Factors Influencing Senior Secondary Mathematics Students' Use of CAS Calculators
Author(s):
Tasos Barkatsas (presenting / submitting) Claudia Orellana
Conference:
ECER 2015
Network:
24. Mathematics Education Research
Format:
Paper

Session Information

24 SES 02, Students' Perspective

Paper Session

Time:
2015-09-08
15:15-16:45
Room:
659.Oktatóterem [C]
Chair:
Man Ching Esther Chan

Contribution

As we move deeper into the 21st century, the use of digital technologies have become such an integral part of the teaching and learning process they are now viewed more as necessities rather than luxuries. As discussed by Hall (2010), there are a variety of technologies now accessible for teaching and learning within the classroom domain including electronic whiteboards, computers, laptops and calculators. Apart from their increased availability, research in the field of education has also recognised the potential for mathematics learning to be transformed by the availability of digital technologies. While the use of technologies have presented many advantages, Drijvers, Doorman, Boon, Reed and Gravemeijer (2010) expressed concern that the integration of technology within mathematics has fallen behind the promising expectations of the past two decades. In Australia, implementation of calculators equipped with computer algebra system technology (CAS) has faced various obstacles, despite becoming an important aspect of the senior secondary mathematics curriculum in the state of Victoria (VCAA, 2013). Factors such as student attitudes, teacher perceptions, time restrictions and the technical skill required to use the CAS have made integration difficult, and as such these technologies continue to play “a marginal role in mathematics classrooms” (Goos & Bennison, 2008, p. 103).

In 2001, CAS calculators were introduced in the Victorian State of Australia's secondary schools as part of a pilot study which aimed to investigate the effects that the use of supercalculators would have on the senior mathematics curriculum. Since then, the senior mathematics curriculum developed a new subject – Mathematical Methods (CAS) – which emphasises the appropriate use of computer algebra system technology (CAS) to support and develop the teaching and learning of mathematics, and in related assessments. This technology is also expected to be used in the alternative subjects, Further Mathematics and Specialist Mathematics. 

CAS calculators are not only a useful technological resource to complete mathematical work, but their time-saving capabilities also allow for a shift in the focus for learning to more conceptual understanding rather than the mastery of algebraic manipulations. However, the advantages of CAS have been overshadowed by the polarised findings of educational research. While in some cases teachers and students have made use of CAS calculators successfully, others have encountered difficulties which have marginalised CAS use in the classroom. It is therefore important to examine the issue of implementation further with Hall (2010) proposing four essential questions in regards to the introduction of new technologies:

  • Is it being used?
  • How well is it being used?
  • What factors are affecting its use/nonuse?
  • What are the outcomes?

While Hall (2010) refined these questions with respect to the change required to implement new digital resources, the student and teacher perspective in relation to these questions is also valuable as they are ultimately the users of these new technological innovations. Without understanding the obstacles faced by each within the mathematics classroom, the benefits of using CAS calculators are essentially lost.

The data analysis reported in this paper is part of a broader study which aims to explore students’ use of CAS calculators in senior secondary mathematics and the possible factors which may influence their use. The purpose of the quantitative dimension of the study is to identify differences between the research instruments' (Mathematics and Technology Attitudes Scale - MTAS) variables and gender, school, grade, year level and years of CAS experience.   

Research questions:

  1. Do technology confidence and mathematics confidence influence how senior mathematics students engage with CAS calculators in mathematics?
  2. Are there any gender differences in senior mathematics students’ engagement with CAS calculators, technology confidence and mathematics confidence?

