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Mathematical Modelling of Self-Heating in Compost Piles

Rebecca Hudson (2012)

Supervisors: Anne Porter and Mark Nelson


This thesis investigated the barriers faced by teachers which prevent them from using technology in the classroom. To this end teachers at 26 public secondary schools in New South Wales, Australia, were surveyed. These secondary schools were located in all areas of New South Wales. One hundred and fourteen secondary mathematics teachers of the New South Wales Department of Education and Training responded to the survey regarding their use or non use of technology in teaching.

A 'mixed-method' methodology was used which combined both qualitative and quantitative methods. The quantitative method used was statistical modelling. In particular, logistic and linear regressions were used that combined simple modeling with mediational analyses. This analysis was supplemented with results from two further studies using interview techniques. The quantitative analysis revealed two statistically significant predictors of computer use. The probability of using computers in the classroom was maximised when teachers had training in Excel and strongly disagreed with the statement that the lack of lesson plans using computers in mathematics were a barrier to computer use. Mediators were analysed to discover if they impacted on computer use.

Four major issues were investigated in the quantitative study: barriers to technology use, the beliefs mathematics teachers hold regarding the use of technology in mathematics teaching, the professional development in computer technology undergone by the teachers and the need for ongoing support using technology in teaching mathematics. It was found that the methodology used to investigate the barriers faced by mathematics teachers was important. Barriers ranked highly by teachers were found to not necessarily predict their computer use. However, logistic regression analysis of ten items found that their attitudes toward the "lack of lesson plans using computers in mathematics" to be statistically significant ( χ2=6.43, df=1, p=0.020) in predicting computer use.

Logistic regression analysis was also used to examine teachers' beliefs regarding the nature of mathematics and the nature of mathematics teaching and learning both with or without computer use. Four of the sixteen beliefs analysed were found to be statistically significant (χ2=31.60, df=4, p<0.0005) predictors of computer use. These beliefs were: mathematics is made up of individual components that incorporate the study and application of number, algebra, geometry, calculus, collection of data and graphs (p=0.009); mathematics is a way of life and a way of thinking (p=0.032) when teachers use computers in the classroom, they are able to spend more time on concepts rather than routine computational skills (p=0.002); and the use of computer technology provides access to huge amount of mathematics resources (p=0.027).

An examination of professional development received by mathematics teachers showed that training on Excel predicted computer use (p<0.0005). The need for teachers to have ongoing support for integrating technology into teaching mathematics, and how this need related to their decision to either use or not to use computers in the classroom, was examined. It was found to be a significant predictor of computer use in the classroom (χ2=3.91, df=2, p=0.042).

The second and third studies were undertaken as a means of triangulating the research by deepening the exploration of why and how teachers teach with or without the use of technology. An 'interview research technique' was employed. The interviewees consisted of prospective teachers, new teachers, retired teachers and current teachers in the workforce. These studies revealed that both experienced and inexperienced teachers used technology in their teaching only when it was appropriate.

The main conclusion drawn from this thesis is that the modelling of computer use in the classroom gives different results to the common methodology of simply listing barriers. The final model for predicting computer use identified three significant factors: ongoing support, had training on Excel and teachers' beliefs regarding the lack of lesson plans using computers in mathematics (χ2=27.71, df=3, p<0.0005)). One interpretation of these results is that teachers who are likely to have the 'intent' to use computers in the classroom are those teachers who 'Had training in the use of Excel'. Another interpretation is that teachers who used computers disagree that the lack of lesson plans is a barrier to computer use. Training on Excel, which was significant in both approaches, is an indication of 'behavioural intention'. Teachers who undertook training in the most commonly used software tool in mathematics appear to be 'intent' on using the tool in the mathematics classroom.

Rebecca Hudson on her graduation day,
                            University of Wollongong campus.
              12th December 2012.
Photograph by Nick Hartgerink.

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Page Created: 20th December 2012.
Last Updated: 1st March 2013.