Erin L. Griesenauer

Abstract: Ethical reasoning is an essential component of applying mathematical modeling in solving real-life problems, both in research and business settings. Our mathematical answers exist in a context of a larger system and have implications on the lives of others, the planet, and future generations. However, mathematics instruction often treats the mathematical work as if it exists in a vacuum devoid of context and omits careful consideration of stakeholders, validity of data, assumptions made, and limitations of the analysis. In this talk, we present a general framework that can be used to modify any mathematical modeling problem or project in a way to help students focus on the missing ethical reasoning perspective in the problem/project. Our framework is generalized in the sense that it can be applied to any course at any level, including the K-12 instruction. The framework provides flexibility to instructors in terms of the types and level of questions that can be asked, as well as the quantity. In addition to describing the general template, we will demonstrate the use of the framework on a specific example to clarify the application of the framework.

Abstract: To find more effective ways to teach series, we apply the Revised Bloom’s Taxonomy to

textbook presentations of series and identify missing categories. In this process, we distinguish

between the perspectives of experts and novices. Once gaps are identified, additional materials

can be developed to better support student learning.:

Abstract: In this talk, I will describe an alternative to exams that gives students ownership of course material, makes room for student creativity, and encourages academic integrity by addressing motivation for academic dishonesty and making it more difficult to find answers online. I will share my experience replacing Calculus tests with a more open-ended, student-constructed review project: students are asked to review the main topics, write and answer their own “exam” questions, and reflect on their learning. This project gives deep insight into students’ knowledge and reasoning. The format of the project reduces student anxiety, increases student feelings of agency, and gives students multiple ways to engage with the material. Many students report enjoying this project and feeling that they have learned more than they would have with a traditional exam. I have found this type of project to be successful in both remote and in-person settings.

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes — lessons that have impacted how I set up my classroom, the assignments that I design, and the topics and content that I cover.

Weekly quizzes are a common method for assessing student learning between unit tests. However, with a few small changes, quizzes can be a useful tool not just for assessing learning but also for promoting student learning. Here I will describe my experience replacing weekly quizzes with more frequent, shorter quizzes and introducing the option for revisions. This strategy takes about the same amount of time in class and requires little extra preparation, but I have found that it encourages students to stay up-to-date on their homework rather than procrastinating, and it increases student test scores.

We all know that syllabus day isn’t effective. Instead, I use the first day to have a class discussion of cultural characteristics that influence students as they step into a mathematics classroom that they likely have never named and thought about explicitly. We discuss individualism, perfectionism, and a focus on quantity over quality. These traits prevent students from getting help when they need it and can lead to anxiety and other the negative feelings about mathematics. Here, I will share my experiences leading this discussion as well as feedback from students suggesting this is a way to increase students’ sense of belonging, help them change behavior to address anxiety, and build more positive feelings about our class.

Session Abstract: This session will focus on an alternative to exams that gives students ownership of course material, makes room for student creativity, and encourages academic integrity by addressing motivation for academic dishonesty and making it more difficult for students to find answers online. I will share my experience replacing Calculus tests with more open-ended, student-constructed review projects: students are asked to review the main topics, write and answer their own “exam” questions, and reflect on their learning. These projects give clear insight into student learning. At the same time, the format of the project removes some of the common motivations for academic dishonesty by reducing student anxiety, increasing student feelings of agency, outlining clear expectations, and giving students multiple ways to engage with the material. It also makes it more difficult for students to use unauthorized resources because the topics included in the assignment are highly course specific: they must know what topics were covered in class during this specific unit, and which topics the instructor emphasized and framed as most important. Moreover, since students are creating their own questions and writing their own reflections, they cannot simply copy answers from online resources. Many students report enjoying these review projects and mention in their reflections the feeling that they have learned more than they would have with a traditional exam. I have found this type of project to be successful in both remote and in-person settings.

Session Outcomes: During this session, participants will learn of a framework for an review project that can be used as an alternative to exams and is broadly applicable. More generally, we will discuss ways to write open-ended questions that showcase student learning and remove the temptation to copy someone else’s answer. We will also discuss motivations for academic dishonesty and how instructors can address them when designing assessments.

We study noncommutative function algebras as subalgebras of n-homogeneous C*-algebras. These algebras may be viewed as cross sections of certain holomorphic matrix bundles which arise naturally in noncommutative function theory and geometric invariant theory. We describe the connection between these algebras and bundles, and show that the function algebras we consider are Azumaya algebras.