By Chuck Pearson, Tusculum College, Tennessee
I honestly don’t remember the point in my teaching career when I realized how hard mathematics was for most of my students.
It’s not that I’ve ever been especially brilliant at mathematics. Sure, I can do a great deal of number crunching in my head without a second effort. But when the vector calculus or the differential equations got too sophisticated for my calculations in my own graduate research, I just looked for somebody else’s software or algorithm and twisted the mess out of it to make it do what I wanted it to do. I could handle the rudimentary stuff. I was horrible at setting up any integral but the simplest, for crying out loud. I knew the guys in my discipline who could handle the hard stuff and who were on another plane, and I wasn’t one of them. Surely I’m the guy who can relate to students who fight the mathematics.
But when I started teaching algebra-based physics at the two-year school in the Georgia swampland, and I had my first instance of a student who simply couldn’t handle solving v = v0 + at for a, I had to take a step back and wonder how to bridge the chasm. When I had the first student who simply couldn’t wrap their head around converting centimeters to meters, I had to take a couple of more steps back.
And lest you get too many suspicions about that two-year school in the Georgia swampland, when I moved to the private, four-year Baptist college, the math difficulties among the students starting the physics sequence redoubled. Same at the regional four-year STEM-centered university in Tennessee. Maybe the folks at our elite institutions don’t have to deal with students who fight basic algebra coming into taking our physics and chemistry courses. Most of us on the front lines deal with that day-in and day-out.
We can have discussions in every direction about what this means about the quality of our secondary school graduates, and those debates don’t ever seem to end. Those of us in long-neglected rural areas or in blighted urban areas find ourselves dealing with underfunding and underresourcing in the schools that provide the bulk of our students, and the support and outreach that is necessary to help those students and their teachers raise their level is different topic, perhaps even a different patchbook.
But the simple fact of the matter is many of us hold our advanced degrees because of our unique passions or uncommon aptitudes. And when we land our teaching roles, when we take responsibility for the education of first- and second-year college students especially, our primary audience becomes students who never have shared those passions, and who have a completely different set of aptitudes than those that got us our graduate degree. We have to adapt.
I’m not going to try to approach this from a scholarly perspective (although scholarship on the high school/college transition exists, especially for my part of the world) but I am going to lean on my own experience across multiple types of institutions over the past decade and a half to describe what has worked for me in a fashion that’s most portable to you in your circumstance. Most of what I’m describing applies specifically to learning in the physical sciences, but there are paths to applicability across the academic disciplines as well. (Because this is going in an open patchbook, there’s also an implied openness to editing to improve applicability; please don’t hesitate to contact, collaborate and even edit to make this narrative fit your needs!)
ADOPTING A DISCIPLINE OF NAMES
I wrote up one of my first philosophy-of-teaching statements when I was a graduate student at Ohio State. In its text was this statement:
The single most important thing I do with a class each quarter I teach is to learn each student’s name, and call them by that name. This is a ridiculously simple thing to do, but on a campus of Ohio State’s size, a student will be totally taken aback and pleasantly amazed by this simple gesture. People want to be recognized; they are turned off in an environment where they are treated like a face in the crowd, and receive a morale-boost when they are personally recognized and treated as if they are important. Basic courtesies like this work wonders in improving the morale of a classroom, and in building strong human relationships between the teacher and the students.
Honestly, I made this “commitment” somewhat selfishly. Being able to walk across The Oval at Ohio State and have a student recognize me and call me out was something of a thrill for the guy who was the Grade-A antisocial nerd in high school. There were precious few TA’s who gave a damn about their students (or, at least, so egotistical me thought); I’m going to make sure my students know I know who they are. It went okay for me. I got a few bonnets for it. It was a good time.
And then I took the job at the small two-year school, and I just maintained that commitment to learning students’ names because of course…and I was floored when one student told me I was the first prof they’d had who made it a point to know them by name and call them by name. And they’d been on campus a full year.
And I kept getting comments like that, across my career.
There is an old teaching cliché that goes “Students don’t care how much you know until they know how much you care” that is stupid and trite and overdone and, in my experience, totally true. That single discipline of knowing my students’ names created so many bridges and gave me credibility I might not otherwise have achieved.
