Linear Algebra I at the University of Toronto is a large course with around 7 sections of 200 students per semester. Recently all Linear Algebra I sections have switched to an active learning approach, with significant components of in-class peer collaboration and full-class discussion. However, the majority of instructors who teach Linear Algebra I are graduate students and postdocs with limited teaching experience and exposure to active learning teaching methods. In this session, I will share with you my program for onboarding instructors to teach an active learning course, that includes an instructor course design manual, peer observations and mock teaching sessions. I will also discuss the successes and challenges of these onboarding activities from a course coordinator perspective.

We will give an introduction to the philosophy behind mastery grading and share our experiences with this mode of grading across a number of STEM courses (Calculus and Linear Algebra) as well as its use in a large scale introductory General Education Statistics Course, where we are using mastery grading at scale. We have experimented with a number of different implementations and will share what we have learned in the process, in particular how to use this system in a set of coordinated courses with a group of instructors. We hope that you can take something useful for your own classes from this talk.

The Mathematical Inquiry Project (MIP) supports statewide faculty collaborationon inquiry-oriented learning in entry-level college mathematics classes. MIP activities beginwith faculty workshops to identify and characterize critical concepts in each entry level course, small collaborative teams to develop resources with guidance from the workshops and feedback from the broader community, regional workshops allowing more faculty to participate and share their expertise, and mentoring relationships to support long-term classroom implementation. We will discuss the foundationaldefinitions of the project and successes and challenges in nurturing a state-wide faculty community of practice around improving instruction and learning in entry-level college mathematics.

PIC Math is a course and program to prepare undergraduate students in mathematics and statistics to succeed in careers in business, industry, and government (BIG). Funded by NSF, PIC Mathincreases awareness among faculty and students about non-academic career options, provides undergraduate research experience using problems from industry, and prepares students for industrial careers. For the course, we have developed prepared materials for the course such as sample syllabi, a set of sample research problems from industry, sample student solutions to industrial research problems, and sample videos of students presenting their research. During the first three years of PIC Math, over 100 universities, 100 faculty members, 1400 undergraduate students, and 100 industrial partners have participated.

In this interactive presentation I will present a preliminary analysis of various artifacts associated with ‘lecture notes’ submitted by participants in a large-scale study of three textbooks written in PreTeXt, Active Calculus by Matt Boelkins, A First Course in Linear Algebra by Robert Beezer, and Abstract Algebra Theory and Applications by Tom Judson. For this analysis, I have provisionally defined lecture notes as a document produced with the goal of teaching a lesson for a specific topic. In the analysis we attend to the constitution of the lecture notes (the dynamic process of generating them and context) and their structure (nature of resources, roles, and relationships), paying attention to how textbooks mediate this work. While there are variations, there are many similarities across the participants, revealing that producing lecture notes is in itself a professional development activity through which the instructors acquire new knowledge, skills, and practices, even when those are not consciously recognized. Participants will be asked to think about and share their own process of lecture notes production.

PrairieLearn is a flexible, open-source platform for writing web-based questions that is in broad use for both homework and exams. We will show how PrairieLearn makes it easy to write questions that can randomize themselves, allowing students to practice repeatedly on different variants of a question, and to auto-grade so that students receive immediate feedback. In comparison to other question-asking platforms, PrairieLearn is highly extensible and permits instructors to develop and share new question components using standard languages such as Python, HTML, and LaTeX. We will demonstrate this flexibility with examples relevant to math education, including symbolic inputs, matrix calculations, graph sketching, and scaffolding activities for proofs. We will also show examples of how PrairieLearn can provide both formative practice for students as well as fully-automated exams when integrated with a computer-based testing facility.

In this very active session, participants will experience doing a mathematical activity in a remote synchronous setting. They will then use this experience to reflect on learning and teaching, especially in the current remote setting. Finally we will think about how we can use communities of practice like the Communities for Mathematics Inquiry in Teaching, COMMITs, to support each other in becoming even better educators.

This presentation will take the form of a brief tour of three parallel threads in recent work updating my freshman-level discrete mathematics course materials: (1) Explicit connections to secondary school content leverage common student experiences, promote communication within the class, and better serve majors pursuing teaching certification. (2) Computer-based interactions (retooled in HTML/JavaScript to be tablet friendly) provide support for an inquiry-based approach to students construct their own understanding of mathematical proof. (3) An extensive MyOpenMath library for discrete mathematics supports online assessment for all topics in the course. And of course, if it’s sunny in Pennsylvania that day, there will be 6 more minutes of presentation.

