In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the…

What is mathematics? What does it mean to be a mathematician? What should students understand about the nature of mathematical knowledge and inquiry? Research in the field of mathematics education has found that students often have naive views about the nature of mathematics. Some believe that mathematics is a body of unchanging knowledge, a…

In this study, a description is provided for the development of two undergraduate students' geometric reasoning about the derivative of a complex-valued function with the aid of "Geometer's Sketchpad" ("GSP") during an interview sequence designed to help them characterize the derivative geometrically. Specifically, a particular…

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier…

A second course in linear algebra that goes beyond the traditional lower-level curriculum is increasingly important for students of the mathematical sciences. Although many applications involve only real numbers, a solid understanding of complex arithmetic often sheds significant light. Many instructors are unaware of the opportunities afforded by…

The subject of fluid mechanics is a rich, vibrant, and rapidly developing branch of applied mathematics. Historically, it has developed hand-in-hand with the elegant subject of complex variable theory. The Westmont College NSF-sponsored workshop on the revitalization of complex variable theory in the undergraduate curriculum focused partly on…

Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…

This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and…

This study aims to explore undergraduate mathematics students' difficulties in their initial encounter with the subgroup test, and in particular in the proof of closure under operation. Subgroup test is one of the first results in an introductory course of Group Theory where students need to cope with the characteristic, for novice students, high…

In this study, we analysed a mathematician's teaching journals on eigenvalues and eigenvectors in a first-year linear algebra course. The research team employed Tall's ["How humans learn to think mathematically: Exploring the three worlds of mathematics." Cambridge University Press] three-world model of embodied, symbolic and formal as a…

As teachers of mathematics we encourage our students to ask good questions, and we strive to help our students find and understand answers to these questions. This journey can be made more meaningful if students conclude by reflecting on their learning process. If we find careful questioning and reflection important, we should include such…

The study aimed at describing university students' ability in constructing mathematical proofs using logical arguments and constructing an effective teaching-learning map. The study adopted a correlational research design. An open-ended mathematics assessment involving questions on mathematical logic and construction of mathematical proofs was…

This article describes a system of specifications-based grading used in an introduction to proofs course. The system was introduced to address two issues that arose in the course: how to spend less time grading and how to encourage use of feedback. We describe the implementation of the system and the results on grading and on students.

In this study, I examined links between College Algebra students' covariational reasoning and their conception of general function notation (y = f(x)). I investigated the following research questions: How might students' conceptions of function impact their conceptions of function notation? How might covariational reasoning related to function…