LISTENING TO STUDENTS EXPLAIN THE SCIENCE
I always thought I did a reasonably good job of listening to my students throughout my career. After all, I got a whole lot of orientation to using the Socratic method in the laboratories I taught (and it followed on with learning about inductive Bible study methods in my undergraduate campus ministry; if Socratic questioning was good enough for the campus Jesus people, it surely was good enough for me). However, especially as I was learning how to teach physics and chemistry, at the moments I wasn’t confident enough in my own explanations, I started feeling like Socratic method was a little bit of a cop-out. It wasn’t me giving a student a chance to explain an idea to me; it was me failing to deliver my own rigorous explanation.
As professors, we are always tempted to be the “sage on the stage” and to make proclamations about fact and truth from positions of authority. This works right about as far as a student needs to learn specific stories and regurgitate those stories. Science isn’t about that, obviously; a student is observing the world around them, is observing a specific phenomenon, and is crafting an explanation for that phenomenon.
The goal is not for the student to mimic your own explanation; the goal is for the student to arrive at their own accurate explanation. That’s not something that happens without intention. That’s something you can make specific plans to develop in the way you organize a class meeting or an assignment. But that requires listening to students in the moment. Feedback isn’t just helpful with a graded report or exam; feedback is useful in the moment, in dialogue with the student where you say as little as possible and you put the student in position to say the most.
It needs to be mentioned that one of the most challenging and rewarding experiences in listening to students I’ve had has been working at Tennessee Technological University, teaching algebra-based physics classes in the LEAP (Learning Environment for Algebra-based Physics) curriculum developed by faculty in the Tennessee Tech physics department. The curriculum gives students the opportunity to develop the core ideas of classical physics through experimentation and observation, and consistently starts by asking students to discuss, with one another and with the class as a whole, the “initial ideas” they hold about the science prior to making the observations that they’ll use to draw scientific conclusions.
I had never listened so intently to student ideas as I did in a structure that was intentionally designed to have students interrogate their own (possibly misguided!) preconceptions about science up-front, before actually exploring the science. Physicists have textbook examples of misconceptions about scientific ideas, and often student misconceptions fit in the textbook examples. But often, those misconceptions are unique and require unique responses. What’s more, those responses aren’t always most effective when they come from my voice of “authority”, but from a classmate who has had a different experience and who has explored ideas in a different way.
Allowing students to draw their own conclusions from their own observations, when planned with deliberate emphasis on student voice, is more effective than a student being told what the correct conclusion should be. We have result after result in the research into science pedagogy that tells us this.
SHOWING WILLINGNESS TO ADAPT ON THE FLY
So we can construct very tight curricula that guide the student through a set of topics in lock-step and in a very programmed fashion, so that we can ensure that every student in a program covers the same amount of material. That’s the fairest way to handle things, right? We want every student to cover as much content as possible, right?
Sure, if you know that every class is the same.
There are a host of reasons why classes don’t go the way you intend for them to. You may have had expectations about prerequisite knowledge the students should have had that they never received – or, more common, they’ve had all the prerequisite courses and they even remember covering what you think they should have covered, but then nobody remembers the idea they need at just this moment and what should be automatic takes far more time than you planned. If it’s a lab course, the lab prep may fail. Or one piece of equipment you thought was at place X isn’t. Or your preparation went perfectly but none of the student preparations do. Or the class might not get along with one another. Or the class might not get along with you.
Not only have all of these things happened to me, all of them have happened to me this year.
We need to have outcomes in mind for the work that our students do in a course, and we need to plan for our students to meet those outcomes, particularly if we know that our students are going to be tested over those outcomes at a later point (and particularly if that test is their entry path to a profession that’s deeply important to them; professor, your pre-meds matter). But getting some outcomes completed in a class that veers off course is more important than stubbornly sticking to your plan and overwhelming your students into failure. You want your students to have an accomplishment they can claim when the term is done, something they can look back upon and recognize the importance of.
