistics, National Taichung University of Education, Taichung, Chinese Taipei.

Graduate Institute of Educational Measurement and Statistics, National Taichung University of Education, Taichung, Chinese Taipei..

Graduate Institute of Educational Measurement and Statistics, National Taichung University of Education, Taichung, Chinese Taipei.

ABSTRACT

The study analyzed students’ misconception based on rough set theory
and combined with interpretive structural model (ISM) to compare students’
degree of two classes. The study then has provided an effective diagnostic
assessment tool for teachers. The participants were 30 fourth grade students in

Cite this paper

T. Sheu, T. Chen, C. Tsai, J. Tzeng, C. Deng and M. Nagai, "Analysis of Students’ Misconception Based on Rough Set Theory,"*Journal of Intelligent Learning Systems and Applications*, Vol. 5 No. 2, 2013, pp. 67-83. doi: 10.4236/jilsa.2013.52008.

T. Sheu, T. Chen, C. Tsai, J. Tzeng, C. Deng and M. Nagai, "Analysis of Students’ Misconception Based on Rough Set Theory,"

References

[1] M. H. Chiu, “Reflections and Implications of Research on Conceptual Change,” Chinese Journal of Science Education, Vol. 8, No. 1, 2000, pp. 1-34.

[2] Ministry of Education, “Grade 1-9 Curriculum Guidelines,” Ministry of Education, Taipei, 2003.

[3] C. Y. Chen, “The Influence of Teaching Confrontation Style on Key Concepts of Elementary School Students,” Bulletin of Educational Psychology, Vol. 36, No. 4, 2005, pp. 375-393.

[4] D. C. Yang and S. M. Hung, “The Study of Remedial Instruction on Fraction,” Journal of Educational Research and Development, Vol. 4, No. 2, 2008, pp. 85-118.

[5] S. C. Wen, “A Study of Integrated Diagnostic Teaching on Fractions for Elementary Fifth-Grade Students,” Chinese Journal of Science Education, Vol. 19, No. 5, 2011, pp. 383-408.

[6] J. K. Lannin, D. D. Barker and B. E. Townsend, “How Students View the General Nature of Their Errors,” Educational Studies in Mathematics, Vol. 66, No. 1, 2007, pp. 43-59. doi:10.1007/s10649-006-9067-8

[7] C. C. Lee and S. C. Hu, “An On-Line Assessment and Misconception Correction Tool for Students Learning Fundamental Mathematics,” Journal of National Taichung University: Mathematics, Science & Technology, Vol. 23, No. 1, 2009, pp. 1-28.

[8] H. K. Tsai, C. C. Chen and H. P. Chang, “A Study of the Relationship between High School Students’ Force Diagrams and Equation Representations in Problem Solving,” Chinese Journal of Science Education, Vol. 18, No. 2, 2010, pp. 155-175.

[9] J. S. Yeh and C. H. Cheng, “Refining Rough Set for Applying Classification of Appendicitis,” The Journal of Taiwan Association for Medical Informatics, Vol. 14, No. 2, 2005, pp. 1-16.

[10] H. Wang, M. Zhou and Z. William, “A New Approach to Establish Variable Consistency Dominance—Based Rough Sets Based on Dominance Matrices,” 2012 International Conference on Intelligent System Design and Engineering Application, Sanya, 6-7 January 2012, pp. 48-51. doi:10.1109/ISdea.2012.636

[11] Y. Ren, T. Xing, Q. Quan and X. Chen, “Attributes Knowledge Reduction and Evaluation Decision of Logistics Centre Location Based on Rough Sets,” 2011 4th International Conference on Intelligent Computation Technology and Automation, Shenzhen, 28-29 March 2011, pp. 67-70. doi:10.1109/ICICTA.2011.24

[12] K. Zaras, J. C. Marin and B. Boudreau-Trude, “Dominance-Based Rough Set Approach in Selection of Portfolio of Sustainable Development Projects,” American Journal of Operations Research, Vol. 2, No. 4, 2012, pp. 502508. doi:10.4236/ajor.2012.24059

[13] G. Ke, L. Mingwu, F. Yong and Z. Xia, “A Hybrid Model of Rough Sets and Shannon Entropy for Building a Foreign Trade Forecasting System,” 2011 4th International Joint Conference on Computational Sciences and Optimization, Yunnan, 15-19 April 2011, pp. 7-11.

