Most students complete their first and only course in linear algebra with the understanding that a real, square matrix "A" has an inverse if and only if "rref"("A"), the reduced row echelon form of "A", is the identity matrix I[subscript n]. That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix…

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

This study was intended to provide a description of teaching and learning patterns seen in the lessons taught by experts and novices in Adapted Physical Education. Two experts who had won previous state teaching awards and served in leadership positions in state associations were filmed and their lessons were analyzed first to develop a systematic…

Minorities are disproportionately affected by HIV/AIDS in the rural Southeast; therefore, it is important to develop targeted, culturally appropriate interventions to support rural minority participation in HIV/AIDS research. Using intervention mapping, we developed a comprehensive multilevel intervention for service providers (SPs) and people…

This Capstone project studied a pilot of the web-based homework system "Hawkes" in developmental mathematics classes at a mid-sized community college. The purpose of the study was to investigate how three instructors of developmental mathematics courses incorporated "Hawkes" in their classes, what obstacles they encountered,…

We represent the main stages of the process of mathematical modelling as fuzzy sets in the set of the linguistic labels of negligible, low intermediate, high and complete success by students in each of these stages and we use the total possibilistic uncertainty as a measure of students' modelling capacities. A classroom experiment is also…

When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…

The predictive value of selection criteria on outcome data from two cohorts of students (Total N = 525) accepted to an urban magnet high school were evaluated. Regression analyses of typical screening variables (suspensions, absences, metropolitan achievement tests, middle school grade point averages [GPAs], Matrix Analogies test scores, and…

In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new…

In component analysis solutions, post-multiplying a component score matrix by a nonsingular matrix can be compensated by applying its inverse to the corresponding loading matrix. To eliminate this indeterminacy on nonsingular transformation, we propose Joint Procrustes Analysis (JPA) in which component score and loading matrices are simultaneously…

The Student Transition project (STP) has collected eleven years of grade 12 and post-secondary enrollment data, since it's inception in 2003. This information is used to track student transitions from grade 12 graduation into post-secondary education, student mobility between post-secondary institutions and post-secondary credential completions.…

Linear algebra has become one of the most useful fields of mathematics since last decade, yet students still have trouble seeing the connection between some of the abstract concepts and real-world applications. In this article, we propose the use of thought-provoking questions in lesson designs to allow two-way communications between instructors…

Students have social and personal needs to fulfill and communicate these needs in different ways. This annotated bibliographic review examined communication studies to provide educators of diverse classrooms with ideas to build an environment that contributes to student well-being. Participants in the studies ranged in age, ability, and cultural…

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding.…

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated direct or step-down methods. Here is a short example demonstrating how Excel's sometimes unknown matrix…