Reflective and formative assessments are commonly used in both K-12 and higher education but are less common in university mathematics courses. In fact, much of mathematics education seems to be heavily reliant on summative assessments. In this article, we introduce a formative assessment in the frame of a reflective homework system that can be…

This paper presents a modified approach to subject-matter didactics, in which the focus is not on the content itself, but on the students' view of the content. The introduction deals with an overview of subject-matter didactics and the notion of beliefs used in this paper. The main portion of the paper deals with presenting the concepts of a book…

This article reports on a reconceptualization of the Precalculus course experience at Florida International University. We discuss the details of the redesign process--unified within a faculty learning community (FLC) model--along with a broader change in the course sequence leading up to Calculus. We provide data, including the comparison between…

In this work we critically examine a mnemonic designed for the pedagogy of first-order ordinary differential equations. The particular mnemonic takes the form of the SHIELDS acronym. We perform a critical analysis on mnemonics, outlining some of their benefits and limitations from the literature. As a result, we propose a general mnemonic model…

An interactive open-source calculus textbook is compared to a popular commercial textbook. Structured as a non-inferiority study, use of the open-source textbook does not harm student outcomes, and there is evidence that the open-source textbook is better than the commercial textbook in promoting post-course enjoyment of mathematics and confidence…

In this paper, we describe the evolution of calculus instruction at a mid-sized, career-oriented, comprehensive public university. Changes in practice, that began with a single faculty member implementing technology as a tool for student inquiry, have spread to other department faculty via support from an internal grant, workshops, and the use of…

In nineteenth-century America, students buried their mathematics books. This practice consistently celebrated the milestone of passing through collegiate mathematics, yet it changed due to national events. This article considers the case of Bowdoin College, where students buried their books differently before and after the Civil War. Antebellum,…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…

Basic calculus skills that are prerequisites for advanced mathematical studies continue to be a problem for a significant proportion of higher education students. While there are many types of revision material that could be offered to students, in this paper we investigate whether short, narrated video recordings of mathematical explanations…

The combination of classroom voting system (clicker) questions and peer instruction has been shown to increase student learning. While implementations in large lectures have been around for a while, mathematics has been increasingly using clickers in classes of a smaller size. In Fall 2008, I conducted an experiment to measure the effect of…

Research on student learning in higher education suggests that threshold concepts within various disciplines have the capacity to transform students' understanding. The present study explores students' understanding in relation to particular threshold concepts in mathematics--integral and limit--and tries to clarify in what sense developing an…

Recent mathematics education reform calls for efforts to create collaborative and student-centered environments, where students have opportunities to reason and construct their understanding as part of a community of learners. Mathematics instruction should provide students opportunities to engage in mathematical inquiry and meaning making through…

Students rarely use their graded exams to study. An alternative method of grading exams, based on self-reflection, encourages students to use their mistakes as a learning resource. In this grading method, the test is returned with each question simply marked as "right" or 'wrong." Students can then go over their exams and resubmit them with…

This article presents an exploratory study that gives account of some students' perceptions of the completeness property of the set of real numbers. Students taking three undergraduate correlative courses in Calculus and Analysis answered a written questionnaire; their scripts are analysed trying to understand how operational is the notion of…

Technology impacts students' learning experiences. The increased use of calculators, computer algebra systems, and computer-based and Web-based assessments opens up new opportunities and challenges for teaching and learning mathematics. Students' lives are becoming busier, and they have less time to dedicate to homework outside the classroom.…