Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope;…

Studying the effectiveness of remedial courses in higher education has attracted a lot of interest from educational researchers and practitioners. Remediation is associated with significant economic and social costs while the results are usually dubious. In this paper, we apply a widely used method called Regression Discontinuity Design (RDD) to…

Faced with students failing to complete Calculus 1 at rates of almost 50%, the Department of Mathematics at Western Michigan University addressed the lack of progression of STEM majors through this gateway course and, thus, through their intended majors. In this case study, we describe the four-year process of redesigning our single variable…

In introductory level math classes, writing prompts can be used as part of weekly homework assignments to encourage students to think more deeply about the subject at hand. These writing prompts present scenarios related to recently learned material in a new context and require students to submit a short written response online. Writing prompts…

The authors describe working with partner disciplines during the process of updating mathematics courses for the general education quantitative literacy requirement. The conversations resulted in significant changes to the business calculus course and a rich listing of applications to be incorporated into the college algebra course from technical…

Following a modeling-first approach to differential equations, inquiry-based learning activities on modeling and controlling the growth of locally relevant species, such as lionfish or sea turtles, are developed by the authors. Emerging exemplary practices are presented, building towards a balanced teaching of differential equations involving…

Meaningful mathematics learning requires creating opportunities for learners to make use of their awareness to contact important mathematical structures. Four first year undergraduates studying engineering, mathematics and education were invited to construct examples meeting specified constraints in order to investigate their awareness of…

Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and…

For institutions offering multiple sections of Calculus 1, course coordination allows for consistency among the sections through the reduction of variation of material and/or instructional approaches. Studies on course coordination have shown that a coordinated system can bring benefits to instructors and promote equality for students across…

This article includes a case study describing our innovative teaching technique of assigning reading journals in a first semester calculus course (Calculus I), as well as an exposition about and recommendations arising from our subsequent experiences implementing similar methods in Junior and Senior mathematics courses. In the primary case study…

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the "testing effect" and "spacing effect" in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional…

This paper reports the results of three questionnaires applied to sixty-seven students preparing to become university-level mathematics teachers; the questionnaires were focused on knowing their conceptions and their mastery of the representations of functions in the development of power series. The theoretical and methodological background rests…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.