Zsolt Lavicza A comparative study of the use of Computer Algebra Systems in teaching university...

Zsolt Lavicza

A comparative study of the use of Computer Algebra Systems

in teaching university mathematics in Hungary, UK, and US

Zsolt LaviczaFaculty of Education

22 June, 2007 2Zsolt Lavicza

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


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)


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


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 )


Computer Algebra Systems

Mathematical softwarethat performs Visual Computational Symbolicoperations.

CAS may run on computer and hand-held devices.

Examples: Derive, Maple, Mathematica, MuPad, Matlab (included), etc.


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?


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


Phase I Phase IIUS

Personal Characteristics

MathematiciansConceptions

ActualCAS use

Culturalinfluences

UK



ActualCAS use

Culturalinfluences

HU



ActualCAS use

Culturalinfluences

Comparison within and among cases

Issues to Investigate

Qu

estio

nn

aire

US

UK

HUCharacterization

of CAS use at Universities

Research design


Results: Phase-I

Emerging issues


External factors

Mathematicians’ conceptions of

Mathematics CASMathematics T/L CAS T/L


Personal characteristics

Two interesting conceptions:

CAS use in teaching correlates with mathematicians’ research area

CAS use in teaching correlates with mathematicians’ age


External factors

Cultural/Institutional – technology related

Courselevel

Departmental-level

University-level

International-level

National-level


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


Identifying relationships-develop models

Personal characteristics - Institutional backgrounds

Conceptions of CAS-assisted teaching

Actual use of CAS in teaching


Questionnaire design


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


HUUKUS

Country

140

120

100

80

60

40

20

0

Co

un

t

128

4854

81

120

5759

136

45

114116

67

8596

65<

56-65

46-55

36-45

<35Age

Bar Chart


HUUKUS

Country

500

400

300

200

100

0

Co

un

t

5035

109

182

310

401

Female

MaleGender

Bar Chart


HUUKUS

Country

300

250

200

150

100

50

0

Co

un

t

Genral maths

No research

S-Social

S-Life

S-Physical

S-Computer

Engineering

Education

Statistics

Applied

PureResearch area

Bar Chart


HUUKUS

Country

200

150

100

50

0

Co

un

t

2130

3826

33

70

28

4854

3646

5944

75

117

77

114

173

Daily

2-3-weekly

1-weekly

1-monthly

<monthly

NeverCAS in research

Bar Chart


HUUKUS

Country

200

150

100

50

0

Co

un

t

6712 7417 1615

47

80

109

181

80

155

184

<75%

50-74%

26-49%

<25%

NeverCAS in Teaching

Bar Chart


Analysis

Data collection lasted longer than expected

Will begin analysis – many aspects Basic Crosstabulations – regression Factor Analyses Structural Equation Modelling Multilevel modelling (future)


Age * CAS in teaching grouped Crosstabulation

106 78 16 200

53.0% 39.0% 8.0% 100.0%

96 105 28 229

41.9% 45.9% 12.2% 100.0%

94 93 28 215

43.7% 43.3% 13.0% 100.0%

94 81 46 221

42.5% 36.7% 20.8% 100.0%

29 14 13 56

51.8% 25.0% 23.2% 100.0%

419 371 131 921

45.5% 40.3% 14.2% 100.0%

Count

% within Age

Count

% within Age

Count

% within Age

Count

% within Age

Count

% within Age

Count

% within Age

<35

36-45

46-55

56-65

65<

Age

Total

Never Ocasionally Frequently

CAS in teaching grouped

Total


Research area * CAS in teaching grouped Crosstabulation

236 164 38 438

53.9% 37.4% 8.7% 100.0%

82 121 57 260

31.5% 46.5% 21.9% 100.0%

24 12 5 41

58.5% 29.3% 12.2% 100.0%

29 39 26 94

30.9% 41.5% 27.7% 100.0%

9 7 2 18

50.0% 38.9% 11.1% 100.0%

10 8 0 18

55.6% 44.4% .0% 100.0%

7 8 1 16

43.8% 50.0% 6.3% 100.0%

7 3 0 10

70.0% 30.0% .0% 100.0%

4 1 1 6

66.7% 16.7% 16.7% 100.0%

7 5 0 12

58.3% 41.7% .0% 100.0%

4 4 1 9

44.4% 44.4% 11.1% 100.0%

419 372 131 922

45.4% 40.3% 14.2% 100.0%

Count

% within Research area

Count


Count


Count


Count


Count


Count


Count


Count


Count


Count


Count


Pure

Appl ied

Statistics

Education

Engineering

S-Computer

S-Physical

S-Life

S-Social

No research

Genral maths

Researcharea

Total

Never Ocasionally Frequently

CAS in teaching grouped

Total


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)


Thank you!Questions? Comments?

Project website:http://cus.cam.ac.uk/~zl221/CAS.htm

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Zsolt Lavicza A comparative study of the use of Computer Algebra Systems in teaching university...

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