Figure 1: Theory of planned behaviour (TPB) (Ajzen, 2006)
| Australasian Journal of Educational Technology 2011, 27(1), 137-151. |
AJET 27 |
Why don't all maths teachers use dynamic geometry software in their classrooms?
Gerrit Stols
University of Pretoria
Jeanne Kriek
University of South Africa
In this exploratory study, we sought to examine the influence of mathematics teachers' beliefs on their intended and actual usage of dynamic mathematics software in their classrooms. The theory of planned behaviour (TPB), the technology acceptance model (TAM) and the innovation diffusion theory (IDT) were used to examine the influence of teachers' attitudes, subjective norms and perceived behavioural control on their intention to use dynamic mathematics software in their classrooms. The study adopted the co-relational research design, with both correlation statistics and regression analysis used to analyse the data. By using stepwise regression analysis, it was possible to identify the most important belief predictors and their weights for the different constructs. The results were verified by the use of partial least squares. This study found that beliefs about the perceived usefulness and beliefs about their level of technological proficiency are the most important predictors of teachers' intended and actual usage of the software. In this preliminary study the suggested simplified model sufficiently explains 15 (83.3%) of the 18 teachers adaption and use of dynamic mathematics software in their classrooms.
However, even if technology is available, it is rarely used for teaching mathematics (Vrasidas & Glass, 2005; Marcinkiewicz, 1994). The question is: if dynamic mathematics software is such a powerful teaching and learning tool, why don't all teachers use it in their classrooms?
Cuban (2001) warns that explaining teachers' behaviour in using or not using technology needs to go beyond popular explanations that tend to blame teachers. Research explains how and why individuals adopt new information technologies (Venkatesh, Morris, Davis & Davis, 2003), but it is not known what influences teachers to use technology in their classroom. This study focuses on the use of dynamic mathematics software by teachers in their mathematics classrooms. To understand teachers' use of technology in their classrooms, we need a better understanding of the beliefs that influence teachers to decide to use technology or not to use it. Hew and Brush (2007), Albion (2001), and Teo (2008) have identified teachers' attitudes and beliefs as barriers to using technology for instruction. Social influence which is about the beliefs of what other people believe also has a direct influence on intention to use technology (Debuse, Lawley & Shibl, 2008).
Problems can emerge when teachers' beliefs are ignored, because "beliefs and values that teachers hold drive many of the choices they make in the classroom" (Cuban, 2001, p. 169). Cuban (2001) argues that beliefs influence what and how teachers choose to teach and what innovations they endorse or reject. In addition, "teachers' beliefs and principles are contextually significant to the implementation of innovations" (Munby, 1984, p. 28). We therefore need a deeper understanding of the nature of beliefs that influence the behaviour of a teacher and how these beliefs are manifested. With this in mind, we introduced dynamic mathematics software (GeoGebra, Cabri, Geometer's Sketchpad) to mathematics teachers in a preliminary study to investigate whether they would use it in teaching mathematics, and which reasons may prevent them from implementing the program.
Together, these three factors will determine the behavioural intention, and hence in the end also the behaviour, given sufficient degree of actual control over the behaviour. Ajzen (1991) explains that behavioural beliefs (BB) are beliefs about the probable outcomes of behaviour and the corresponding judgements about these outcomes, while normative beliefs (NB) are about the expectations of other people and motivation to comply with their expectations.
Figure 1: Theory of planned behaviour (TPB) (Ajzen, 2006)
Control beliefs (CB) include beliefs about both internal and external factors that may facilitate or impede performance of behaviour. Internal factors include skills, abilities and emotions, while external factors include environmental factors such as beliefs about infrastructure, support staff and access to computers.
The TBP explains human behaviour in general settings. To elucidate and explain behavioural beliefs (BB) in the context of information technology, various models about the adoption of technology innovations were investigated. Information technology researchers have developed various models for studying the software utilisation choices of users; for example the technology acceptance model (TAM) and the theory of innovation diffusion (IDT). These models can also be used to clarify and explain behavioural beliefs in the context of the use of technology for instruction (Thang, Murugaiah, Lee, Hazita Azman, Tan & Lee, 2010).
