This study investigates the responses to prior knowledge errors that Calculus I instructors make when assessing students. Prior knowledge is operationalized as any skill or understanding that a student needs to successfully navigate through a Calculus I course. A two part qualitative study consisting of student exams and instructor interviews was…

The purpose of this study was to investigate how modeling-based instruction combined with an interactive-engagement teaching approach promotes students' problem solving abilities. I focused on students in a calculus-based introductory physics course, based on the matter and interactions curriculum of Chabay & Sherwood (2002) at a large state…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

In this article we focus on university lecturers' approaches to the service teaching and factors that influence their approaches. We present data obtained from the interviews with 19 mathematics and three physics lecturers along with the observations of two mathematics lecturers' calculus courses. The findings show that lecturers' approaches to…

Research on technology-use for teaching and learning statistics is sparse compared to that in algebra and calculus. This paper addresses the deficiency with regard to teaching and learning about "trend" in bivariate data. Available research findings are reviewed and an empirical inquiry in a year 12 (upper secondary) class is reported. Treatment…

To help struggling seniors with the expectations of a high school precalculus course, their lack of confidence, and the "new" intimidation they feel in the classroom, the teacher discusses additional study skills necessary for performing well in the mathematics classroom. The author compares studying mathematics to the practice necessary to…

The Fundamental Theorem of Calculus is discovered based on the use of data analysis techniques applied to a variety of common families of functions. (Contains 8 figures and 6 tables.)

Issues related to college access and the need for a pipeline of STEM teachers, provided the impetus for the Ohio Board of Regents (OBR) to issue a call for Ohio universities to design pre-college experiences for high school students with three major goals in mind: (a) improvement in mathematics, science, or foreign language learning; (b) increased…

At the University of Toronto at Scarborough, we provide enhanced flexibility to our students using a blended learning approach (i.e., the webOption) whereby classes are videotaped as they are offered in a traditional manner, then posted online for subsequent student access. Students can attend lectures live, watch them online at their convenience,…

Because statistical analysis requires the ability to use mathematics, students typically are required to take one or more prerequisite math courses prior to enrolling in the business statistics course. Despite these math prerequisites, however, many students find it difficult to learn business statistics. In this study, we use an ordered probit…

The calculus-based, introductory physics course is the port of entry for any student interested in pursuing a college degree in the sciences, mathematics, or engineering. There is increasing demand for online delivery options that make the course more widely available, especially those that use best practices in student engagement. However,…

Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

Lesson Study is a process by which a team of instructors works collaboratively to plan, teach, observe and revise one particular lesson. A successful lesson study will not only result in a student-focused lesson plan that maximizes student understanding, but will also encourage teaching-centered collaboration among colleagues and increase the…

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…