The experience of teaching statistics to non-specialist students in Saudi universities

Undoubtedly, statistics has become one of the most important subjects in the modern world, where its applications are ubiquitous. The importance of statistics is not limited to statisticians, but also impacts upon non-statisticians who have to use statistics within their own disciplines. Several studies have indicated that most of the academic departments around the world have realized the importance of statistics to non-specialist students. Therefore, the number of students enrolled in statistics courses has vastly increased, coming from a variety of disciplines. Consequently, research within the scope of statistics education has been able to develop throughout the last few years. One important issue is how statistics is best taught to, and learned by, non-specialist students. This issue is controlled by several factors that affect the learning and teaching of statistics to non-specialist students, such as the use of technology, the role of the English language (especially for those whose first language is not English), the effectiveness of statistics teachers and their approach towards teaching statistics courses, students’ motivation to learn statistics and the relevance of statistics courses to the main subjects of non-specialist students. Several studies, focused on aspects of learning and teaching statistics, have been conducted in different countries around the world, particularly in Western countries. Conversely, the situation in Arab countries, especially in Saudi Arabia, is different; here, there is very little research in this scope, and what there is does not meet the needs of those countries towards the development of learning and teaching statistics to non-specialist students. This research was instituted in order to develop the field of statistics education. The purpose of this mixed methods study was to generate new insights into this subject by investigating how statistics courses are currently taught to non-specialist students in Saudi universities. Hence, this study will contribute towards filling the knowledge gap that exists in Saudi Arabia. This study used multiple data collection approaches, including questionnaire surveys from 1053 non-specialist students who had completed at least one statistics course in different colleges of the universities in Saudi Arabia. These surveys were followed up with qualitative data collected via semi-structured interviews with 16 teachers of statistics from colleges within all six universities where statistics is taught to non-specialist students in Saudi Arabia’s Eastern Region. The data from questionnaires included several types, so different techniques were used in analysis. Descriptive statistics were used to identify the demographic characteristics of the participants. The chi-square test was used to determine associations between variables. Based on the main issues that are raised from literature review, the questions (items scales) were grouped and five key groups of questions were obtained which are: 1) Effectiveness of Teachers; 2) English Language; 3) Relevance of Course; 4) Student Engagement; 5) Using Technology. Exploratory data analysis was used to explore these issues in more detail. Furthermore, with the existence of clustering in the data (students within departments within colleges, within universities), multilevel generalized linear models for dichotomous analysis have been used to clarify the effects of clustering at those levels. Factor analysis was conducted confirming the dimension reduction of variables (items scales). The data from teachers’ interviews were analysed on an individual basis. The responses were assigned to one of the eight themes that emerged from within the data: 1) the lack of students’ motivation to learn statistics; 2) students' participation; 3) students’ assessment; 4) the effective use of technology; 5) the level of previous mathematical and statistical skills of non-specialist students; 6) the English language ability of non-specialist students; 7) the need for extra time for teaching and learning statistics; and 8) the role of administrators. All the data from students and teachers indicated that the situation of learning and teaching statistics to non-specialist students in Saudi universities needs to be improved in order to meet the needs of those students. The findings of this study suggested a weakness in the use of statistical software applications in these courses. This study showed that there is lack of application of technology such as statistical software programs in these courses, which would allow non-specialist students to consolidate their knowledge. The results also indicated that English language is considered one of the main challenges in learning and teaching statistics, particularly in institutions where English is not used as the main language. Moreover, the weakness of mathematical skills of students is considered another major challenge. Additionally, the results indicated that there was a need to tailor statistics courses to the needs of non-specialist students based on their main subjects. The findings indicate that statistics teachers need to choose appropriate methods when teaching statistics courses.

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.