[14] C. J. Lai and K. L. Wen, “Application of Rough Set Approach to Credit Screening Evaluation,” Journal of Quantitative Management, Vol. 12, No. 1, 2005, pp. 69-78.

[15] D. Chao and P. Sulin, “The BSC Alarm Management System Based on Rough Set Theory in Mobile Communication,” 2011 7th International Conference on Computational Intelligence and Security, Hainan, 3-4 December 2011, pp. 1557-1561.

[16] A. N. Hossam, “A Probabilistic Rough Set Approach to Rule Discovery,” International Journal of Advanced Science and Technology, Vol. 30, 2011, pp. 25-34.

[17] Z. Qu and X. Wang, “Application of Clustering Algorithm and Rough Set in Distance Education,” 2009 1st International Workshop on Education Technology and Computer Science, Wuhan, 7-8 March 2009, pp. 489-493. doi:10.1109/ETCS.2009.117

[18] A. S. Salama and H. M. Abu-Donia, “Generalizations of Rough Functions in Topological Spaces by Using PreOpen Sets,” Journal of Intelligent Learning Systems and Applications, Vol. 4, No. 2, 2012, pp. 127-134. doi:10.4236/jilsa.2012.42012

[19] J. Shen, J. Wang and H. Ai, “An improved Artificial Immune Systembased Network Intrusion Detection by Using Rough Set,” Communications and Network, Vol. 4, No. 1, 2012, pp. 41-47. doi:10.4236/cn.2012.41006

[20] X. Zhang and W. Xu, “Rough Computational Approach to UAR Based on Dominance Matrix in IOIS,” Intelligent Information Management, Vol. 3, No. 4, 2011, pp. 131136. doi:10.4236/iim.2011.34016

[21] K. L. Wen, M. Nagai, T. C. Chang and H. C. Wang, “An Introduction to Rough Set Theory and Application,” Chuan Hwa Publishing Ltd., Taipei, 2008.

[22] Z. Pawlak, “Rough Sets,” International Journal of Computer and Information Sciences, Vol. 11, No. 5, 1982, pp. 341-356. doi:10.1007/BF01001956

[23] Z. Pawlak, “Drawing Conclusions from Data—The Rough Set Way,” International Journal of Intelligent Systems, Vol. 16, No. 1, 2001, pp. 3-11. doi:10.1002/1098-111X(200101)16:1<3::AID-INT2>3.0.CO;2-I

[24] Z. Pawlak, “Rough Set Theory and Its Applications,” Journal of Telecommunications and Information Technology, Vol. 3, 2002, pp. 7-10.

[25] Z. Pawlak, “Rough Sets and Intelligent Data Analysis,” Information Science, Vol. 147, No. 1-4, 2002, pp. 1-12. doi:10.1016/S0020-0255(02)00197-4

[26] Y. Y. Yao, “Probabilistic Approaches to Rough Sets,” Expert System, Vol. 20, No. 5,2003, pp. 287-297. doi:10.1111/1468-0394.00253

[27] Z. Pawlak, “Rough Sets, Decision Algorithms and Bayes’ Theorem,” European Journal of Operational Research, Vol. 136, No. 1, 2002, pp. 181-189. doi:10.1016/S0377-2217(01)00029-7

[28] Z. Pawlak, “Decision Algorithms and Flow Graphs; a Rough Set Approach,” Journal of Telecommunications and Information Technology, Vol. 3, 2002, pp. 98-101.

[29] J. N. Warfield, “Societal Systems Planning, Policy and Complexity,” John Wiley & Sons Inc., New York, 1976.

[30] J. N. Warfield, “Interpretive Structural Modeling (ISM) Group Planning & Problem Solving Methods in Engineering,” John Wiley & Sons Inc., New York, 1982.

[31] T. W. Sheu, T. L. Chen, J. W. Tzeng, C. P. Tsai and M. Nagai, “Analyzing the Structure of Factors Influencing of Learning Interest in Mathematics,” International Journal of Kansei Information, Vol. 3, No. 2, 2012, pp. 103-120.

