Volume 13, Number 4

Embedding New Technologies in the Practice of Mathematics Education:  Selected papers from ICTMT-7

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

 

Embedding New Technologies in Complex Ongoing Practices of School Mathematics Education
Kenneth Ruthven

University of Cambridge, Faculty of Education, Cambridge CB2 8PQ, UK;
kr18@cam.ac.uk

This paper argues that better understanding of the educational integration of new technologies calls for broader account to be taken of the complex ongoing practices of school mathematics education.  To frame its concerns, the paper opens by drawing on key studies of the general place of technology in classroom practice and teacher thinking.  The focus then looks more specifically at mathematics teaching in secondary schools in England, drawing first on a study of practitioner ideas about the contribution of computer-based tools and resources, and thence on a study focusing on archetypal practice in using dynamic geometry software.  Findings from these studies are synthesised with others to develop a speculative activity-system model of technology integration in school practices.

Developing the 3DMath Dynamic Geometry Software: Theoretical Perspectives on Design
Constantinos Christou1, Marios Pittalis1, Nicholas Mousoulides1 and Keith Jones2

1Department of Education, University of Cyprus, P.O.Box 20537, 1678, Nicosia, Cyprus
2School of Education, University of Southampton, UK
edchrist@ucy.ac.cy; m.pittalis@ucy.ac.cy; n.mousoulides@ucy.ac.cy; d.k.jones@soton.ac.uk

Designing successful learning environments entails drawing on theoretical perspectives on learning while, at the same time, being cognisant of the affordances and constraints of the technology.  This paper reports on the development of a software environment called 3DMath, a dynamic three-dimensional geometry microworld aimed at enabling learners to construct, observe and manipulate geometrical figures in a 3D-like space.  During the development of 3DMath, the key elements of visualisation, including theoretical ideas of mental images, external representations, and the processes and abilities of visualisation, were taken into consideration.  The aim of this paper is to illustrate how the design of this particular software was informed by these elements of visualisation, as well as by theories related to the philosophical basis of mathematical knowledge and by semiotics.  The paper illustrates how the features of software can be designed to take account of relevant theoretical notions and to satisfy the characteristics of instructional techniques that are appropriate to theoretical perspectives on learning.

 

The Theory of Transactional Distance as a Framework for the Analysis of Computer Aided Teaching of Geometry
Ioannis Papadopoulos and Vassilios Dagdilelis.

University of Patras, 26500 Patras, Greece; University of Macedonia, 54006, Thessaloniki, Greece
ypapadop@otenet.gr; dagdil@uom.gr

In this paper, difficulties of students in the case of computer-mediated teaching of geometry in a traditional classroom are considered within the framework of ‘transactional distance’, a concept well known in distance education.  The main interest of this paper is to record and describe in detail the different forms of ‘distance’ during students’ efforts to cope with tasks concerning the calculation of the area of irregular shapes.

Uses of ICT by Preservice Teachers; Towards a Professional Instrumentation
Maha Abboud-Blanchard and Jean-Baptiste Lagrange

DIDIREM, Research Team in the Didactics of Mathematics, University Paris 7, France
maha.blanchard@math.jussieu.fr; jb.lagrange@reims.iufm.fr

In this paper, our focus is on 'young' mathematics teachers during their pre-service training because of the conditions that might enable them to develop professional uses of technology more easily than ‘older’ teachers.  By describing some aspects of teacher training in France, especially the distinction between level 1 (general) and level 2 (professional) competence in ICT, we explain our idea of ‘professional instrumentation of ICT'.  The question we then consider is what ‘instrumentation’ trainees can achieve in the year of training, a time that is also their first year of teaching.  Our empirical data comes from questionnaires and an analysis of trainees' professional dissertations.  Given that Level 1 competence, when more or less achieved by a trainee teacher, ensures a limited ‘instrumentation’ in the part of the trainee's activity outside the classroom (for example, in terms of lesson preparation), we found that, at the moment, a majority of trainees do not go much beyond this, and do not develop, a better ‘instrumentation’ that might help them to develop ‘instrumented’ activities related to classroom use of information and communications technology.

 

Learning Together: Student Teachers, Children and Graphics Calculators
Declan O Reilly

University of Sheffield, School of Educational Studies, 388 Glossop Road, Sheffield S10 2JA
d.oreilly@sheffield.ac.uk

This paper recounts the experiences of eighteen student teachers who used graphics calculators to teach mathematics in secondary schools.  As part of their formal assessment, they submitted twenty accounts, listing the problems and benefits they had encountered in the course of using this technology.  These accounts are analysed in terms of the triad: graphics calculators, children and teachers.  The limitations of these categories are acknowledged but it is argued that the process of attempting to identify problems and benefits at this grain size of analysis carries with it great potential for avoiding or minimising problems and for capitalising on the possible benefits. 

 

Development and Use of a Computer-Based Interactive Resource for Teaching and Learning Probability in Primary Classrooms
Maria Trigueros, Maria Dolores Lozano and Ana Elisa Lage

ILCE, Enciclomedia, México
trigue@itam.mx; mdolores@ilce.edu.mx; ana.lageramirez@asu.edu

Enciclomedia is a Mexican project for primary school teaching using computers in the classroom.  Within this project, and following an enactivist theoretical perspective and methodology, we have designed a computer-based package called Dados, which, together with teaching guides, is intended to support the teaching and learning of probability.  The purpose of this paper is to report on the development and use of both Dados and the teaching guides by teachers.  These resources were created after careful analysis of the content of the mandatory textbooks used in primary schools in Mexico and following ideas found in the research literature.  Results show that the use of the tools we have developed can help teachers in carrying out classroom activities that promote students’ learning of probability.

 

Why Teaching Business Mathematics with Technology Might Be Very Important In Today's Mathematics Education
Maryam Vulis and Margot Small

Department of Mathematics and Computer Science, Queensborough Community College, Bayside, NY 11364, USA
mlv88@earthlink.net; msmall@qcc.cuny.edu

Mathematicians in industry need to have skills in formulating, modeling, and solving problems from diverse and changing areas.  Our position, in this discussion paper, is that these attributes are also desirable for students on business courses and that, in this context, providing business problems for students to tackle using a spreadsheet can help to develop these sorts of skills.  Our invitation is to others to share their approaches to using technology in the teaching of financial mathematics.

 

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