Development of GeoBlock: a micro-world for learning and teaching geometry

  • Kazuyoshi Hidaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 602)


GeoBlock is a micro-world software tool for learning and teaching geometry, and has been prototyped on personal computers. It was designed according to the concept of direct manipulation of geometric figures under geometric constraints. A block is constructed to correspond to each complicated figure that is under geometric constraints, and it can be changed, re-used, and observed interactively on the computer's display. From practical use in classrooms, we are convinced that GeoBlock is effective in two phases of geometry lessons. One is the phase of discovering rules among geometric webs that the students have not yet studied. The other is the phase of assimilating geometrical facts that they have already studied. GeoBlock shows one way in which a computer can help students to learn geometry, and can help teachers to give persuasive geometry lessons.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Hid90]
    K. Hidaka. A Tool for Learning Geometry, The Journal of Science Education in Japan, Vol. 14, No. 2, Japan Society for Science Education, 1990.Google Scholar
  2. [Sch89]
    J. L. Schwartz. Intellectual Mirrors: A Step in the Direction of Making Schools Knowledge-Making Places, Harvard Educational Review, Vol. 59, No. 1, pp. 51–61, Harvard College, 1989.Google Scholar
  3. [McC9l]
    L. P. McCoy. The Effect of Geometry Tool Software on High School Geometry Achievement, Journal of Computers in Mathematics and Science Teaching, Vol. 10(3), Spring 1991.Google Scholar
  4. [Cabri]
    Cabri-Geometre: An Interactive Notebook for Learning and Teaching Geometry, User's Manual for Version 2.0: Laboratoire de Structures Discretes et de Diadique: Institut D'Informatique et de Mathematiques Appliquees de Grenoble Universite Joseph Fourier-CNRS, 1988Google Scholar
  5. [Sut63]
    I. E. Sutherland. Sketchpad: A Man-Machine Graphical Communication System, Lincoln Laboratory Technical Report, No. 296, Massachusetts Institute of Technology, 1963.Google Scholar
  6. [Bor86]
    A. Borning. Graphically Defining New Building Blocks in ThingLab, Human-Computer Interaction, Vol. 2, pp. 269–295, New Jersey: Lawrence Erlbaum Associates, Inc., 1986.Google Scholar
  7. [Nel85]
    G. Nelson. Juno: A Constraint-Based Graphics System, SIGGRAPH Computer Graphics, Vol. 19, No. 3, pp. 235–243, 1985.Google Scholar
  8. [Lig80]
    R. A. Light. Symbolic Dimensioning in Computer-Aided Design, M.S. Thesis, Massachusetts Institute of Technology, 1980.Google Scholar
  9. [Lin-Gos81]
    V. C. Lin, D. C. Gossard, and R. A. Light. Vanational Geometry in Computer-Aided Design, Computer Graphics, Vol. 15, No. 3, pp. 171–177, 1981.Google Scholar
  10. [Arb-Win87]
    F. Arbab and J. M. Wing. Geometric Reasoning: A New Paradigm for Processing Geometric Information, Design Theory for CAD, International Federation for Information Processing, 1987.Google Scholar
  11. [Inu-Kim88]
    M. Inui and F. Kimura. Geometric Constraint Solving for Constructing Geometric Models, Proceedings of Graphics and CAD Symposium, pp. 181–190, Information Processing Society of Japan, 1988.Google Scholar
  12. [Zan-Mye90]
    B. V. Zanden and B: A. Myers. A Constraints Primer, Computer, pp. 74–75, November 1990.Google Scholar
  13. [Nak89]
    Y. Nakayama. Mathematical Formula Editor for CAI, Proceedings of ACM CHI'89, pp. 387–392, 1989.Google Scholar
  14. [Sas91]
    M. Sasaki. A Practical Use of a Computer in Mathematics Education, Tokyo Gakugei Journal of Mathematics Education, Vol. 3, pp. 87–97, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Kazuyoshi Hidaka
    • 1
  1. 1.Tokyo Research LaboratoryIBM JapanTokyoJapan

Personalised recommendations