1. Zsolt Lavicza A comparative study of the use of Computer Algebra Systems in teaching university mathematics in Hungary, UK, and US Zsolt Lavicza Faculty of Education

2. Zsolt Lavicza 22 June, 2007 2 Outline  Rationale for the study  Research questions  Research design and data collection  Some results from Phase-I  Data collection in Phase-II  Preliminary results from Phase-II

3. Zsolt Lavicza 22 June, 2007 3 The slow integration of technology  Explosion of technology use in schools was predicted in the 1980s (Steen, 1998; Kaput, 1992)  At the school level the predicted explosion has not taken place (Cuban, Kilpatrick, & Peck, 2001; Ruthven & Hennessy, 2002)  Several studies attempted to find the reasons behind the slow integration of technology (Becker et. al, 2001; Ruthven & Hennessy, 2002)

4. Zsolt Lavicza 22 June, 2007 4 University-level research  Little attention paid to university teaching  Especially on mathematicians’ thinking and practices  Increasingly important domain of research  Student enrollment is rapidly increasing  Students’ mathematical preparedness is declining  Failing traditional teaching practices  Emergence of new technologies

5. Zsolt Lavicza 22 June, 2007 5 Importance of teachers’ conceptions  Recent (school-level) studies have begun focusing on teachers  Technology integration is greatly influenced by teachers’ conceptions, beliefs, attitudes, and motivations  (of mathematics, mathematics teaching, and technology)  And social and cultural factors (Hennessy et. al, 2005 )

6. Zsolt Lavicza 22 June, 2007 6 Computer Algebra Systems Mathematical software that performs  Visual  Computational  Symbolic operations. CAS may run on computer and hand-held devices. Examples: Derive, Maple, Mathematica, MuPad, Matlab (included), etc.

7. Zsolt Lavicza 22 June, 2007 7 Research questions  Extent – current use  To what extent and manner are Computer Algebra Systems currently used in university mathematics departments?  Mathematicians’ conceptions  What mathematical and pedagogic beliefs and conceptions mathematicians hold with regard to CAS including factors influencing their professional use of CAS? Vision?  Influence of teaching traditions  To what extent nationally situated teaching traditions, frequently based on unarticulated assumptions, influence mathematicians’ conceptions of and motivation for using CAS?

8. Zsolt Lavicza 22 June, 2007 8 Research design Mixed-method approach (Johnson & Onwuegbuzie, 2004)  Phase I. – Qualitative – Grounded Theory approach  Semi-structured Interviews (22 mathematicians)  Class observations  Collection of course materials  Data collection sites at (8) universities in  Hungary  United Kingdom  United States  Phase II. – Quantitative – Large-scale survey study  Web-based questionnaires has been sent to 4500 mathematicians in Hungary, UK, US  Received 25% response rate

9. Zsolt Lavicza 22 June, 2007 9 Phase I Phase II US Personal Characteristics Mathematicians Conceptions Actual CAS use Cultural influences UK Personal Characteristics Mathematicians Conceptions Actual CAS use Cultural influences HU Personal Characteristics Mathematicians Conceptions Actual CAS use Cultural influences Comparison within and among cases Issues to Investigate Questionnaire US UK HU Characterization of CAS use at Universities Research design

10. Zsolt Lavicza 22 June, 2007 10 Results: Phase-I  Emerging issues Personal Characteristics External factors Mathematicians’ conceptions of Mathematics  CAS Mathematics T/L  CAS T/L

11. Zsolt Lavicza 22 June, 2007 11 Personal characteristics  Two interesting conceptions:  CAS use in teaching correlates with mathematicians’ research area  CAS use in teaching correlates with mathematicians’ age

12. Zsolt Lavicza 22 June, 2007 12 External factors Cultural/Institutional – technology related Course level Departmental-level University-level International-level National-level

13. Zsolt Lavicza 22 June, 2007 13 Development of the questionnaire  Incorporate findings from Phase I  Relate concepts to literature  Mathematicians’ conceptions  decide what aspects of conceptions to investigate Response rate worries  Keep the questionnaire relatively short  Develop closed questionnaire items  Difficult to obtain responses for open items  Obtain adequate information from closed items

14. Zsolt Lavicza 22 June, 2007 14 Identifying relationships-develop models Personal characteristics - Institutional backgrounds Conceptions of CAS-assisted teaching Actual use of CAS in teaching

15. Zsolt Lavicza 22 June, 2007 15 Questionnaire design

16. Zsolt Lavicza 22 June, 2007 16 Received data Sent out  4500 questionnaires  One set of reminder  Responded to lots of e-mails Received  1104 filled questionnaires  Around 600 e-mails  150 pages written responses  Very positive feedback Follow up  Thank you notes  Research reports  297 volunteers for future studies

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22. Zsolt Lavicza 22 June, 2007 22 Analysis  Data collection lasted longer than expected  Will begin analysis – many aspects  Basic Crosstabulations – regression  Factor Analyses  Structural Equation Modelling  Multilevel modelling (future)

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25. Zsolt Lavicza 22 June, 2007 25 Results, potentials, future plans  Examine what is the current state of CAS use in universities  Identify issues influencing CAS integration  Mathematicians vision of CAS integration  Develop diagnostic instrument for technology integration  Identify people and institutions  Close examination of particular departments (successful, transition, no-CAS)  Focus on transition issues (secondary to university)

26. Zsolt Lavicza 22 June, 2007 26 Thank you! Questions? Comments? Project website: http://cus.cam.ac.uk/~zl221/CAS.htm