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.

Supporting self-management: development and evaluation of a digital resource for adults with asthma

The problem: Around 300 million people worldwide have asthma and prevalence is increasing. Support for optimal self-management can be effective in improving a range of outcomes and is cost effective, but is underutilised as a treatment strategy. Supporting optimum self-management using digital technology shows promise, but how best to do this is not clear. Aim: The purpose of this project was to explore the potential role of a digital intervention in promoting optimum self-management in adults with asthma. Methods: Following the MRC Guidance on the Development and Evaluation of Complex Interventions which advocates using theory, evidence, user testing and appropriate modelling and piloting, this project had 3 phases. Phase 1: Examination of the literature to inform phases 2 and 3, using systematic review methods and focussed literature searching. Phase 2: Developing the Living Well with Asthma website. A prototype (paper-based) version of the website was developed iteratively with input from a multidisciplinary expert panel, empirical evidence from the literature (from phase 1), and potential end users via focus groups (adults with asthma and practice nurses). Implementation and behaviour change theories informed this process. The paper-based designs were converted to the website through an iterative user centred process (think aloud studies with adults with asthma). Participants considered contents, layout, and navigation. Development was agile using feedback from the think aloud sessions immediately to inform design and subsequent think aloud sessions. Phase 3: A pilot randomised controlled trial over 12 weeks to evaluate the feasibility of a Phase 3 trial of Living Well with Asthma to support self-management. Primary outcomes were 1) recruitment & retention; 2) website use; 3) Asthma Control Questionnaire (ACQ) score change from baseline; 4) Mini Asthma Quality of Life (AQLQ) score change from baseline. Secondary outcomes were patient activation, adherence, lung function, fractional exhaled nitric oxide (FeNO), generic quality of life measure (EQ-5D), medication use, prescribing and health services contacts. Results: Phase1: Demonstrated that while digital interventions show promise, with some evidence of effectiveness in certain outcomes, participants were poorly characterised, telling us little about the reach of these interventions. The interventions themselves were poorly described making drawing definitive conclusions about what worked and what did not impossible. Phase 2: The literature indicated that important aspects to cover in any self-management intervention (digital or not) included: asthma action plans, regular health professional review, trigger avoidance, psychological functioning, self-monitoring, inhaler technique, and goal setting. The website asked users to aim to be symptom free. Key behaviours targeted to achieve this include: optimising medication use (including inhaler technique); attending primary care asthma reviews; using asthma action plans; increasing physical activity levels; and stopping smoking. The website had 11 sections, plus email reminders, which promoted these behaviours. Feedback during think aloud studies was mainly positive with most changes focussing on clarification of language, order of pages and usability issues mainly relating to navigation difficulties. Phase 3: To achieve our recruitment target 5383 potential participants were invited, leading to 51 participants randomised (25 to intervention group). Age range 16-78 years; 75% female; 28% from most deprived quintile. Nineteen (76%) of the intervention group used the website for an average of 23 minutes. Non-significant improvements in favour of the intervention group observed in the ACQ score (-0.36; 95% confidence interval: -0.96, 0.23; p=0.225), and mini-AQLQ scores (0.38; -0.13, 0.89; p=0.136). A significant improvement was observed in the activity limitation domain of the mini-AQLQ (0.60; 0.05 to 1.15; p = 0.034). Secondary outcomes showed increased patient activation and reduced reliance on reliever medication. There was no significant difference in the remaining secondary outcomes. There were no adverse events. Conclusion: Living Well with Asthma has been shown to be acceptable to potential end users, and has potential for effectiveness. This intervention merits further development, and subsequent evaluation in a Phase III full scale RCT.

Trapping phosphorus (III) into polyoxometalates: synthesis, characterisation and electronic behaviour study

