HAL Id: hal-00190695
https://telearn.archives-ouvertes.fr/hal-00190695
Submitted on 23 Nov 2007
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Normalising Geometrical Constructions: A Context for the Generation of Meanings for Ratio and Proportion
Giorgos Psycharis, Chronis Kynigos
To cite this version:
Giorgos Psycharis, Chronis Kynigos. Normalising Geometrical Constructions: A Context for the
Generation of Meanings for Ratio and Proportion. Annual Meeting of the International Group for
the Psychology of Mathematics Education (PME 28) (28th, Bergen, Norway, July 14-18, 2004), 2004,
Bergen, Norway. pp.65-72. �hal-00190695�
NORMALISING GEOMETRICAL CONSTRUCTIONS:
A CONTEXT FOR THE GENERATION OF MEANINGS FOR RATIO AND PROPORTION
Abstract:This paper describes aspects of 13 year-olds’ activity in mathematics as emerged during the implementation of proportional geometric tasks in the classroom.
Pupils were working in pairs using a piece of software specially designed for multiple representation (symbolic and graphical) of the variation in parametric procedures with dynamic manipulation of variable. In this paper we discuss children’s use of normalising, an activity in which children ‘correct’ the geometrical figures while developing meanings for ratio and proportion. We discuss the potential of normalising for the construction of mathematical meanings in relation to particular aspects of the pedagogical setting including pupil’s interaction within the computational environment as well as task design.
THEORETICAL FRAMEWORK
normalizing
4–66 PME28 – 2004
as a process
during
RESEARCH SETTING AND TASKS
purposeful utility
The Dynamic Alphabet of your own class’
Fig. 1: Constructing ‘A’ with three variables
4–68 PME28 – 2004
METHOD
VISUAL MANIPULATION OF THE INTERDEPENDENCE OF VARIABLES
original pattern
GRAPHICAL AND NUMERIC CONTROL OF THE SIMILARITY RATIO
Fig. 2: Distortions of ‘A’ constructed with three variables.
4–70 PME28 – 2004
GRAPHICAL DISCONTINUITY OF THE COVARIANT MAGNITUDES
Fig. 3: Changing ‘A’ with one variable
DISCUSSION
4–72 PME28 – 2004
REFERENCES
Educational Studies in Mathematics
Proceedings ofthe 26thPME Conference
Ethnography and Qualitative Design in Educational Research
Constructionism: Research Reports and Essays
Proceedings ofthe 15thPME Conference
Children’s Understanding of Mathematics
Ratio:Children's Strategies and Errors
Journal of Mathematical Behavior
Proceedings ofthe 13thPME Conference
Proceedings of the 15th PME Conference,
Journal of Educational Computing Research,
27th PME Conference,
Cognition in Practice
Windows on Mathematical Meanings
Educational Studies in Mathematics,