Mastery-grading techniques such as mastery-based grading, specifications grading, and standards-based grading are assessment techniques professors are implementing in order to support a growth mindset of learning, decrease test anxiety, and help students develop a deeper understanding of course objectives. In this paper, we provide an analysis of…

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…

What if your students could access "any" resource during a test? How would they react? How would "you" react? This paper presents some results from a trial of allowing students access to notes, calculators, and any device connected to the internet, which occurred during a midterm in a second-year ordinary differential equations…

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.

In the continual pursuit of classroom learning effectiveness, researchers and educators aim to develop strategies that improve student performance and learning. One such strategy is to create academically homogeneous environments where students are grouped into classes based on their preconceived academic ability. The research team tests this…

In 2011, Sonoma State University developed a STEM first-year experience (supported by NSF STEP grant 1068445) that combines general education requirements in mathematics, biology, and critical thinking. The mathematics content includes topics from precalculus and elementary statistics, with a particular focus on using functions and modeling with…

Gateway testing is an important pedagogic tool employed by many university mathematics departments in calculus and precalculus courses. With a goal of ensuring that students attain needed basic skills in courses with a conceptual "reform" orientation, these tests provide an efficient means of assessing a large volume of student work,…

Reflections are presented on the first time flipping of an introductory Ordinary Differential Equations course. Assessment results, student motivation, and student attitudes are compared between flipped and traditional learning pedagogies in this course over two terms at a small technical university in the northeast United States. Assessments and…

The percentage of college students receiving unproductive grades in introductory mathematics courses is a concern for post-secondary institutions across the country. Many factors can be targeted as potential explanations for this lack of success, yet none of these issues are more noteworthy than the fact that many students enter college…

In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

Many active learning practices highly depend on students' advance preparation for the class. However, reading Calculus can be a challenging task to students. We address this concern by assigning targeted pre-class readings in multiple Calculus courses. We report on our implementations, provide students' feedback, and discuss the lessons learned…

In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students…

This paper gives a blueprint for reacting to the various issues that an instructor will face in their day-to-day life as the manager of a Mastery-Based Testing (MBT) classroom. For example, I created a rubric to compare traditional testing with MBT, adapted my office hours to accommodate more retake opportunities, and required effort between…

As educators, it is important for us to recognize that our assessment methods affect student attitudes. If we want students to learn from their mistakes and counteract a fixed-mindset of learning, perhaps we should look at what we incentivize in the classroom. Some professors are attempting to counteract math and test anxiety, poor STEM retention,…

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…