[32] P. Y. Tsai and C. J. Chung, “The Study of Applying Interpretive Structural Modeling in Instructional Structural Design,” Educational Research & Information, Vol. 11, No. 2, 2003, pp. 1-40.

[33] T. W. Sheu, J. W. Tzeng, C. P. Tsai and T. L. Chen, “Applying Problem-Concept Chart Combined with Structural Analysis to Investigate the Learning Misconcept—Simple Equation with One Variable for Example,” Journal of Grey System, Vol. 15, No. 1, 2012, pp. 55-66.

[1] M. H. Chiu, “Reflections and Implications of Research on Conceptual Change,” Chinese Journal of Science Education, Vol. 8, No. 1, 2000, pp. 1-34.

[2] Ministry of Education, “Grade 1-9 Curriculum Guidelines,” Ministry of Education, Taipei, 2003.

[3] C. Y. Chen, “The Influence of Teaching Confrontation Style on Key Concepts of Elementary School Students,” Bulletin of Educational Psychology, Vol. 36, No. 4, 2005, pp. 375-393.

[4] D. C. Yang and S. M. Hung, “The Study of Remedial Instruction on Fraction,” Journal of Educational Research and Development, Vol. 4, No. 2, 2008, pp. 85-118.

[5] S. C. Wen, “A Study of Integrated Diagnostic Teaching on Fractions for Elementary Fifth-Grade Students,” Chinese Journal of Science Education, Vol. 19, No. 5, 2011, pp. 383-408.

[6] J. K. Lannin, D. D. Barker and B. E. Townsend, “How Students View the General Nature of Their Errors,” Educational Studies in Mathematics, Vol. 66, No. 1, 2007, pp. 43-59. doi:10.1007/s10649-006-9067-8

[7] C. C. Lee and S. C. Hu, “An On-Line Assessment and Misconception Correction Tool for Students Learning Fundamental Mathematics,” Journal of National Taichung University: Mathematics, Science & Technology, Vol. 23, No. 1, 2009, pp. 1-28.

[8] H. K. Tsai, C. C. Chen and H. P. Chang, “A Study of the Relationship between High School Students’ Force Diagrams and Equation Representations in Problem Solving,” Chinese Journal of Science Education, Vol. 18, No. 2, 2010, pp. 155-175.

[9] J. S. Yeh and C. H. Cheng, “Refining Rough Set for Applying Classification of Appendicitis,” The Journal of Taiwan Association for Medical Informatics, Vol. 14, No. 2, 2005, pp. 1-16.

[10] H. Wang, M. Zhou and Z. William, “A New Approach to Establish Variable Consistency Dominance—Based Rough Sets Based on Dominance Matrices,” 2012 International Conference on Intelligent System Design and Engineering Application, Sanya, 6-7 January 2012, pp. 48-51. doi:10.1109/ISdea.2012.636

[11] Y. Ren, T. Xing, Q. Quan and X. Chen, “Attributes Knowledge Reduction and Evaluation Decision of Logistics Centre Location Based on Rough Sets,” 2011 4th International Conference on Intelligent Computation Technology and Automation, Shenzhen, 28-29 March 2011, pp. 67-70. doi:10.1109/ICICTA.2011.24

[12] K. Zaras, J. C. Marin and B. Boudreau-Trude, “Dominance-Based Rough Set Approach in Selection of Portfolio of Sustainable Development Projects,” American Journal of Operations Research, Vol. 2, No. 4, 2012, pp. 502508. doi:10.4236/ajor.2012.24059

[13] G. Ke, L. Mingwu, F. Yong and Z. Xia, “A Hybrid Model of Rough Sets and Shannon Entropy for Building a Foreign Trade Forecasting System,” 2011 4th International Joint Conference on Computational Sciences and Optimization, Yunnan, 15-19 April 2011, pp. 7-11.

[14] C. J. Lai and K. L. Wen, “Application of Rough Set Approach to Credit Screening Evaluation,” Journal of Quantitative Management, Vol. 12, No. 1, 2005, pp. 69-78.

[15] D. Chao and P. Sulin, “The BSC Alarm Management System Based on Rough Set Theory in Mobile Communication,” 2011 7th International Conference on Computational Intelligence and Security, Hainan, 3-4 December 2011, pp. 1557-1561.