In a seminal paper, Nolan and Temple Lang (2010) argued for the fundamental role of computing in the statistics curriculum. In the intervening decade the statistics education community has acknowledged that computational skills are as important to statistics and data science practice as mathematics. There remains a notable gap, however, between our intentions and our actions. To understand that gap, together with Nick Horton, we assembled a collection of papers for a special issue of the Journal of Statistics and Data Science Education (2021) focused on what has changed over the last ten years with respect to computing in the statistics curriculum. Broadly, the collection of papers (1) suggest creative structures to integrate computing, (2) describe novel data science skills and habits, and (3) propose ways to teach computational thinking. My talk describes the special issue with particular focus on the last of the three aspects: the role of computational thinking: The computer as part of the thinking process and not only a tool for implementing mathematical theory.

Last spring, with the unexpected move to online instruction and colleagues reporting, “There’s cheating all over the place,” I opted to give oral exams to students in my ODEs and Math-for-Physics classes. Special circumstances (which I’ll describe) provided an opportunity to deliver oral final exams in the two multi-section Calculus-I courses I was coordinating.I’ll discuss the pros and cons of oral exams, making a case that, for an experienced instructor, the pros outweigh the cons, even for classes whose enrollments are as large as 50 students. I'll conclude by discussing my fairly positive experience this fall delivering common written exams through WebAssign to students in a multi-section Calculus-I course.

I will describe the development of a new classroom observation protocol, FILL+, which generates a timeline showing the type of activity taking place at each second ("lecturer talk", "student question", etc). This provides much finer detail about classroom practices than other protocols (such as COPUS, which notes activities taking place in 2-minute intervals). The timeline can be summarised quantitatively, for instance by computing the proportion of time spent on lecturer talk compared with other activities, or counting how often lecturers pose questions to the class and how often students respond. I will present some of the insights gained from applying FILL+ to recordings of 220 STEM lectures, including 94 in mathematics. A key finding was that the FILL+ protocol can be applied reliably by novice coders, following minimal training.

Only recently has there been research on what sort of mathematics training is actually useful to teachers. I will begin with brief survey of this research, for both elementary and high school teaching. I will discuss some recent results on how policy tends to be more consistent with these findings at the elementary level than at the high school level, and why this may be. I will conclude with some open questions about the mathematical preparation of high school teachers, and the potential role of mathematicians in addressing these questions.

Project-based learning can take many forms, from small challenges in a single class to longer assignments. Let's have a conversation. How do you develop problems that your students find meaningful? How do you handle individual and group aspects of learning? How often do you regroup for a mini-lesson? How do you structure assessment? What are important considerations for distance learning? I look forward to sharing some experience and learning from each other.

Now is probably as good a time as any, unfortunately, to argue for a first-semester Calculus course that begins with the S-I-R, or Susceptible-Infected-Recovered, dynamical system from epidemiology. I’ll describe how I use S-I-R to kick-start a course, that, eventually, gets to all of the usual Calc I stuff, and is richly satisfying to math geeks (like me) while still appealing to students who are perhaps less geeky, or geeky in different directions. This course is based on the brilliantly subversive, but wonderfully accessible, text Calculus and Context by the Five-College Calculus Team: James Callahan, David A. Cox, Kenneth R. Hoffman, Donal O'Shea, Harriet Pollatsek, and Lester Senechal.

This talk is co-sponsored by TPSE-Math.

Many institutions of higher education have transitioned to online teaching over the past few weeks in response to the novel coronavirus. As a result mathematics faculty are being asked to rapidly translate their courses from brick-and-mortar classrooms to virtual environments. These online modalities require faculty to reassess how they engage students. We faced a similar challenge five years ago when founding the Minerva Schools. In the time since we have taught hundreds of college students math in real-time virtual classrooms. In our experience, synchronous classes are most effective when students are actively engaging in well-defined tasks throughout the session. In this seminar, you will take the role of a student in a portion of a Minerva calculus class session. After the class simulation and debrief, we will have anopen discussion about translating active learning techniques to synchronous, virtual classrooms.

Because of the coronavirus, mathematics faculty are transitioning to teaching online. To help us all deliver the best learning experience, TPSE has drafted a list of the key strategies that every online course should incorporate. We will describe those strategies, and solicit reactions and feedback in the discussion.

