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.

Mid-infrared photonic sensors based on metamaterial structures

In this work three different metallic metamaterials (MMs) structures such as asymmetric split ring resonators (A-SRRs), dipole and split H-shaped (ASHs) structures that support plasmonic resonances have been developed. The aim of the work involves the optimization of photonic sensor based on plasmonic resonances and surface enhanced infrared absorption (SEIRA) from the MM structures. The MMs structures were designed to tune their plasmonic resonance peaks in the mid-infrared region. The plasmonic resonance peaks produced are highly dependent on the structural dimension and polarisation of the electromagnetic (EM) source. The ASH structure particularly has the ability to produce the plasmonic resonance peak with dual polarisation of the EM source. The double resonance peaks produced due to the asymmetric nature of the structures were optimized by varying the fundamental parameters of the design. These peaks occur due to hybridization of the individual elements of the MMs structure. The presence of a dip known as a trapped mode in between the double plasmonic peaks helps to narrow the resonances. A periodicity greater than twice the length and diameter of the metallic structure was applied to produce narrow resonances for the designed MMs. A nanoscale gap in each structure that broadens the trapped mode to narrow the plasmonic resonances was also used. A thickness of 100 nm gold was used to experimentally produce a high quality factor of 18 in the mid-infrared region. The optimised plasmonic resonance peaks was used for detection of an analyte, 17β-estradiol. 17β-estradiol is mostly responsible for the development of human sex organs and can be found naturally in the environment through human excreta. SEIRA was the method applied to the analysis of the analyte. The work is important in the monitoring of human biology and in water treatment. Applying this method to the developed nano-engineered structures, enhancement factors of 10^5 and a sensitivity of 2791 nm/RIU was obtained. With this high sensitivity a figure of merit (FOM) of 9 was also achieved from the sensors. The experiments were verified using numerical simulations where the vibrational resonances of the C-H stretch from 17β-estradiol were modelled. Lastly, A-SRRs and ASH on waveguides were also designed and evaluated. These patterns are to be use as basis for future work.