[16] A. N. Hossam, “A Probabilistic Rough Set Approach to Rule Discovery,” International Journal of Advanced Science and Technology, Vol. 30, 2011, pp. 25-34.

[17] Z. Qu and X. Wang, “Application of Clustering Algorithm and Rough Set in Distance Education,” 2009 1st International Workshop on Education Technology and Computer Science, Wuhan, 7-8 March 2009, pp. 489-493. doi:10.1109/ETCS.2009.117

[18] A. S. Salama and H. M. Abu-Donia, “Generalizations of Rough Functions in Topological Spaces by Using PreOpen Sets,” Journal of Intelligent Learning Systems and Applications, Vol. 4, No. 2, 2012, pp. 127-134. doi:10.4236/jilsa.2012.42012

[19] J. Shen, J. Wang and H. Ai, “An improved Artificial Immune Systembased Network Intrusion Detection by Using Rough Set,” Communications and Network, Vol. 4, No. 1, 2012, pp. 41-47. doi:10.4236/cn.2012.41006

[20] X. Zhang and W. Xu, “Rough Computational Approach to UAR Based on Dominance Matrix in IOIS,” Intelligent Information Management, Vol. 3, No. 4, 2011, pp. 131136. doi:10.4236/iim.2011.34016

[21] K. L. Wen, M. Nagai, T. C. Chang and H. C. Wang, “An Introduction to Rough Set Theory and Application,” Chuan Hwa Publishing Ltd., Taipei, 2008.

[22] Z. Pawlak, “Rough Sets,” International Journal of Computer and Information Sciences, Vol. 11, No. 5, 1982, pp. 341-356. doi:10.1007/BF01001956

[23] Z. Pawlak, “Drawing Conclusions from Data—The Rough Set Way,” International Journal of Intelligent Systems, Vol. 16, No. 1, 2001, pp. 3-11. doi:10.1002/1098-111X(200101)16:1<3::AID-INT2>3.0.CO;2-I

[24] Z. Pawlak, “Rough Set Theory and Its Applications,” Journal of Telecommunications and Information Technology, Vol. 3, 2002, pp. 7-10.

[25] Z. Pawlak, “Rough Sets and Intelligent Data Analysis,” Information Science, Vol. 147, No. 1-4, 2002, pp. 1-12. doi:10.1016/S0020-0255(02)00197-4

[26] Y. Y. Yao, “Probabilistic Approaches to Rough Sets,” Expert System, Vol. 20, No. 5,2003, pp. 287-297. doi:10.1111/1468-0394.00253

[27] Z. Pawlak, “Rough Sets, Decision Algorithms and Bayes’ Theorem,” European Journal of Operational Research, Vol. 136, No. 1, 2002, pp. 181-189. doi:10.1016/S0377-2217(01)00029-7

[28] Z. Pawlak, “Decision Algorithms and Flow Graphs; a Rough Set Approach,” Journal of Telecommunications and Information Technology, Vol. 3, 2002, pp. 98-101.

[29] J. N. Warfield, “Societal Systems Planning, Policy and Complexity,” John Wiley & Sons Inc., New York, 1976.

[30] J. N. Warfield, “Interpretive Structural Modeling (ISM) Group Planning & Problem Solving Methods in Engineering,” John Wiley & Sons Inc., New York, 1982.

[31] T. W. Sheu, T. L. Chen, J. W. Tzeng, C. P. Tsai and M. Nagai, “Analyzing the Structure of Factors Influencing of Learning Interest in Mathematics,” International Journal of Kansei Information, Vol. 3, No. 2, 2012, pp. 103-120.

[32] P. Y. Tsai and C. J. Chung, “The Study of Applying Interpretive Structural Modeling in Instructional Structural Design,” Educational Research & Information, Vol. 11, No. 2, 2003, pp. 1-40.

[33] T. W. Sheu, J. W. Tzeng, C. P. Tsai and T. L. Chen, “Applying Problem-Concept Chart Combined with Structural Analysis to Investigate the Learning Misconcept—Simple Equation with One Variable for Example,” Journal of Grey System, Vol. 15, No. 1, 2012, pp. 55-66.