Many of us are suddenly being asked to conduct the rest of this semesters classes online. How do we make this mode of instruction student-centered? How do we listen to students remotely? How do we poll them? How do we look over their shoulders at the work they are doing? How do we ensure equity in this technological regime? This special meeting of ESME will gather a panel to lead a discussion about these and other questions that many of us are struggling with.

Mathematics is a human endeavor. In other words, mathematics is done, taught, discovered and learned by people. All people have various identifying characteristics and experiences that affect how they interact with other people and how people interact with them. The identities of the people who are perceived as belonging to the mathematics community is important. Data will be presented about the diversity and demographics of the mathematics community in the United States, followed by a discussion of the significance and implications of the under-representation of certain groups.

Introductory ordinary differential equations is the most challenging sophomore level mathematics course for most science, engineering, and mathematics majors. Over the past decade it has evolved into a hybrid course involving large lectures, group work in smaller discussion sections, team-based projects, and on-line material in pdf and video format. The materials developed have also been used by a local community college and by a local high school AP class. It incorporates both formative and summative evaluation. We will describe the course and survey its evolution.

In this discussion, we will address common unspoken beliefs of math teachers that hold us back from improving our practice, specific group work facilitation strategies for college classes of up to 50 students, and the creation of group-worthy tasks.

There is a long history of engaged teaching in the Mathematics Department at Cornell. We will give an overview of two significant projects focused on Calculus 1: the Good Questions project and the Active Learning Initiative. We will give some of our preliminary findings about what has an impact on student learning. We will also discuss implications of our work for TA and instructor training.

In IBL, students learn through guided exploration with the help of experienced instructors. We engage the students and emphasize discovery, analysis, and investigation to deepen their understanding of the material and its applications. Students solve problems, conjecture, experiment, explore and create. These practices have been strongly supported by the CBMS, MAA, and the NRC. I will discuss inquiry based learning as we have introduced it over the last fifteen years at U Michigan, a bit about the history and the “struggle”, and their effect on both students and instructors. I will describe our training of instructors, especially postdoctoral fellows, assessment, the role undergraduates play as course assistants and our course materials.

Practicing basic computational skills and developing conceptual understand are two of the many things that happen in the math classroom. Using videos and online homework to 'flip the classroom' is a beginning, but more can be done to promote higher order thinking skills. The University of Minnesota is in its sixth year of a redesign of its Pre-Calculus curriculum that 'flips the formula'. Instead of the professor beginning with the generalization and passing the formula to students who solve specific cases, students now begin with specific cases and develop algorithms for general solutions

A war is on in probability and statistics: between the objective approach, a.k.a. frequentist or orthodox statistics, and the subjective approach, a.k.a. Bayesian statistics. For my sins, I find myself fascinated by fields where the unorthodox view is correct, so I made and taught an undergraduate course on "Bayesian Inference and Reasoning." I will illustrate, with many examples, several hopefully transferrable aspects of the course.

I will report on a still on-going project to develop and improve the largest linear algebra course offered by the Department of Mathematics at Illinois. This course is a (non-proof based) first course in linear algebra taken by more than 1600 non-math majors each year (the majority of these students are sophomores and juniors whose major is in engineering). The two main goals of this redesign are to increase the active learning component and to identify applications and develop activities that showcase the power of linear algebra. Discussing both successes and failures, I hope that the experiences I have to share, prove useful to others who are redesigning/re-imagining large service courses at (large) universities.

In this workshop/lecture, we’ll explore ways to structure in-class learning activities: how we might lead an IBL activity, or even an entire IBL course. In addition, we’ll learn how the speaker wound up using IBL to teach a class on isomorphisms of quotient groups in a bagel shop.

Interactive Engagement in the classroom can take many forms: Inquiry Based Learning, Think-Pair-Share, Flipped classrooms, and more. And beyond being a totally trendy pedagogical innovation, interactive engagement increasingly has demonstrated improved outcomes in student learning and retention of mathematics and science. This workshop will attempt to help participants increase their ability to put theory into practice within their own courses.

Calculus is often said to be the most difficult class in which to implement inquiry-based learning (IBL) techniques. There are questions of class coverage, larger class sizes, and the mathematical maturity of the students taking calculus. Instead, IBL is historically known to be used in upper-division mathematics courses where students are responsible for generating proofs with little to no help from the professor. In this seminar, I will discuss ways to successfully incorporate IBL into the calculus classroom. A variety of techniques will be discussed ranging from adding short active learning strategies into a lecture based classroom to a classroom where little to no lecture is given by the instructor.