Method

The questionnaire used in this study is the Mathematics and Technology Attitudes Scale (MTAS) designed by Pierce, Stacey and Barkatsas (2007). The questionnaire consists of 20 items divided into five subscales measuring the affective variables technology confidence (TC), mathematics confidence (MC), affective engagement (AE), attitude to learning mathematics with technology (MT) and behavioural engagement (BE). Four statements are allocated to each subscale and for each statement students indicate their extent of agreement on a five-point scale ranging from strongly agree to strongly disagree, or from nearly always to hardly ever (for behavioural engagement). Additional items relating to gender, school, grade, year level, years of CAS use and frequency of CAS use were also added to the questionnaire. To analyse the MTAS responses, each participant’s overall score for each subscale was determined. This was achieved by adding together the scores for the four individual items in each subscale with values ranging from 5 (strongly agree/nearly always) to 1 (strongly disagree/hardly ever). Each participant can obtain a maximum score of 20 and a minimum score of 4 for each subscale. According to Pierce et al. (2007), subscale scores of 17 or above are considered to be high scores, indicating a positive response to the examined factor. Scores of 13-16 are considered to be moderately high, and scores of 12 of below are considered to be low scores indicating a neutral or negative attitude. The 367 participants came from six secondary schools across Victoria, Australia. Three were government schools (two co-educational and one all girls’), two were independent co-educational schools and one was a catholic co-educational school. The questionnaire was administered to mathematics students in Years 11 and 12 (final two years of secondary schooling) as these are the years in which the CAS calculator is used most extensively. The 20 items of the MTAS were subjected to a Principal Components Analysis (PCA). The PCA results revealed that the five resulting components (all with eigenvalues greater than 1) explained 66.5% of the variance with the first component (mathematics confidence) contributing to 30.37% and the second component (attitudes to learning mathematics with technology) contributing to 13.97%. Analysis of MTAS subscales Analysis of variance (ANOVA) techniques were also used to compare the means of each subscale against different variables (e.g. gender). In addition, post hoc analyses were also conducted to determine where the significant differences between each of the groups lie.

Expected Outcomes

Post hoc analyses determined the following results: • Boys achieve a higher average score on the technology confidence and mathematics confidence subscales compared to girls. • Significant differences between schools were evident for the mathematics confidence, affective engagement and attitude to learning mathematics with technology subscales. • Students with grades in the A Grade range (80-100%) score higher in the mathematics confidence, affective engagement and behavioural engagement subscales than students with grades in the B range (70-79%) or C range (60-69%). • Students in Year 12 score higher on the technology confidence subscale than students in Year 11. • Higher technology confidence scores were evident if a student had used CAS calculators for 2 or 3 years compared to a student who has used CAS calculators for only one year. Gender Differences There were statistically significant differences between male and female students in the technology confidence and mathematics confidence subscales. Males achieved a higher average score than females on both affective variables which is consistent with prior large-scale studies conducted by Pierce et al. (2007) and Barkatsas (2011). Year Level and Years of CAS experience Statistically significant differences were found in the technology confidence subscales for both Year Level and Years of CAS experience. Students in Year 12 scored higher, on average, for technology confidence than students in Year 11. Further, students who had used the CAS calculator for two or three years scored significantly higher, on average, for this subscale compared to students who had used this technology for only one year. It could be argued that the more time students have to familiarise themselves with the CAS calculator, the more confident they become with this technology.

References

Barkatsas, A. (2011). Learning Mathematics with Computer Algebra Systems (CAS): middle and senior secondary students’ achievement, CAS experience and gender differences. Mathematics and Technology: Fifteenth Asian Technology Conference in Mathematics Electronic Conference Proceedings (pp. 1-9). Blacksburg, VA: USA. pp. 1-9. Barkatsas, A., Kasimatis, K., & Gialamas, V. (2009). Learning secondary mathematics with technology: exploring the complex interrelationship between students’ attitudes, engagement, gender and achievement. Computers and Education, 52(2), 562-570. Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213-234. Goos, M., & Bennison, A. (2008). Surveying the technology landscape: teachers’ use of technology in secondary mathematics classrooms. Mathematics Education Research Journal, 20(3), 102-130. Hall, G. E., (2010). Technology’s Achilles heel: achieving high-quality implementation. Journal of Research on Technology in Education, 42(3), 231-253. Pierce, R., Stacey, K., & Barkatsas, A. (2007). A scale for monitoring students’ attitudes to learning mathematics with technology. Computers and Education, 48(2), 285-300. Victorian Curriculum and Assessment Authority. (2013). Mathematics: Victorian Certificate of Education study design. Retrieved from: http://www.vcaa.edu.au/vce/studies/ mathematics/mathsstd.pdf.

Author Information

Tasos Barkatsas (presenting / submitting)
RMIT University, Australia, Australia
Claudia Orellana
Monash University, Australia

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