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Zsolt Lavicza

Faculty of Education. A comparative study of the use of Computer Algebra Systems in teaching university mathematics in Hungary, UK, and US. Zsolt Lavicza. Outline. Rationale for the study Research questions Research design and data collection Some results from Phase-I

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Zsolt Lavicza

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

  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. 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. 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. 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. 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. Computer Algebra Systems

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

  10. External factors Personal Characteristics Mathematicians’ conceptions of Mathematics  CAS Mathematics T/L  CAS T/L Results: Phase-I • Emerging issues

  11. Personal characteristics • Two interesting conceptions: • CAS use in teaching correlates with mathematicians’ research area • CAS use in teaching correlates with mathematicians’ age

  12. International-level National-level University-level Departmental-level Course level External factors Cultural/Institutional – technology related

  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. Identifying relationships-develop models Personal characteristics - Institutional backgrounds Actual use of CAS in teaching Conceptions of CAS-assisted teaching

  15. Questionnaire design

  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

  17. Analysis • Data collection lasted longer than expected • Will begin analysis – many aspects • Basic Crosstabulations – regression • Factor Analyses • Structural Equation Modelling • Multilevel modelling (future)

  18. 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)

  19. Thank you! Questions? Comments? Project website: http://cus.cam.ac.uk/~zl221/CAS.htm

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