Undergraduate mathematics education today faces a number of challenges and difficulties. One way to address these challenges is to build on promising theoretical advances and instructional approaches, even those not originally developed with undergraduate mathematics in mind. The Inquiry Oriented Differential Equations Project (IODE) is one such effort, which can serve as model for other undergraduate course innovations. In this presentation I describe central characteristics of the IODE approach, report on results of a comparison study, and provide an overview of the modeling sequence that leads to the emergence of a bifurcation diagram, a surprising and illustrative example of student reinvention. The overview and examples of student work tendered offers a fresh perspective on modeling and how an inquiry-oriented sequence of tasks can lead to the reinvention of significant mathematics.

I've used history to motivate and organize introductory real analysis and Lebesgue integration. This talk will explain how it should be used to improve calculus instruction. The standard order of the four big ideas—limits then derivatives then integrals then series—is all wrong both historically and pedagogically. In addition, the standard models for derivatives and integrals, slopes of tangents lines and areas under curves, also throw obstacles in the path of many students. Drawing on history and recent research in undergraduate mathematics education, I'll make the case for calculus introduced first as problems of accumulation (integration), then ratios of change (differentiation), then sequences of partial sums (series), and finally the algebra of inequalities (limits).

In 1997, Virginia Tech dramatically changed how they taught lower division mathematics courses. They abandoned lectures and created a 500 seat “Mathematics Emporium” computer lab where students learned calculus and linear algebra assisted by software together with individualized input from teams of graduate students. Success rates soared and instructional costs plummeted. Other institutions soon adapted this model to their own needs with similar success. Emporiums, large and small, sprouted all over the country. They became popular for teaching remedial mathematics, often in highly modularized formats. A commonly reported outcome was a 25% increase in student success rates along with a 25% reduction in instructional costs. Most Emporiums were instructor-centered, driven by MyMathLab software, with students progressing through the curriculum lock step as a cohort. At Kent State we took a different, more student-centered approach. In 2010, we created a 250 seat Emporium driven by adaptive, “artificially intelligent” ALEKS software. This builds and constantly updates an accurate representation of each student’s “knowledge space.” It allows students to choose individualized pathways through the curriculum and to advance efficiently, focusing their efforts primarily on learning what they don’t already know. We’ll discuss how and why we set up our ALEKS Emporium, describe a variety of positive outcomes, outline a recent radical metamorphosis, and situate everything within an emerging national agenda.

The Illinois Geometry Lab (IGL) was founded in 2011 to promote undergraduate research and community outreach in the Department of Mathematics at the University of Illinois. From modest origins, the IGL has grown substantially: Spring 2018 witnesses nineteen IGL-sponsored research projects involving over 80 undergraduates and 23 graduate students. The IGL has also quickly become the premier departmental organization focusing on engagement with and outreach to community organizations and schools. I will discuss the IGL’s history and modus operandi, and the challenges and rewards of administering a large-scale undergraduate research enterprise within a research-oriented public mathematics department. The IGL partners with a number of similar undergraduate research labs across the country as part of the umbrella organization Geometry Labs United (GLU). I will briefly describe GLU’s vision for a nationwide network of experimental research labs for undergraduates in the mathematical sciences.

Active learning has many documented benefits both for students and instructors. Moreover, there is increasing evidence that it disproportionately benefits women, students of color, and students who previously denied the same learning opportunities as others. However, the empirical evidence for this disproportionate benefit doesn't explain why it happens, nor does it guarantee that all students will benefit from active learning. In fact, my own experience with active learning is that it is difficult to do well and sometimes it can have detrimental effects on students if we're not careful. So, we should aim not just for active learning, but learning that is both active and inclusive. We'll discuss some principles and practical strategies for making active learning more inclusive. (If you are able to, please watch David Pengelley's EMES presentation on active learning before this session.)

We discuss a dozen years of experience in course development with an aim of changing students' perceptions of what mathematics is and what success in mathematics classes ought to entail. Key components are identifying important common student misunderstandings and designing activities, often in-class, to address those, and aiming for authenticity of student practice. We share ground-up (re)design of three courses: introduction to proofs, math for preservice elementary school teachers, and mathematical modeling in preparation for college algebra, the latter of which has very positive though small-population data which indicates some success. We end with discussion of the challenges presented to campuses in trying to strategically implement such practice-focussed courses.