Finding and designing tasks that allow for students to make connections among mathematical ideas is important for mathematics educators. One such task, which affords students the opportunity to make connections and engage with significant mathematical ideas through a variety of problem-solving approaches, is described in this article. Three…

This article presents a lesson in which least common multiples helps students not only develop a perspective on an ancient culture but also draw on the cultural background of classmates. The Maya calendar received a lot of attention in the years leading up to December 21, 2012, because of the mythological end of "creation." Co-author…

The Transcontinental Railroad began laying track east from Sacramento, California, in 1863 and west from Omaha, Nebraska, in 1865; the two lines eventually met in Promontory Summit, Utah, in 1869. One of the train towns, Ogallala, Nebraska, consisted of only a section house and water tank alongside newly laid track. Over the next few years, train…

This project integrates cooperative learning strategy in teaching developmental mathematics courses. This study uses a quasi-experimental non-equivalent control design comparing student's outcomes with and without implementing cooperative learning in these courses. The results of the data analysis shows that there is an increase in student's…

A rich understanding of key ideas in linear algebra is fundamental to student success in undergraduate mathematics. Many of these fundamental concepts are connected through the notion of equivalence in the Invertible Matrix Theorem (IMT). The focus of this paper is the ways in which one student, Abraham, reasoned about solutions to Ax = 0 and Ax =…

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

Mastering mathematics is important for all students, not only because such success increases college and career options and prospects for future income, but also because mathematics literacy helps citizens and policy leaders to make sound judgments (NMAP, 2008). Research suggests that the rural achievement gap can be addressed with modifiable…

In his "Proofs and Refutations," Lakatos identifies the "Primitive Conjecture" as the first stage in the pattern of mathematical discovery. In this article, I am interested in ways of reaching the "Primitive Conjecture" stage in an undergraduate classroom. I adapted Realistic Mathematics Education methods in an…

Concepts from asset pricing and financial markets theory are used to illustrate concepts of linear algebra and linear programming.

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential…

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…

This Information Capsule answers the most frequently asked questions about Miami-Dade County Public Schools' (M-DCPS) academic performance during the 2018-2019 school year. M-DCPS earned a District Performance Grade of "A" in 2019. The percentage of M-DCPS schools earning a School Performance Grade of "A" remained stable from…

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Almost 20 years ago, Cuoco, Goldenberg, and Mark wrote a seminal paper for the "Journal of Mathematical Behavior" entitled "Habits of Mind: An Organizing Principle for Mathematics Curricula" (Cuoco et al., 1996). The article remains as relevant today as when it was originally published. The premise of their paper is that…

Modules in Computer Algebra Systems (CAS) make Mathematics interesting and easy to understand. The present study focused on the implementation of the algebraic, tabular (numerical), and graphical approaches used for the construction of the concept of absolute value function in teaching mathematical content knowledge along with Maple 9. The study…