The leap into the wonderful world of differential calculus can be daunting for many students, and hence it is important to ensure that the landing is as gentle as possible. When the product rule, for example, is met in the "Australian Curriculum: Mathematics", sound pedagogy would suggest developing and presenting the result in a form…

Mathematics textbooks are a significant pedagogical tool, particularly in light of the growing interest in "flipped" classrooms. However, there has been little research on how mathematics students read and comprehend textbooks. This article uses the ideas of the implied reader, sense-making frames, and sense-making gaps to analyze…

The calculus concepts of concavity and inflection points are often given meaning through the shape or curvature of a graph. However, there appear to be deeper core ideas for these two concepts, though the research literature has yet to give explicit attention to what these core ideas might be or what it might mean to "understand" them.…

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…

In the context of a generic harmonic oscillator, we investigated students' accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple-choice tests developed in an iterative process, we assessed students in both…

Teaching mathematics by project-based learning (PBL) method on the use of educational technology offers an innovative teaching pedagogy at college. The "World Culture Art Created with Calculus Graphs of Equations" poster project was designed by the first author and was completed in the pilot Calculus course during the spring 2016…

Tutoring centres are common in universities in the United States, but there are few published studies that statistically examine the effects of tutoring on student success. This study utilizes multiple regression analysis to model the effect of tutoring attendance on final course grades in Calculus I. Our model predicted that every three visits to…

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

In this paper I present a case study to illustrate conflicts between different 'realizations' of the concept of 'continuous function' held by a university first year student. Sfard's commognitve framework is used in the analysis of a student's work on continuity. I point out how these conflicting realizations have arisen from the inconsistent…

The flipped classroom is becoming a popular course structure in many academic disciplines, but particularly in STEM disciplines, including mathematics. Considerable research has addressed potential advantages and challenges of teaching a flipped course, as well as examining students' attitudes towards the flipped classroom. Studies on students'…

As part of Middle Tennessee State University's (MTSU's) initiative to improve retention of at-risk STEM majors, they recruit first-time, full-time freshman STEM majors with mathematics ACT scores of 19 to 23 to participate in MTSU's "Mathematics as a FirstSTEP to Success in STEM" project (FirstSTEP). This article overviews MTSU's…

This paper describes an intervention for improving the quality of peer assessment conferences in calculus. Although a body of work highlights the learning benefits of peer assessment, few papers have described the nature of student conversations during peer conferences/assessment in detail. This paper provides deeper insight into what those…

Improved access to technology has led to an increase in the number of online courses and degree programs in higher education. Despite continuous progress, little attention is paid to "understanding" students prior to implementation of learning and teaching processes. Being a valuable input for design of online learning environments and…