Advertisement

Elements of Difficulty Level in Mathematics

  • Taku JiromaruEmail author
  • Tetsuo Kosaka
  • Tokuro Matsuo
Part of the Studies in Computational Intelligence book series (SCI, volume 569)

Abstract

It is important for each leader to know relationship of the reason why each learner mistakes the problem of Mathematics. But, it does not exist about previous research. Therefore, in this research, we collected answers of each learner for knowing element of difficulty level in Mathematics. And we identified 10 types. 10 types are “lack of understand(problem statement, Number & Symbol, Formula, Concept)”, “circumstances of learner (inside)”, “circumstances of learner (outside)”, “Miscalculation”, “Copy miss”, “Lack of logical thinking (Deduction)” and “Lack of logical thinking (Induction)”.

Keywords

Incorrect reason arithmetic mathematics classification difficulty 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baker: Item Response Theory: Parameter Estimation Technique. Marcel Dekker, United States (1992)Google Scholar
  2. 2.
    Barbu, C.O., Beal, R.C.: Effects of Linguistic Complexity and Math Difficulty on Word Problem Solving by English Learners. International Journal of Education 2(2), 1–19 (2010)CrossRefGoogle Scholar
  3. 3.
    Belton, V., Gear, T.: The legitimacy of rank reversal-A Comment. OMEGA the International Journal of Management Science 13(3), 14444 (1985)CrossRefGoogle Scholar
  4. 4.
    Chalmers, D.J.: The conscious mind: In search of a fundamental theory. Oxford University Press, Oxford (1996)zbMATHGoogle Scholar
  5. 5.
    Hirasihima, Y., Mori, T., Tani, T.: On the System of Numbers Considered from the Degree of Difficulty. Journal of JAPAN Society of Mathematical Education 37(10), 148–151 (1955)Google Scholar
  6. 6.
    Kohonen, T.: Self-Organizing Maps. Series in Information Sciences, pp. 1–521 (2000)Google Scholar
  7. 7.
    Maeda, M., Nishio, Y.: Research on Difficulty of Multiplication and Division Word Problems. Mathematics Education Research, 531–137 (2000)Google Scholar
  8. 8.
    Meece, J.L., Wigfield, A., Eccles, J.S.: Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. Journal of Educational Psychology 82(1), 60–70 (1990)CrossRefGoogle Scholar
  9. 9.
    Joslyn, C., Rocha, L.: Towards semiotic agent-based models of socio-technical organizations. In: Proc. AI, Simulation and Planning in High Autonomy Systems (AIS 2000), pp. 70–79 (2000)Google Scholar
  10. 10.
    Hill, H.C., Ball, D.L., Schilling, S.G.: Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education 39(4), 372–400 (2008)Google Scholar
  11. 11.
    Jiromaru, T., Matsuo, T.: OMES: Employment support system for high education. CIEC, Computer & Education 32, 71–76 (2012)Google Scholar
  12. 12.
    Mogi, K.: Generation and qualia in brain. In: Suzuki, H. (ed.) Emergent and Conception of Intelligence, pp. 25–40. Ohmsha (2006)Google Scholar
  13. 13.
    Penrose, R.: Emperor’s New Mind. Oxford University Press, Oxford (1989)Google Scholar
  14. 14.
    Raghubar, K., Cirino, P., Barnes, M., et al.: Journal of Learning Disabilities, 4356–4371 (2009)Google Scholar
  15. 15.
    Riley, N.S., Greeno, J.G.: Developmental Analysis of Understanding Language About Quantities and of Solving Problems. Cognition and Instruction 5(1), 49–101 (1988)CrossRefGoogle Scholar
  16. 16.
    Saaty, L.S.: How to Make a Decision: The Analytic Hierarchy Process. Interfaces 24(6), 19–43 (1994)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Searle, J.: The Chinese room revisited. Behavioral and Brain Sciences 5(2), 345–348 (1982)CrossRefGoogle Scholar
  18. 18.
    Shimizu, H., Ide, S.: Gaps in students’ learning in elementary mathematics classes. Journal of Japan Society of Mathematical Education 85(10), 11–18 (2003)Google Scholar
  19. 19.
    Shojima, K.: Neural Test Theory: A Test Theory for Standardizing Qualifying Tests. The Journal of Institute of Electronics Information and Communication Engineers 92(12), 1014016 (2009)Google Scholar
  20. 20.
    Soga, C., Miyake, S., Wada, C.: Differences in Physiological Responses Induced by Mental Tasks with Different Difficulty Levels. The Japanese Journal of Ergonomics 45(1), 29–35 (2009)CrossRefGoogle Scholar
  21. 21.
    Roberts, R.J., Varney, N.R., et al.: The neuropathology of everyday life: The frequency of partial seizure symptoms among normals. Neuropsychology 4(2), 65–85 (1990)CrossRefGoogle Scholar
  22. 22.
    Tsukihara, Y., Suzuki, K., Hirose, H.: A small implementation case of the mathematics tests with the item response theory evaluation into an e-learning system. CIEC, Computer & Education 24, 70–76 (2008)Google Scholar
  23. 23.
    Weaver, W.: Science and complexity. American Scientist 36, 536–544 (1948)Google Scholar
  24. 24.
    Yamagata University Faculty of Engineering, Past entry-exam data (2013), http://www2.yz.yamagata-u.ac.jp/admission/admissiondata.html (accessed April 24, 2014)
  25. 25.
    Yoshizawa, M.: Classification of Students’ Stumbles while Learning Mathematics. Journal of Japan Society of Mathematical Education 88(3), 228 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of EngineeringYamagata UniversityYamagataJapan
  2. 2.Advanced Institute of Industrial TechnologyTokyoJapan

Personalised recommendations