By: Matt Stamps, Yale-NUS College
When Yale-NUS College reviewed the curriculum for its Mathematical, Computational, and Statistical (MCS) Sciences major in the autumn of 2018, I spent several weeks reading about mathematics programs at similar institutions. A common learning objective among many of the programs was a variation of “preparing students to become lifelong learners.” I really like this goal because, among many other reasons, it reminds teachers that students are human beings who have lives beyond their studies, and it reminds students that learning is not confined to the early years of one’s life. As I reflect on my life of learning thus far, I cannot help but notice how significantly the way I learn has changed since I was a student. Some of these differences arose naturally with changes in my circumstances over the years, while others could have been addressed while I was still a student.
In this post, I want to share some observations about how my approach to learning has changed since I started working as a professional mathematician, and how I have changed my approach to teaching with the hope of helping my students develop more effective and relevant learning strategies earlier in their mathematical journeys.
Interview with Ari Nieh, with commentary from Yvonne Lai
Like many of us, I began teaching online this Spring. Unlike many of us, I began doing so at the start of the semester. I am co-teaching a class at Michigan State, and I live in Nebraska. One of the most useful conversations I had in preparation for this assignment happened in 2013, well before the current coronavirus epidemic. The math department at the University of Nebraska-Lincoln had been considering a synchronous online version of a mathematics course, for rural teachers. I chatted with Ari Nieh, then an instructor for Art of Problem Solving, about what it would take to teach online, especially via chat forum technology. (Ari then became a lecturer in Writing, Rhetoric, and Professional Communication at MIT; and now he is a game designer at Wizards of the Coast.) In the end, that course was run asynchronously (and in many ways consistent with the advice given in a previous post). Nonetheless, much of the advice I received 7 years ago aged well. With Ari’s permission, I share snippets of our conversation in this post, edited for readability, and with commentary from present-day me.
Abbe Herzig, AMS Director of Education
In the midst of the upheaval due to the Coronavirus, students and faculty are transitioning to new virtual classrooms. Many of us haven’t chosen to learn or teach, but here we are, making the best of this new reality.
In this post, I describe some guidelines that may help students manage the transition to online learning as smoothly as possible. Instructors can support students by helping them to learn online, and I encourage instructors reading this to pass it along to your students. I offer these suggestions with a caveat: Some of these ideas may not be feasible for everyone, and that’s ok. We all have unique living, learning, and life situations, and what works for one of us may not work for others. Take what you can, and leave the rest. Keep realistic expectations of yourself, understanding that these circumstances are less than ideal. While the suggestions in this post are directed toward students, I also offer “teaching tips” to help instructors support their students.
By Abbe Herzig, AMS Director of Education
Many of us are experiencing stress as schools, colleges and universities move instruction out of the classroom. Fortunately, even if distance learning is new to you, it isn’t new, and there is a lot of wisdom to draw on.
This document describes some practical strategies that will hopefully get you started, along with some helpful web-based resources. From there, you can do a deeper dive by accessing the open community on MAA Connect called “Online Teaching and Distance Learning.” MAA members can log in with their member credentials, and anyone who creates a free profile can join this group. This is an extensive platform to exchange ideas with other faculty and to access resources and advice for developing your courses. The STEM faculty blundering through remote teaching in a pandemic FaceBook page is another great place for faculty to share ideas and figure all this out together. Continue reading
By: Yvonne Lai, University of Nebraska-Lincoln
Ray Levy, Mathematical Association of America
This is cross-posted in MathValues and Abbe Herzig has written a companion post. Additional resources and future meetings are also available here: https://tinyurl.com/OnlineTalkshop.
In times of crisis we need community. With schools, colleges and universities mandating online teaching and learning in response to COVID-19, often with only a week of preparation time, people are scrambling for resources and information. Dr. Ray Levy, aås Deputy Executive Director of the MAA, asked an online group whether they would like a Zoom space to discuss online learning. With only 12 hours of notice, Dr. Jeneva Clark helped co-facilitate, and 36 people gathered. The next day, with only a few hours of notice Dr. Abbe Herzig and Dr. Yvonne Lai joined as co-facilitators, and 86 people gathered. Below is some of what we learned in the second meeting.
By: Kristin Pfabe, Nebraska Wesleyan University
“I am sad this class is going to be over,” said one student. “What am I going to do with myself?” asked another during the last week of an Intermediate Algebra class that I taught last summer at the Lincoln Correctional Center (LCC) with Meggan Hass, then a University of Nebraska graduate student.
Meggan and I were sad, too. It’s not often that we hear these types of comments from students, but as I have learned, the unexpected can happen when one teaches in prison.
