When exposed to principal components analysis for the first time, students can sometimes miss the primary purpose of the analysis. Often the focus is solely on data reduction and what to do after the dimensions of the data have been reduced is ignored. The datasets discussed here can be used as an in-class example, a homework assignment, or a…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…

The Functional Behavioural Assessment (FBA) is an investigative process that examines the context of challenging behaviours in the classroom. Information gleaned from the FBA process is used to develop a behaviour intervention plan to address the challenging behaviour and teach a socially acceptable replacement behaviour. However, the FBA has…

A general method is presented for evaluating the sums of "m"th powers of the integers that can, and that cannot, be represented in the two-element Frobenius problem. Generating functions are introduced and used for that purpose. Explicit formulas for the desired sums are obtained and specific examples are discussed.

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

The Educational Leaders in Mathematics (ELM) Project, was an experimental inservice program for teachers of mathematics, grades kindergarten to 12. The major focus on the project was to help teachers develop and implement approaches to mathematics instruction based on a constructivist view of learning. ELM demonstrated the significant impact of…

Summarizes various stakeholder surveys and factor analyses that attempt to delineate transferable skills, such as problem solving, communication, teamwork, and critical thinking. Points out that employer skill requirements may vary among countries and these differences may not always be cultural, but are related to different uses of terminology…

Provides an exercise for introducing research methods to undergraduates. The students view a graph revealing that left-handed people are underrepresented in older age groups. Small group discussions attempt to explain this phenomenon. A follow-up class discussion focuses on the different approaches and methods available for interpreting the data.…