The idea of ‘interpretative flexibility’ underpins new approaches to studying technological artefacts and curricular
resources in use. This paper opens by reviewing – in this light – the evolving design of dynamic geometry, its pioneering
use within classroom projects, and early sketches of its mainstream use in ordinary classrooms. After examining curricular
context and its instrumental dimension, the paper then reports a study of teacher constructions of dynamic geometry in
classroom practice, conducted in professionally well-regarded mathematics departments in English secondary schools.
From departmental focus-group interviews, four teacher-nominated examples of successful practice were selected for study
in depth through lesson observation and post-lesson interview. Iterative thematic analysis was employed, first to establish a
narrative outline of each case, and then the ideas and issues salient across cases. The study illustrates the interpretative
flexibility surrounding the emergent use of dynamic geometry. It found important differences in practical elaboration of
the widespread idea of employing dynamic geometry to support guided discovery. The process of evaluating the costs and
benefits of student software use was influenced by the extent to which such use was seen as providing experience of a mathematical
reference model, and more fundamentally as promoting mathematically disciplined interaction. Approaches to handling
apparent mathematical anomalies of software operation depended on whether these were seen as providing
opportunities to develop students’ mathematical understanding, in line with a more fundamental pedagogical orientation
towards supporting learning through analysis of mathematical discrepancies. Such variation was associated with differences
in positioning dynamic geometry in relation to curricular norms and in privileging a mathematical register for framing figural
properties. Across all cases, however, incorporating dynamic manipulation into mathematical discourse moved implicitly
beyond established norms when dragging was used to focus attention on continuous dynamic variation, rather than being
treated as an efficient means of generating multiple static figures.
%0 Journal Article
%1 ruthven2008cdg
%A Ruthven, Kenneth
%A Deaney, Rosemary
%A Hennessy, Sara
%D 2008
%I Elsevier
%J Computers & Education
%K design education geometry imported interpretativeflexibility learning mathematics postviva
%N 1
%P 297-317
%T Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice
%U http://www.educ.cam.ac.uk/people/staff/ruthven/RuthvenCEpreprint.pdf
%V 51
%X The idea of ‘interpretative flexibility’ underpins new approaches to studying technological artefacts and curricular
resources in use. This paper opens by reviewing – in this light – the evolving design of dynamic geometry, its pioneering
use within classroom projects, and early sketches of its mainstream use in ordinary classrooms. After examining curricular
context and its instrumental dimension, the paper then reports a study of teacher constructions of dynamic geometry in
classroom practice, conducted in professionally well-regarded mathematics departments in English secondary schools.
From departmental focus-group interviews, four teacher-nominated examples of successful practice were selected for study
in depth through lesson observation and post-lesson interview. Iterative thematic analysis was employed, first to establish a
narrative outline of each case, and then the ideas and issues salient across cases. The study illustrates the interpretative
flexibility surrounding the emergent use of dynamic geometry. It found important differences in practical elaboration of
the widespread idea of employing dynamic geometry to support guided discovery. The process of evaluating the costs and
benefits of student software use was influenced by the extent to which such use was seen as providing experience of a mathematical
reference model, and more fundamentally as promoting mathematically disciplined interaction. Approaches to handling
apparent mathematical anomalies of software operation depended on whether these were seen as providing
opportunities to develop students’ mathematical understanding, in line with a more fundamental pedagogical orientation
towards supporting learning through analysis of mathematical discrepancies. Such variation was associated with differences
in positioning dynamic geometry in relation to curricular norms and in privileging a mathematical register for framing figural
properties. Across all cases, however, incorporating dynamic manipulation into mathematical discourse moved implicitly
beyond established norms when dragging was used to focus attention on continuous dynamic variation, rather than being
treated as an efficient means of generating multiple static figures.
@article{ruthven2008cdg,
abstract = {The idea of ‘interpretative flexibility’ underpins new approaches to studying technological artefacts and curricular
resources in use. This paper opens by reviewing – in this light – the evolving design of dynamic geometry, its pioneering
use within classroom projects, and early sketches of its mainstream use in ordinary classrooms. After examining curricular
context and its instrumental dimension, the paper then reports a study of teacher constructions of dynamic geometry in
classroom practice, conducted in professionally well-regarded mathematics departments in English secondary schools.
From departmental focus-group interviews, four teacher-nominated examples of successful practice were selected for study
in depth through lesson observation and post-lesson interview. Iterative thematic analysis was employed, first to establish a
narrative outline of each case, and then the ideas and issues salient across cases. The study illustrates the interpretative
flexibility surrounding the emergent use of dynamic geometry. It found important differences in practical elaboration of
the widespread idea of employing dynamic geometry to support guided discovery. The process of evaluating the costs and
benefits of student software use was influenced by the extent to which such use was seen as providing experience of a mathematical
reference model, and more fundamentally as promoting mathematically disciplined interaction. Approaches to handling
apparent mathematical anomalies of software operation depended on whether these were seen as providing
opportunities to develop students’ mathematical understanding, in line with a more fundamental pedagogical orientation
towards supporting learning through analysis of mathematical discrepancies. Such variation was associated with differences
in positioning dynamic geometry in relation to curricular norms and in privileging a mathematical register for framing figural
properties. Across all cases, however, incorporating dynamic manipulation into mathematical discourse moved implicitly
beyond established norms when dragging was used to focus attention on continuous dynamic variation, rather than being
treated as an efficient means of generating multiple static figures.},
added-at = {2009-05-28T13:36:32.000+0200},
author = {Ruthven, Kenneth and Deaney, Rosemary and Hennessy, Sara},
biburl = {https://www.bibsonomy.org/bibtex/2658e397d1faa66c45f2c0262b998b5e8/yish},
interhash = {b3ce518d12b5da93781cb5005dcff1dd},
intrahash = {658e397d1faa66c45f2c0262b998b5e8},
journal = {Computers & Education},
keywords = {design education geometry imported interpretativeflexibility learning mathematics postviva},
number = 1,
pages = {297-317},
publisher = {Elsevier},
timestamp = {2009-05-28T13:36:32.000+0200},
title = {Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice},
url = {http://www.educ.cam.ac.uk/people/staff/ruthven/RuthvenCEpreprint.pdf},
volume = 51,
year = 2008
}