The course will equip student with adequate theoretical background, content and statistical tools and techniques required for analyses of quantitative research data. For each of the statistical tools and techniques the objective is to provide opportunities for students to develop a conceptual understanding of what that statistical tool is, when to use it (including the underlying assumptions and how to test them), how to use it, and how to interpret the results. Students will be exposed to the use of Predictive Analytics Software (PASW) and Microsoft Excel to run the various analyses. Topics include: The Power of Statistical Test; Point-Biserial Correlation; Multivariate analysis of variance – MANOVA, Analysis of covariance – ANCOVA; Analysis of covariance – ANCOVA; Scale Construction- levels of measurement,  factor analysis, cyclical scale refinement; Multiple regression analysis; Structural Equation Modelling; Cluster analysis; Effect Size and Post Hoc Analyses; Various non-parametric statistics: Mann-Whitney, Wilcoxon, Friedman & Kruskal Wallis, Logistic Regression and Kendall’s concordance will also be discussed. 

The course will expose students to the theories that underpin the qualitative and mixed methods research paradigms. It aims at the development of the knowledge and skills of students to enable them conduct a variety of qualitative and mixed methods studies aimed at improving teaching and learning of science in schools and other educational settings. It is expected that at the end of the course students will write a research proposal for a study that could be the focus of their thesis. Topics to be covered include: Various qualitative research approaches such as case studies, content analysis, ethnography, phenomenology, teaching experiments, and grounded research theories; Sequential and concurrent mixed methods approaches; Validity and reliability. Development of qualitative instruments, as well as data collection methods, and analyses will also be explored both manually and the use of the NVivo software.

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving direct sum of subspaces, complement of subspace in a vector space and dimension of the sum of two subspaces. Other topics to be covered are one-to one, onto and bijective linear transformations, isomorphism of vector spaces, matrix of a linear transformation relative to a basis, orthogonal transformations, rotations and reflections, real quadratic forms, and positive definite forms.

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving matrices and vectors to study linear systems of equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, eigenvalues and eigenvectors and their applications.  The topics to be covered are axioms for vector spaces over the field of real and complex numbers. Subspaces, linear independence, bases and dimension. Row space, Column space, Null space, Rank and Nullity.  Inner Products Spaces. Inner products, Angle and Orthogonality in Inner Product Spaces, Orthogonal Bases, Gram-Schmidt orthogonalization process. Best Approximation. Eigenvalues and Eigenvectors. Diagonalization. Linear transformation, Kernel and range of a linear transformation. Matrices of Linear Transformations.