Are Teachers Aware of Students’ Lack of Spontaneity in Diagram Use? Suggestions from a Mathematical Model-Based Analysis of Teachers’ Predictions

  • Yuri Uesaka
  • Emmanuel Manalo
  • Masanori Nakagawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7352)


Although many studies have shown that diagrams are effective tools for problem solving, research evidence shows that students do not always use diagrams effectively. One of the most serious problems is their lack of spontaneity in diagram use. However, no previous studies have examined whether teachers are adequately aware of this problem. In this investigation, data were gathered on students’ mathematics performance (including their spontaneous use of diagrams) and teachers’ predictions of the students’ performance. Using a mathematical model (Uesaka & Nakagawa, 2010) to analyze the data, it was found that the parameter representing the accuracy of teachers’ prediction was lower for their assessment of spontaneous diagram use compared to other mathematical tasks. This suggests that spontaneity in diagram use is an overlooked aspect in teachers’ view of student performance.


spontaneous diagram use math problem solving teachers’ awareness mathematical model based analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cheng, P.C.H.: Electrifying Diagrams for Learning: Principles for Complex Representational Systems. Cognitive Science 26, 685–736 (2002)MATHCrossRefGoogle Scholar
  2. 2.
    Uesaka, Y., Manalo, E., Ichikawa, S.: What Kinds of Perceptions and Daily Learning Behaviors Promote Students’ Use of Diagrams in Mathematics Problem Solving? Learning and Instruction 17, 322–335 (2007)CrossRefGoogle Scholar
  3. 3.
    Uesaka, Y., Suzuki, M., Kiyokawa, S., Seo, M., Ichikawa, S.: Using COMPASS (Componential Assessment) to Reveal Japanese Students’ Actual Competence in the Fundamentals of Mathematics: Is it True that “Students are Generally Fine with the Fundamentals, and that the Problems Exist Only in Applications”? (submitted)Google Scholar
  4. 4.
    Ichikawa, S., Haebara, T., Sugisawa, T., Seo, M., Kiyokawa, S., Inuzuka, M., Murayama, K., Uesaka, Y., Kobayashi, H., Shinogaya, K.: Development of COMPASS: Componential Assessment for Basic Competence and Study Skills in Mathematics. Cognitive Studies 16(3), 333–347 (2009)Google Scholar
  5. 5.
    Uesaka, Y., Nakagawa, M.: Development and Application of Mathematical Model Analyzing Teachers’ Accuracy of Predication of Students’ Performance: Proposing Empirical Methods Detecting Overlooked Competences and Learning Skills. In: Paper in Proceedings of the Annual Conference of the Japanese Cognitive Science Society, pp. 350–356 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yuri Uesaka
    • 1
  • Emmanuel Manalo
    • 2
  • Masanori Nakagawa
    • 3
  1. 1.Graduate School of EducationThe University of TokyoJapan
  2. 2.Faculty of Science and EngineeringWaseda UniversityTokyoJapan
  3. 3.Graduate School of Decision Science & TechnologyTokyo Institute of TechnologyTokyoJapan

Personalised recommendations