Investigating problem-based learning in Saudi Arabian mathematics education: a TIMSS-related study

The aim of this study is to investigate the effectiveness of problem-based learning (PBL) on students’ mathematical performance. This includes mathematics achievement and students’ attitudes towards mathematics for third and eighth grade students in Saudi Arabia. Mathematics achievement includes, knowing, applying, and reasoning domains, while students’ attitudes towards mathematics covers, ‘Like learning mathematics’, ‘value mathematics’, and ‘a confidence to learn mathematics’. This study goes deeper to examine the interaction of a PBL teaching strategy, with trained face-to-face and self-directed learning teachers, on students’ performance (mathematics achievement and attitudes towards mathematics). It also examines the interaction between different ability levels of students (high and low levels) with a PBL teaching strategy (with trained face-to-face or self-directed learning teachers) on students’ performance. It draws upon findings and techniques of the TIMSS international benchmarking studies. Mixed methods are used to analyse the quasi-experimental study data. One -way ANOVA, Mixed ANOVA, and paired t-tests models are used to analyse quantitative data, while a semi-structured interview with teachers, and author’s observations are used to enrich understanding of PBL and mathematical performance. The findings show that the PBL teaching strategy significantly improves students’ knowledge application, and is better than the traditional teaching methods among third grade students. This improvement, however, occurred only with the trained face-to-face teacher’s group. Furthermore, there is robust evidence that using a PBL teaching strategy could raise significantly students’ liking of learning mathematics, and confidence to learn mathematics, more than traditional teaching methods among third grade students. Howe ver, there was no evidence that PBL could improve students’ performance (mathematics achievement and attitudes towards mathematics), more than traditional teaching methods, among eighth grade students. In 8th grade, the findings for low achieving students show significant improvement compared to high achieving students, whether PBL is applied or not. However, for 3th grade students, no significant difference in mathematical achievement between high and low achieving students was found. The results were not expected for high achieving students and this is also discussed. The implications of these findings for mathematics education in Saudi Arabia are considered.

Simulation tools for the analysis of single electronic systems

Developments in theory and experiment have raised the prospect of an electronic technology based on the discrete nature of electron tunnelling through a potential barrier. This thesis deals with novel design and analysis tools developed to study such systems. Possible devices include those constructed from ultrasmall normal tunnelling junctions. These exhibit charging effects including the Coulomb blockade and correlated electron tunnelling. They allow transistor-like control of the transfer of single carriers, and present the prospect of digital systems operating at the information theoretic limit. As such, they are often referred to as single electronic devices. Single electronic devices exhibit self quantising logic and good structural tolerance. Their speed, immunity to thermal noise, and operating voltage all scale beneficially with junction capacitance. For ultrasmall junctions the possibility of room temperature operation at sub picosecond timescales seems feasible. However, they are sensitive to external charge; whether from trapping-detrapping events, externally gated potentials, or system cross-talk. Quantum effects such as charge macroscopic quantum tunnelling may degrade performance. Finally, any practical system will be complex and spatially extended (amplifying the above problems), and prone to fabrication imperfection. This summarises why new design and analysis tools are required. Simulation tools are developed, concentrating on the basic building blocks of single electronic systems; the tunnelling junction array and gated turnstile device. Three main points are considered: the best method of estimating capacitance values from physical system geometry; the mathematical model which should represent electron tunnelling based on this data; application of this model to the investigation of single electronic systems. (DXN004909)