Micro-Level Automatic Assessment Supported by Digital Technologies

  • Chris Sangwin
  • Claire Cazes
  • Arthur Lee
  • Ka Lok Wong
Chapter
Part of the New ICMI Study Series book series (NISS, volume 13)

Abstract

This paper describes computer aided assessment of mathematics by focusing on the micro-level of automatically assessing students' answers. This is the moment at which a judgment takes place and so it forms the keystone the mathematical assessment process, so fundamental to the learning cycle. We describe the principle of automatic assessment at this micro-level and report some of the significant technical developments of the last two decades through examples of internet based systems.

Keywords

Assessment Computer aided assessment Task design Technology 

References

  1. Abboud-Blanchard, M., Cazes, C., & Vandebrouck, F. (2007). Teachers' activity in exercises-based lessons. Some case studies, Proceedings of Conference of European society of Research in Mathematics Education (CERME 5), Larnaca, Chypre. Février 2007.Google Scholar
  2. Black, P., & Wiliam, D. (1998a). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139–148.Google Scholar
  3. Black, P., & Wiliam, D. (1998b). Assessment and classroom learning. Assessment in Education, 5(1), 7–74CrossRefGoogle Scholar
  4. Cazes, C., Gueudet, G., Hersant, M., & Vandebrouck, F. (2006). ‘Using E-exercise bases in mathematics: case studies at university’. International Journal of Computers for Mathematical Learning, 11(3), 327–350.CrossRefGoogle Scholar
  5. Churchhouse, R. F.,. (1986). The Influence of Computers and Informatics on Mathematics and its Teaching. Cambridge: Cambridge University Press.Google Scholar
  6. Dahlberg, R. P., & Housman, R. P. (1997). Facilitating learning events through example generation, Educational Studies in Mathematics, 33, 283–299.CrossRefGoogle Scholar
  7. Gibbs, G., & Simpson, C. (2004). Conditions under which assessment supports students' learning. Learning and Teaching in Higher Education, 1(1), 3–32.Google Scholar
  8. Gill, M., & Greenhow, M. (2007). Computer-Aided Assessment in Mechanics: question design and test evaluation. Teaching Mathematics and its Applications, 26, 124–133.CrossRefGoogle Scholar
  9. Gray, E. M., & Tall, D. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26(2), 115–141.Google Scholar
  10. IPC (2005). International Program Committee ICMI Study 17. Digital technologies and mathematics teaching and learning: rethinking the terrain (“technology revisited”). Discussion Document for the Seventeenth ICMI Study. L'Enseignement Mathématique, 51, 351–363.Google Scholar
  11. Klai, S., Kolokolnikov, T., & Van den Bergh, N. (2000). Using Maple and the web to grade mathematics tests. In Proceedings of the International Workshop on Advanced Learning Technologies , Palmerston North, New Zealand, 4–6 December.Google Scholar
  12. Lee, A. M. S., Wong, K. L., & Leung, A. Y. L. (2006). Developing learning and assessment tasks in a dynamic geometry environment. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction (pp. 334–341). Hanoi Institute of Technology and Didirem Université Paris 7.Google Scholar
  13. Michener, E. R., (1978). Understanding understanding mathematics. Cognitive Science, 2, 361–381.CrossRefGoogle Scholar
  14. Nicaud, J. F., Bouhineau, D., & Chaachoua, H. (2004). Mixing microworlds and CAS features in building computer systems that help students learn algebra. International Journal of Computers for Mathematical Learning, 9(2), 169–211.CrossRefGoogle Scholar
  15. Ramsden, P., & Sangwin, C. J. (2007). Linear syntax for communicating elementary mathematics. Journal of Symbolic Computation, 42(9), 902–934.Google Scholar
  16. Ruthven, K., & Hennessy, S. (2002). A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning. Educational Studies in Mathematics, 49(2–3), 47–86.CrossRefGoogle Scholar
  17. Sangwin, C. J. (2005). On building polynomials. The Mathematical Gazette, 89(516), 441–451.Google Scholar
  18. Sangwin, C. J., & Grove, M. J. (2006). STACK: addressing the needs of the “neglected learners”. In Proceedings of the WebAlt Conference, Eindhoven.Google Scholar
  19. Vandebrouck, F., & Cazes, C. (2005). Analyse de fichiers de traces d'étudiants: aspects didactiques. Revue STICEF, 12, ISSN:1764-7223.Google Scholar
  20. Watson, A., & Mason, J. (2002). Student-generated examples in the learning of mathematics. Canadian Journal for Science, Mathematics and Technology Education, 2(2), 237–249.CrossRefGoogle Scholar
  21. Watson, A., & Mason, J. (2005). Mathematics as a Constructive Activity: Learners Generating Examples. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.Google Scholar
  22. Wiliam, D., & Black, P. J. (1996). Meanings and consequences: a basis for distinguishing formative and summative functions of assessment? British Educational Research Journal, 22(5), 537–548.CrossRefGoogle Scholar
  23. Xiao G. (2000). Interactive Mathematics Server Journal of online Mathematics and its Applications. http://www.jama.org/articles/xiao/xiaotop/html.

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Chris Sangwin
    • 1
  • Claire Cazes
    • 2
  • Arthur Lee
    • 3
  • Ka Lok Wong
    • 3
  1. 1.School of MathematicsUniversity of BirminghamBirminghamUK
  2. 2.Pierre and Marie Curie (UPMC)University Paris VIParisFrance
  3. 3.The University of Hong KongHong KongHong Kong

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