A few years ago we began to revamp our introductory physics course for life science students. We knew that this cohort would be less prepared and less adventurous mathematically than engineering, physical science, or mathematics majors. Moreover, from our own experience and the mathematics education literature, we knew that trigonometry would be…

Historical accounts of trigonometry refer to the works of many Indian and Arab astronomers on the origin of the trigonometric functions as we know them now, in particular Abu al-Wafa (ca. 980 CE), who determined and named all known trigonometric functions from segments constructed on a regular circle and later on a unit circle (Moussa 2011;…

Over the past three decades, researchers have found cooperative learning to have positive effects on student achievement in various subject areas and levels in education. However, there are limited studies on the impact of cooperative learning on student achievement in the area of high school mathematics. This study examined the impact of…

At our Historically-Black University, about 89% of first-year students place into developmental mathematics, negatively impacting retention and degree completion. In 2012, an NSF-funded learning enrichment project began offering the introductory and developmental mathematics courses on-line over the summer to incoming science, technology,…

A visual proof that sin x/x is monotonically increasing on (0, pi/2). For tan x/x, see p. 420 (EJ1017686).

A visual proof that tan x/x is monotonically increasing on (0, pi/2). For sin x/x, see p. 408 (EJ1017684).

Organization for Economic Co-operation and Development (OECD) (2016) released the results of Programme for International Student Assessment (PISA) 2015 and reported that the students' performance in mathematics of Singapore and Indonesia had significant differences. There is a strong relationship between textbooks used and mathematics performance…

Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the…

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This…

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

Researchers promoting the inclusion of technology for teaching and learning have recently called for the integration of mathematical technologies into the preparation of future teachers. This report analyzes the dynamic geometry sketches produced by preservice secondary mathematics teachers when investigating trigonometric relationships. We…

An extensive body of research describes the stark social and academic disparities that characterize large, comprehensive public high schools. Advocates have argued that smaller high schools, with their necessarily more constrained curricula, have the potential to improve student academic outcomes and their equitable distribution. Using propensity…

Mathematics educators agree that linking mathematical ideas by using multiple approaches for solving problems (or proving statements) is essential for the development of mathematical reasoning. In this sense, geometry provides a goldmine of multiple-solution tasks, where a myriad of different methods can be employed: either from the geometry topic…

This study's focus was two-fold, first to look at forms of gestures teachers of multilingual mathematics classes use during teaching; and second to find out how teachers of multilingual mathematics classes utilize learners' home language, language of learning and teaching and gestures to foster understanding in the teaching of mathematics. This…

The simple process of iteration can produce complex and beautiful figures. In this article, Robin O'Dell presents a set of tasks requiring students to use the geometric interpretation of complex number multiplication to construct linear iteration rules. When the outputs are plotted in the complex plane, the graphs trace pleasing designs…