Figure 2: Technology acceptance model (TAM)
This model ignores the role of normative beliefs (see the TRA), and replaces behavioural beliefs about the outcome with only two beliefs - perceived ease of use (PEOU) and perceived usefulness (PU) (see Figure 2). Although this model is much simpler than the TPB, it matches up quite favourably in the IT context (Venkatesh & Davis, 2000). Perceived usefulness is about the extent "to which a person believes that using the system will enhance his or her job performance", while perceived ease of use is about "a person's beliefs that using the specific technology will be free of effort" (Davis, 1989, p. 320). Several researchers have replicated Davis's research and found perceived usefulness to be a strong determinant of user intentions (Venkatesh & Davis, 2000, p. 186):
Numerous empirical studies have found that TAM consistently explains a substantial proportion of the variance (typically about 40%) in usage intentions and behavior... In 10 years, TAM has become well-established as a robust, powerful, and parsimonious model for predicting user acceptance.Sheppard, Hartwick and Warsaw (1988) found a correlation coefficient (r) of 0.54 between behaviour intention and actual use within the field of consumer behaviour. Currently TAM is a well-established model and is widely accepted among researchers in the field of IT.
The subjective norm (SN) in the TBP is "the person's perception that most people who are important to him think he should or should not perform the behaviour in question" (Fishbein & Ajzen 1975, p. 302). In a teaching context, the people who could influence teachers' normative beliefs are typically the principal, learners, parents, and colleagues.
Perceived behaviour control (PBC) is influenced by individuals' control beliefs. According to McCabe (2004, p. 503), control beliefs are a function of both external and internal control beliefs: "Thus intention to behave is a function of perceived internal control (i.e. confidence in skills and abilities) and behaviour is a function of external control (i.e. opportunity and resources available)". In the case of this study, the internal control beliefs are about the teachers' general technology proficiency (GTP), while the external control beliefs are about the availability of the IT infrastructure (ITI).
Combining the TPB, TAM and IDT results in a new model (see Figure 3) which will be referred to as the Combined Model and has the potential to improve our understanding of technology use by teachers in general, and also in their classroom for instruction. This Combined Model will be used as a framework for analysing the reflections.
Figure 3: The Combined Model
| N | Minimum | Maximum | Mean | Standard deviation | ||
| Behaviour intention | 20 | 1.67 | 7.00 | 5.5833 | 1.73332 | |
| Attitude | 22 | 5.00 | 7.00 | 6.5114 | 0.66134 | |
| Pedagogical compatibility | 23 | 4.00 | 7.00 | 5.8261 | 1.00689 | |
| Perceived ease of use | 23 | 3.29 | 6.43 | 4.3602 | 0.70496 | |
| Perceived usefulness | 22 | 4.86 | 7.00 | 6.3214 | 0.60799 | |
| Subjective norm | 23 | 4.50 | 7.00 | 6.1739 | 0.77765 | |
| Normative beliefs (colleagues) | 23 | 3.50 | 7.00 | 5.5833 | 1.00722 | |
| Normative beliefs (parents) | 23 | 2.50 | 7.00 | 4.9167 | 1.42697 | |
| Control beliefs | 21 | 2.90 | 6.90 | 5.1333 | 1.03795 | |
| General technology proficiency | 23 | 1.20 | 5.50 | 3.6435 | 1.17892 | |
| IT Infrastructure | 20 | 2.00 | 7.00 | 4.9333 | 1.94245 | |
The highly significant correlation of 0.902 between the perceived usefulness (PU) and perceived compatibility (PC) of using dynamic geometry software for teaching indicates that these teachers think about the usefulness of dynamic geometry software in terms of the pedagogical compatibility (see Table 2). Ertmer (2005, p. 36) argues that "if we truly hope to increase teachers' uses of technology, especially uses that increase student learning, we must consider how teachers' current classroom practices are rooted in, and mediated by, existing pedagogical beliefs". Zhao and Cziko (2001, p. 17) use the perceptual control theory (PCT) to explain this phenomenon in terms of a hierarchy: "Since technology use is at a lower level of the hierarchy than pedagogical beliefs and teaching approaches, and because lower level goals are easier to vary, it is no surprise that many teachers adopt technology without changing their pedagogy."
| A | |
| Perceived usefulness (PU) | 0.889(**) |
| Perceived ease of use (PEOU) | -0.137 |
| Pedagogical compatibility (PC) | 0.816(**) |
| Predictor | r | r square | F | Sig. | df |
| Perceived usefulness (PU) | 0.885 | 0.784 | 65.300 | 0.000 | 1 |
| Predictor | B | Std error | Beta | t | Sig. |
| Perceived usefulness (PU) | 0.972 | 0.120 | 0.885 | 8.081 | 0.000 |
From the regression analyses, however, it emerged that the most significant predictor of attitude towards the use of dynamic geometry software is its perceived usefulness (PU) (see Table 3). The implication is that the perceived compatibility (PC) does not directly determine the attitude but rather works through the perceived usefulness (PU) to influence the attitude. The perceived ease of use (PEOU) of dynamic geometry software had a negative but insignificant influence on the attitude towards its use.