Here is my story.
It started with a visit by Bryan Stevenson, author of Just Mercy, to Nebraska Wesleyan University, where I work. Stevenson is a lawyer who defends incarcerated individuals, many of whom are on death row. In his talk, he urged us to:
“Get proximate. Get uncomfortable. Change the narrative. Have hope.”
I was sold. In the coming months, I put in a request to adjust my Spring 2018 sabbatical.
By: Edwin O’Shea, James Madison University
In Marilynne Robinson’s Gilead, Reverend Ames testifies that each person in his flock has “a kind of incandescence in them… quick, and avid, and resourceful. To see this aspect of life is a privilege of the ministry which is seldom mentioned.” I think this is a privilege of the educator too. But our flock’s life cycle, the fourteen weeks from the cradle of the first day syllabus to the grave of the final grade, has a different rhythm to that of a liturgical calendar.
In a semester where I have over 100 students, witnessing each student’s luminosity is challenging, and by the time I get to know even half of them the semester is likely to be halfway through. So I ask my students to help me to see them. I ask what their values are, to tell me about the work they’ve done and are about to do, and to share their hopes and aspirations as people. I ask them about the concrete challenges that they might face as the semester progresses and what they wish previous mathematics teachers understood about them.
I do this because understanding my students holistically aids in my support of each student individually and can cultivate active learning communities. I do this because if the semester gets rough on my end — it invariably does — I have a wealth of prior empathy and insight to fall back on so that my students succeed in their goals. I do this because knowing only their placement scores and/or GPAs is not enough! There’s also a body of research supporting that when students’ values are affirmed in STEM [i], they are more likely to succeed in that course and continue as a STEM major.
by Doug O’Roark
Executive Director, Math Circles of Chicago
The New York Times recently published an article entitled “The Right Answer? 8,186,699,633,530,061 (An Abacus Makes It Look Almost Easy)”. Its lead photograph features over 100 children seated at desks, facing forward, working individually. This is yet another in a long series of public relations disasters for mathematics. This depiction of mathematics is nothing new, and I most suspect readers experienced no cognitive dissonance in seeing mathematics represented this way.
Traditional Forms of Math Enrichment — and the Problem with Contests
Mathematicians collaborate to explore exciting open-ended questions. Unfortunately, this may be the world’s best kept secret. The problem? We have two major gateways to participation in the community of mathematics: the classroom and the contest. The classroom, of course, is universally familiar, and innumerable efforts have been made to improve the student experience in the classroom.
Kathleen Melhuish & Kristen Lew
Texas State University
“[Functions] are completely different, which is what makes this course so challenging.” – Abstract Algebra Student
Functions are hard for students, even students in abstract algebra courses. Even if students have seen the definition and worked with examples of real functions throughout high school and college, their understanding might be stretched to a breaking point when it comes to ideas like homomorphisms on groups or rings. Fundamentally, we might know students don’t understand functions, but the extent to which they don’t understand functions goes deeper than we might think. In this blogpost, we will share some insights from our projects on key places where students’ idea of function can be detrimental to learning concepts of abstract algebra, and what we as instructors might be able to do about this.
By Michael Pershan, St. Ann’s School
What do primary/secondary math educators think of the teaching that happens in colleges? And — the other way around — what do mathematics professors think of primary and secondary math teaching?
I’m nearing my tenth year as a primary and secondary classroom math teacher, and every once in a while I end up in a conversation with a graduate student or professor who suggests (politely, almost always!) that math education before college is fundamentally broken. A few weeks ago, a mathematician told me that PhDs are needed to help redeem secondary teaching from its “sins.” Once, at the summer camp where I teach, a young graduate student told me that there is simply no real math happening in American schools.
Well — I disagree! But how widespread is that view? And why does it exist?
The flipside phenomenon is also interesting. When a mathematician criticizes primary/secondary math education, primary/secondary educators sometimes lash back. Often we point our collective finger at pure lecture. Primary/secondary educators tend to think of pure lecture as uniquely ineffective. It gives the teacher no knowledge of whether students understand the material, and students no chance to practice new ideas in class. It is rarely used in primary/secondary math classes. Still, pure lecture was the main teaching mode in my own college classes, across subjects. We therefore bristle at mathematicians critiquing our work; “Let those without pedagogical sin throw the first stone!” I’ve even said this before, or something not far from it.
I have heard this “anti-lecture” critique expressed by some primary/secondary educators, but I wonder how widely held this view is. Is it held even by some math professors? And, in general, do primary and secondary educators tend to see flaws in the way math is taught in colleges?
In short, I wanted to better understand how mathematics professors and educators of younger students relate to each other’s teaching.