Learning to prove by investigations: a promising approach in Dutch secondary education |
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| Authors: | Louis van Schalkwijk Theo Bergen Arnoud van Rooij |
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| Institution: | (1) Graduate school of education, Didactics of Mathematics, institute University of Nijmegen, Nijmegen, The Netherlands;(2) Graduate school of education, University of Nijmegen, Nijmegen, The Netherlands;(3) Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands |
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| Abstract: | The Mathematics Department of the University of Nijmegen in collaboration with the Graduate School of Education has developed
a math course in the field of fractals and dynamic processes for volunteer students in the second phase of secondary education
in the Netherlands. The students, of approximately 16 years of age, show a special interest in, and an aptitude for mathematics
and informatics. One of the main goals of the course was to highlight the deductive aspect of mathematics, an aspect that
is neglected in the ordinary math curriculum of secondary education in the Netherlands. That goal was pursued by giving the
students ample opportunity to conduct investigations on their own and in a way that they would be responsible for judging
the correctness of their arguments in making mathematical deductions. In that way proving is imbedded in a larger structure
and becomes a tool for the students to convince each other. During the courses we searched for the right way for teachers
to coach these investigations, that is: to find a balance between mere concentration on guiding the process of the students'
investigations and active intervention in the learning process of proving. In this article we illustrate with two examples
– the first from the '95–'96 course and the second from the '96–'97 course – in what way we adjusted our coaching. Our results
are explorative, but our approach appears promising and we are convinced that investigations as learning environment for proving
would also be a valuable part for the regular secondary math education in the Netherlands.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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