Volume 13, Number 3

Digital Technologies in Mathematics Education: Selected Papers from ICTMT-7

Guest editors:
Keith Jones, University of Southampton, UK
Federica Olivero, University of Bristol, UK

Capturing the Real World in the Classroom
André Heck and Peter Uylings

Universiteit van Amsterdam, AMSTEL Institute, Kruislaan 404, 1098SM, Amsterdam, The Netherlands.
heck@science.uva.nl; uylings@science.uva.nl

Practical investigation tasks are part of the Dutch examination programme of senior secondary education. In mathematics and science, pupils are expected to develop a broad range of research skills, which includes connecting real world phenomena with the scientific world, understanding the problems at hand and asking the right questions, making a project plan, designing and carrying out an experiment, and collecting, representing, analysing, and interpreting information. Pupils need ICT tools that make such investigation tasks feasible and that enable them to work at an appropriate level. In this paper we report on a classroom experiment in which pupils in pre-vocational secondary education develop and practise research skills by carrying out a small investigation task using digital video technology. We also discuss how one can deal with three particular problems experienced in practice, viz., perspective distortion of images, the complexity of recording video clips, and the amount of time needed for collecting data.

Motion, Technology, Gestures in Interpreting Graphs
Ornella Robutti

Dipartimento di Matematica, Università di Torino, Italy
ornella.robutti@unito.it

This report is part of a long-term research on the construction of mathematical meanings through the interaction with various technologies. The research involved a set of teaching experiments based on body motion with sensors and calculators at different school levels, from kindergarten to secondary school. Here I refer to the one developed in a junior high school, involving 20 students of 8th grade (age 13). The focus is on the cognitive evolution of the students towards the construction of meaning for the performed motion, from a functional point of view. Particularly, the passage from a uniform to an accelerated motion is analysed. The data are interpreted within a semiotic-cultural approach, as stated by Radford (2003), by looking at the progression in the introduction of signs and the shared use of them.

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Interpreting Motion Graphs through Metaphorical Projection of Embodied Experience
Galit Botzer and Michal Yerushalmy

Faculty of Education, University of Haifa, Israel
botzer@construct.haifa.ac.il; michalyr@construct.haifa.ac.il

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and expanding, research on embodied cognition, we analyse both the gestures and the terms that the students use, and probe the cognitive processes that their actions and discourse reflect. In the experimental study, the students faced three main challenges: modelling 2D motion, understanding a rest situation, and dealing with instantaneous rest. We show how the students used the source-path-goal schema to meet these challenges, which we analyze in the context of the philosophical and psychological complexities of the conceptualisation of time. We conclude that the computerised representations that were available to students added to the visible path information that they had about time. This helped the students to conceptualise the physics of motion and to link these concepts to the mathematical properties of the graphs.

Patterns of Interactions as Affected by Graphing Software: Developing a Theoretical Framework
Marie Joubert Gibbs

Graduate School of Education, University of Bristol, UK
M.Gibbs@bris.ac.uk

This paper extends and develops theories of mathematical learning to provide a framework for the analysis of classroom video data of students working at a computer in a task aimed at increasing understanding of multiple representations of quadratic functions. Student interactions are coded using novel software tools in the process of analysis, and for the presentation of results. In combination with the theoretical framing these techniques provide a rigorous approach to the analysis of the data. The analysis traces the development of mathematical learning over the course of one lesson and highlights the importance of feedback in the process. Of particular importance is the role of the computer in providing this feedback.

What Do Students Do With Personal Technology and How Do We Know? How One Student Uses Her Graphical Calculator
Louise Sheryn

School of Education, University of Leeds, Leeds, LS2 9JT
louise.sheryn@ntlworld.com

Within this paper I report on aspects of a study aimed at not only discovering how and when students use a graphical calculator within an Advanced-Level (pre-University) Mathematics course, and what operations and calculations they perform with such calculators, but also the depth and type of learning that takes place when students use graphical calculators. To this end I collected various types of data: interviews; observations; student e-journals; key-stroke data from graphical calculators, and combinations of all four. The key-stroke data was collected using a piece of software called Key Recorder that runs in the background of a graphical calculator recording all the user’s key strokes. It is then possible to playback the data file to see what the user saw and determine how they used their graphical calculator. Within the paper I outline how I used the features of the Key Recorder software and provide an analysis of the data on one student’s activities with her graphical calculator, showing how this particular student’s use of her graphical calculator developed, and changed, over the course of a year.

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