A well-developed understanding of rate is foundational to conceptual understanding of introductory calculus. Many students achieve procedural competence with the application of rules for differentiation without developing an awareness of the connection between derivative and rate. In addition, rate-related reasoning is needed to make informed…

Under the backdrop of the investigation of rational functions and their respective curved asymptotes, the reader is invited to experience the mathematical process alongside the authors and observe the application of the NCTM Process Standards and the use of multiple representations in the investigation and solution of a problem. (Contains 9…

Social cognitive research has linked students' perceived academic capabilities, or self-efficacy, to academic choices, self-regulation, and performance in diverse contexts from reading comprehension to mathematical problem solving. This study addressed a need to investigate the interactions among prior achievement, self-efficacy, calibration (the…

This study investigated the effects of problem-based learning on students' beliefs about physics and physics learning and conceptual understanding of Newtonian mechanics. The study further examines the relationship between students' beliefs about physics and their conceptual understanding of mechanics concepts. Participants were 124 Turkish…

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.

As part of developmental research for an inquiry-oriented differential equations course, this study investigates the change in students' beliefs about mathematics. The discourse analysis has identified two different types of perspective modes--i.e., discourse of the third-person perspective and discourse of the first-person perspective--in the…

The aim of this paper is to present a simple way of establishing the general solution of the linear, second-order differential equation without using complex numbers.

Undergraduate retention and eventual graduation is of paramount importance to universities globally. Approximately 58% of students who began their college career at a four-year institution with the intention of receiving a bachelor's degree actually received that degree in a 6-year timeframe, according to the National Center for Education…

This article discusses the incorporation of biological content into existing calculus courses without significantly changing the courses. This is exemplified by the common laboratory course taken by students in all first semester calculus courses at Benedictine University. Several biologically oriented projects are implemented in this laboratory…

Games are a useful and fun way to review material in class, and encourage students to actively participate in review sessions. In fact, researchers have concluded that playing games can be an effective learning tool, especially in mathematics, in situations where the goal is to reinforce specific ideas or concepts. Two places this type of…

The Laplace Transform is an object of fundamental importance in pure and applied mathematics. In addition, it has special pedagogical value in that it can provide a natural and concrete setting for a student to begin thinking about the modern concepts of "operator" and "functional". Most undergraduate textbooks, however, merely define the…

The careful use of notation and language in the statement of both the definitions and problems of calculus can begin the process of making students mathematically literate while allowing them to enjoy working on challenging problems and applications without the aid of numerous examples. Engaging the students to participate in the precise use of…

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional his understanding of periodic functions was unconventional David engaged…