We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

This paper describes how one university mathematics department was able to improve student success in Calculus I by requiring a co-requisite lab for certain groups of students. The groups of students required to take the co-requisite lab were identified by analyzing student data, including Math ACT scores, ACT Compass Trigonometry scores, and…

Over the last 10 years faculty members in the Department of Mathematical Sciences at the United States Air Force Academy have incorporated individual oral exams into mathematics courses. We have experimented with various approaches, shared results and ideas with other department members, and refined our techniques. We have found that this…

Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

The use of open-book tests, closed-book tests, and notecards on tests in an introductory statistics course is described in this article. A review of the literature shows that open-book assessments are universally recognized to reduce anxiety. The literature is mixed however on whether deeper learning or better preparation occurs with open-book…

This article offers our ideas on why it is important to teach our students how to speak about mathematics and some practical resources for incorporating speaking activities, helping students prepare, evaluating student presentations, and getting your department to talk about student presentations. The ideas in this article were compiled when the…