The introduction of electronically-active heteroanions into polyoxometalates (POMs) is one of the emerging topics in this field. The novel clusters have shown unprecedented intramolecular electron-transfer features that can be directly mediated by the incorporated heteroanions. In this thesis, we will focus on the study of phosphite (HPO32-) as new non-traditional heteroanions, discover HPO32- templated nanostructures, investigate their electronic behaviours as well as understand the self-assembly process of HPO32--templated species. The thesis starts with incorporating HPO32- into POM cages. The feasibility of this work was illustrated by the successful trapping of HPO32- into a “Trojan Horse” type {W18O56} nanocage. The reactivity of embedded {HPO3} was fully studied, showing the cluster undergoes a structural rearrangement in solution whereby the {HPO3} moieties dimerise to form a weakly interacting (O3PH···HPO3) moiety. In the crystalline state a temperature-dependent intramolecular redox reaction and structural rearrangement occurs. This rearrangement appears to proceed via an intermediate containing two different templates, a pyramidal {HPO3} and a tetrahedral {PO4} moiety. {HPO3} templated POM cages were then vigorously expanded and led to the isolation of five either fully oxidised or mixed-valence clusters trapped with mono-, di-, or tri- {HPO3}. Interestingly, an intriguing 3D honeycomb-like host-guest structure was also synthesised. The porous framework was self-aggregated by a tri-phopshite anion templated {W21} cluster with a {VO4} templated Wells-Dawson type {W18} acting as a guest species within the hexagonal channels. Based on this work, we further extended the templating anions to two different redox-active heteroanions, and discovered a unique mixed-heteroatom templated system built by pairing redox-active {HPIIIO3} with {TeO3}, {SeO3} or {AsO3}. Two molecular systems were developed, ie. “Trojan Horse” type [W18O56(HPO3)0.8(SeO3)1.2(H2O)2]8- and cross-shaped [H4P4X4W64O224]32-/36-, where X=TeIV, SeIV, AsIII. In the case of {W18(HPO3)0.8(SeO3)1.2}, the compound is found to be a mixture of heteroleptic {W18(HPO3)(SeO3)} and homoleptic {W18(SeO3)2} and {W18(HPO3)2}, identified by single crystal x-ray diffraction, NMR as well as high resolution mass spectrometry. The cluster exhibited similar temperature-dependent electronic features to “Trojan Horse” type {W18(HPO3)2O56}. However, due to the intrinsic reactivity difference between {HPO3} and {SeO3}, the thermal treatment leads to the formation of an unusual species [W18O55(PO4)(SeO3)]5-, in which {HPO3} was fully oxidised to {PO4} within the cage, whereas and lone-pair-containing {SeO3} heteroanions were kept intact inside the shell. This finding is extremely interesting, as it demonstrated that multiple and independent intramolecular electronic performance can be achieved by the coexistence of distinct heteroatoms within a single molecule. On the other hand, the cross-shaped [H4P4X4W64O224]32-/36- were constructed by four {W15(HPO3)(XO3)} building units linked by four {WO6} octahedra. Each building unit traps two different heteroatoms. It is interesting to note that the mixed heteroatom species show self-sorting, with a highly selective positional preference. Smaller ionic sized {HPO3} are self-organised into the uncapped side of {W15} cavity, whereas closed side are occupied by larger heteroatoms, which is surprisingly opposed to steric hindrance. Density functional theory (DFT) calculations are currently underway to have a full understanding of the preference of heteroatom substitutions. This series of clusters is of great interest in terms of achieving single molecule-based heteroatom-dependent multiple levels of electron transfer. It has opened a new way to design and synthesise POMs with higher diversity of electrical states, which may lead to a new type of Q-bits for quantum computing. The third chapter is focused on developing polyoxotungstate building blocks templated by {HPO3}. A series of building blocks, {W15O48(HPO3)2}, {W9O30(HPO3)} {W12O40(HPO3)2} and hexagonal {W6O18(HPO3)} have been obtained. The first four building blocks have been reported with {SeO3} and/or {TeO3} heteroanions. This result demonstrates {HPO3} has a similar reactivity as {SeO3} and {TeO3}, therefore studying the self-assembly of {HPO3}-based building blocks would be helpful to have a general understanding of pyramidal heteroatom-based molecular systems. The hexagonal {W6O18(HPO3)} is observed for the first time in polyoxotungstates, showing some of reactivity difference between {HPO3} and {SeO3} and {TeO3}. Furthermore, inorganic salts and pH values have some directing influence on the formation and transformation of various building blocks, resulting in the discovery of a family of {HPO3}-based clusters with nuclearity ranging from {W29} to {W106}. High resolution mass spectrometry was also carried out to investigate the cluster solution behaviour and also gain information of building block speciation. It is found that some clusters experienced decomposition, which gives rise to potential building blocks accountable for the self-assembly.