This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students' horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

This paper reports on mathematics remediation efforts at a public 4-year institution. Specifically, it describes redesign efforts that led to the implementation of co-requisite mathematics remediation. Data on this program were collected and analyzed with respect to completion rates, length of time to earn college mathematics credit, and factors…

We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to…

We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. The arguments can be…

The utilization of mathematical software offers numerous points of interest to students, which are fundamentals in the teaching-learning process in the four corners of the classroom. The study determined the effects of Mathcad as an instructional and a computational tool in teaching College Algebra to the Education students in the University of…

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

In this paper the author investigates how the one-year math throughput rate of community college students varies according to the highest level of math completed in high school, with a particular focus on the implications of successfully completing Algebra 2 while in high school. Community college math throughput rates for students with different…

This report examines the effects of taking math in 12th grade on several academic outcomes, including high school grade point average, A-G course completion, college enrollment, and college persistence. We also investigate whether particular types of math courses (for example, Calculus or Statistics) are especially beneficial for students'…

This report examines the impact of taking a math course in twelfth grade on L.A. Unified students' science, technology, engineering, and math (STEM) college course taking and academic achievement. We also investigate whether particular types of math courses (for example, Calculus or Statistics) are especially beneficial for students' postsecondary…

Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…

As a residential college within Michigan State University that focuses on STEM fields, Lyman Briggs College developed a STEM learning community to support students with low mathematics placement test scores, the Instilling Quantitative and Integrative Reasoning program (INQUIRE). INQUIRE serves some of those students considered historically…

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

This article reports on a study designed to estimate the effect of high school coursetaking in the algebra-calculus pipeline on the likelihood of placing out of postsecondary remedial mathematics. A nonparametric variant of propensity score analysis was used on a nationally representative data set to remove selection bias and test for an effect…

In spring 2015 Mississippi began testing the college readiness of all grade 11 public high school students and found that approximately 18 percent were ready for college math, a percentage that had changed little by 2017/18. This study examined: (1) the sequences of math courses that Mississippi students took in grades 6-11; (2) the math…