Partial least squares were used to determine the reliability of the above results. The model effect loadings for prediction of PU, PEOU and PC on attitudes were 0.610, -0.128 and 0.621 respectively, with weights of 0.664, -0.086 and 0.608. It can be concluded that only beliefs about PU and PC influence attitudes and therefore this result is highly consistent with the results from the regression analyses and correlation statistics.
| SN | |
| NB (colleagues) | 0.363(*) |
| NB (parents) | 0.017 |
The correlation coefficient of 0.363 between subjective norm and normative beliefs (colleagues) is significant at the 0.10 level only.
| Predictor | r | r square | F | Sig. | df |
| Colleagues | 0.363 | 0.132 | 3.196 | 0.088 | 1 |
| Predictor | B | Std error | Beta | t | Sig. |
| Colleagues | 0.274 | 0.154 | 0.363 | 1.788 | 0.088 |
From Tables 4 and 5 it is clear that the expectations of the parents or colleagues did not have any significant impact on the subjective norm of these teachers. This non-significant impact was also confirmed by the factor analysis of partial least squares. This is understandable, because in a normal schooling context teachers have the authority to make their own decisions in the classroom. They act relatively independently within their classrooms and have considerable autonomy over their teaching activities (Hu, Clark & Ma, 2003). The pressure from peers or colleagues to use technology for instruction is therefore limited.
| PBC | |
| GTP | 0.754(**) |
| ITI | 0.498(*) |
| Predictor | r | r square | F | Sig. | df |
| GTP | 0.754 | 0.568 | 22.391 | 0.000 | 1 |
| Predictor | B | Std error | Beta | t | Sig. |
| GTP | 1.160 | 0.245 | 0.754 | 4.732 | 0.000 |
Both the general technology proficiency (GTP) of the teacher and the availability of IT infrastructure (ITI) relate to the perceived behavioural control (PBC). A strong positive, statistically significant correlation of 0.754 was found between perceived behavioural control (PBC) and the general technology proficiency (GTP) of the teachers. A weaker but significant correlation of 0.498 exists between perceived behavioural control (PBC) and the IT infrastructure (ITI). Table 7 shows that the general technology proficiency (GTP) of a teacher explains 56.8% of his or her perceived behavioural control (PBC).
The partial least squares model effect loadings for GTP and ITI on PBC were 0.647 and 0.530 respectively, with effect weights of 0.714 and 0.471. The regression and partial correlation results suggest that GTP and ITI mediate the effect of PBC.
| BI | |
| A | 0.551(*) |
| SN | 0.233 |
| PBC | 0.677(**) |
| Predictor | r | r square | F | Sig. | df |
| PBC | 0.671 | 0.451 | 13.942 | 0.002 | 1 |
| Predictor | B | Std error | Beta | t | Sig. |
| PBC | 0.597 | 0.160 | 0.671 | 3.734 | 0.002 |
The partial least squares model effect loadings for A, SN, and PBC on BI were 0.448, 0.214, and 0.502, with effect weights of 0.464, 0.206, and 0.577 respectively. The regression and partial correlation results suggest that A and PBC influence BI and that SN does not contribute to BI.
Three months after the workshop, we managed to contact 18 (82%) of the 22 teachers. From the questionnaire it was clear that 14 teachers indicated that they intended to use dynamic geometry software in their classrooms to develop concepts in the context of transformations, functions, or geometry (see Table 10). The four teachers with an average score of less than 4 on the Likert scale (for behavior intention) did not use dynamic geometry software in the end. Only 3 of the 14 teachers who had intended to use dynamic geometry software had not used it.
