We introduce learning modules in cryptography that can be crafted to motivate many abstract mathematical ideas, and we illustrate with a sample module. These modules can be used in a variety of ways, such as the core for a cryptography course or as motivating topics in other courses such as abstract and linear algebra or number theory.

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A…

Educational modules can play an important part in revitalizing the teaching and learning of complex analysis. At the Westmont College workshop on the subject in June 2014, time was spent generating ideas and creating structures for module proposals. Sharing some of those ideas and giving a few example modules is the main purpose of this paper. The…

Explaining is one of the fundamental teaching practices. Yet, much is still unknown about the ways in which pre-service secondary teachers (PSTs) learn to create instructional explanations. Even less is known about how technology can support PSTs in this process. This paper describes an instructional module which used video to enhance PSTs'…

This research study examines the development of the ability of pre-service teachers to notice signs of students' understanding of the derivative concept. It analyses preservice teachers' interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results…

Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…

Oulipo (Ouvroir de Littérature potentielle, or Workshop on potential literature), an over 50-year old movement that began in France, seeks to apply mathematical constraints to literature and the arts. In this article, I will give a brief survey of this movement and how I have built a learning module based on it for my mathematics for the liberal…

In this paper, the authors describe how two institutions are helping their undergraduate biology students build quantitative competencies. Incorporation of quantitative skills and reasoning in biology are framed through a discussion of two cases that both concern introductory biology courses, but differ in the complexity of the mathematics and the…

Motion planning is a core problem in robotics concerned with finding feasible paths for a given robot. Motion planning algorithms perform a search in the high-dimensional continuous space of robot configurations and exemplify many of the core algorithmic concepts of search algorithms and associated data structures. Motion planning algorithms can…

Failure rates in first year calculus courses are high in most post-secondary institutions across North America and other parts of the world. This Inukshuk-funded open education project involved the development of five stand-alone pre-calculus learning modules. The design and revision phases of this project occurred between the fall of 2007 and…

This project was designed to be used in a freshman calculus class whose students had already been introduced to logistic functions and basic data modeling techniques. It need not be limited to such an audience, however; it has also been implemented in a topics in mathematics class for college upperclassmen. Originally intended to be presented in…

This study developed twelve instructional modules based on the National Assessment of Educational Progress for mathematics content and methods courses for preservice elementary and middle school teachers and examined their impact on PSTs' mathematical content knowledge and self-efficacy beliefs about teaching mathematics. The modules help…

The purpose of this study was to measure the difference in achievement between those students enrolled in a beginning-level, university Algebra course in southeastern Idaho university the spring semester of 2012 who received an Algebra Exponents and Polynomials instructional unit in a traditional face-to-face setting and those students who…

Teacher educators are constantly searching for ways to better prepare preservice teachers to enter the education field. One way that has gained prominence in the last twenty years is through examining and discussing authentic student work samples. Research suggests that doing so helps preservice teachers to (1) gain insight into their own beliefs…