| Teaching style | Average score for behaviour intention | Actual use of dynamic geometry software |
| Traditional | 2.3 (no) | no |
| Constructivist | 2.7 (no) | no |
| Traditional | 2.7 (no) | no |
| Constructivist | 3.0 (no) | no |
| Constructivist | 4 0 (yes) | yes |
| Constructivist | 4.3 (yes) | yes |
| Constructivist | 6.0 (yes) | yes |
| Constructivist | 6.0 (yes) | yes |
| Traditional | 6.0 (yes) | no |
| Constructivist | 6.3 (yes) | yes |
| Constructivist | 6.3 (yes) | yes |
| Traditional | 6.7 (yes) | no |
| Traditional | 7.0 (yes) | no |
| Constructivist | 7.0 (yes) | yes |
| Constructivist | 7.0 (yes) | yes |
| Constructivist | 7.0 (yes) | yes |
| Constructivist | 7.0 (yes) | yes |
| Constructivist | 7.0 (yes) | yes |
These results suggest a simplification of the original model in Figure 1. From the regression and the correlation analyses, it emerged that these teachers based their decision on whether to use dynamic geometry software or not on their belief about the perceived usefulness of using dynamic geometry software in relation to their existing teaching practices (see Figure 4).
The suggested Simplified Model (see Figure 4) sufficiently explains the use of dynamic geometry software in 15 (83.3%) of the 18 teachers classrooms. The fact that 3 of the 14 teachers who intended to use dynamic geometry software did not use it was contradictory to the projection of the TBP. But according to Ertmer (2005), additional barriers related to teachers' pedagogical beliefs may be at work. In investigating possible reasons for why they did not in the end use dynamic geometry software in their classroom, we interviewed the teachers. In contrast with the other teachers' constructivist approach, these three teachers revealed a more traditional teaching style (see Table 10). This emerged from their responses to the question: "Describe the most effective way to teach mathematics".
Figure 4: Simplified model for dynamic software
(the dotted line indicates the Pearson correlation coefficient)
These teachers believe that the most effective way to teach mathematics is to "be patient, repeat, and drill", "explain, explore, and give lots of exercises", and "explain and drill". Unlike those of the other teachers who are using dynamic geometry software, these responses represent a more traditional approach, while the use of dynamic geometry software, in general, promotes a more constructivist approach. This suggests that a relationship exists between pedagogical beliefs and technological use. We repeat here the statement by Ertmer (2005), whose study confirmed the importance of these findings: "If we truly hope to increase teachers' uses of technology, especially uses that increase student learning, we must consider how teachers' current classroom practices are rooted in, and mediated by, existing pedagogical beliefs." We can therefore conclude that the teaching style of the three teachers who intended to use dynamic geometry software but did not use it was not compatible with the use of dynamic geometry software.
The second objective of the study was to determine the impact of teachers' attitudes, subjective norm, and perceived behaviour control on their intention of using dynamic geometry software in their classrooms to develop concepts in the context of transformations, functions, or geometry. Although this study found a positive significant correlation between attitudes and behaviour intention, only perceived behavioral control, in terms of general technology proficiency, signifcantly determines their behaviour intention.
Finally these teachers' actual behaviour is influenced by the perceived usefulness of the technology or its ability to make their life in the classroom easier. However, if teachers do not have the general technology proficiency to use it in the classroom, it will not be used. A way to improve teachers' use of dynamic geometry software in their classrooms is therefore, firstly, to ensure that the teachers possess general computer proficiency and, secondly, to let them experience the advantage of using the software. In line with our findings, Ertmer (2005) proposes that when considering ways to change teachers' practice, particularly regarding the use of technology, you have to take teachers' pedagogical beliefs into account. He proposes that you introduce teachers to the types of technology use that could support their immediate needs (Ertmer, 2005) in order to increase teachers' confidence in using technology.
These preliminary findings will be able to focus the attention of district officials on what aspects they will have to consider if they want teachers to use dynamic geometry software in their classrooms. This exploratory study yielded important preliminary data and will be used in the design of a full scale study. Further investigations should focus on how and for what purpose teachers used dynamic geometry software in their classrooms.
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| Authors: Dr Gerrit Stols Department of Science, Mathematics and Technology Education, Faculty of Education (Groenkloof Campus) University of Pretoria, Pretoria, South Africa Email: gerrit.stols@up.ac.za Professor Jeanne Kriek Institute for Science and Technology Education University of South Africa, Pretoria, South Africa Email: kriekj@unisa.ac.za Please cite as: Stols, G. & Kriek, J. (2011). Why don't all maths teachers use dynamic geometry software in their classrooms? Australasian Journal of Educational Technology, 27(1), 137-151. http://www.ascilite.org.au/ajet/ajet27/stols.html |