Listening to students means not only recognizing when they do or don’t understand, but recognizing when an explanation or a method isn’t working and you might just need to start over, or recognizing when a more fundamental idea isn’t understood and you need to backtrack. If it’s necessary, do it. Blow up your plans and reset midterms if that’s necessary to allow your students to claim a win. If you know that the trust is there, ask your students for suggestions on how you can shift – and, if you ask, listenand follow through on their requests.
For many of us, the thought of giving up control over our desired outcomes for a class is terrifying. It might feel like changing your plans is irresponsible; it might feel like letting an outcome fall to the side is impossible to consider. And I certainly don’t want to confuse making an adaptation to a class with lowering expectations or giving up on goals – although a specific set of circumstances might make doing one or both of those necessary (as anybody who’s taught through a semester of snow days can attest – especially when the learning requires experience, if students can’t be together in groups or in the lab, you lose the capacity to do a lot).
But you have to believe that your students really are in the class to learn. They might be fighting their tendencies towards laziness or shortcuts, but they retain curiosity; they retain the capacity to wonder. It’s worth taking the time to get to know your classes and working towards teaching in ways that unleash that curiosity and wonder.
And those ways won’t necessarily be the same generation to generation, or year to year, or even day to day.
REMEMBERING THE SUBJECT MATTER IS DIFFICULT
It won’t even necessarily be the same from student to student. Everybody who teaches a bit of science wants those students who have been fascinated by science from kindergarten, who has chased every last ounce of mathematical understanding, who will always be awake and excited the moment you say the word “now, let’s consider this system…”
It’s not going to happen. It’s not going to happen even in an upper-division course, let alone a freshman course that counts for general education credit. In the room with those strivers who will always get their A are students who have been persuaded, over the course of their entire schooling, that math and science are hard and walking into this class is one of the most intimidating things they will ever do.
There is a narrative that dominates a lot of these discussions that faculty have with students, and that narrative demands that the student accept that the difficulty is a matter of perception. With a certain level of effort and concentration and patience, the story goes, all of this material is accessible to any student and the difference between success and failure simply comes down to the character of the student.
I firmly believe that narrative is a lie.
Much of the material I teach is centered around thermodynamics, that discipline that deals with the nature of temperature, the transfer of heat and the spontaneity of physical processes. There are a ton of definitions I have to put in front of students to introduce the formal nature of the discipline. There’s heat and work. The sum of heat transfer and work done typically gets its own symbol, change in internal energy. Then there’s enthalpy change, which is the transfer of heat at constant pressure. And then there’s free energy change, the energy that defines the spontaneity of a process, which is typically put in front of students in the form of Gibbs’ definition – although when you study deeper, you find there are competing definitions of free energy, one from Gibbs that focuses on constant pressure circumstances and one from Helmholtz that focuses on constant volume.
All of those represent energy changes. All of those are measured in the same units. But they all describe very different things. And they take different symbols when they appear in mathematical equations. Work is simple enough – w. But heat is described with q? Who ordered that? Internal energy gets U? Enthalpy gets H? And what’s with this delta that keeps running around everything? The professor keeps saying it represents change, but why do U and H change and w and q don’t?
So two equations get put in front of students in their second semester of freshman chemistry (ΔU = q + w, ΔG = ΔH – TΔS) that have to be interpreted like a foreign language. And they get applied to systems of gases that the student typically never has had reason to consider.
You might say “hah, lucky for me I don’t have to do anything with thermodynamics, I just got through my general chemistry and I was done.” But here’s the thing – none of those ideas happened by accident, none of those symbols were chosen just to confuse the freshman, none of the examples were provided just because of the professor’s convenience. Thermodynamics is difficult to understand, and years of developing and refining the ideas means these are the ways we’ve come up with that are the easiest for students to understand at first approach.
Here’s the other thing: if you found those ideas twisted and tangled, every emotion you had going through those paragraphs were the same emotions I had studying human anatomy. I have a PhD in molecular biophysics and I ran pell-mell away from any organ-system physiology as soon as I could because there are just too many weird bones and muscles and organs and trying to decipher how they connected to one another was just too much. I tell pre-med students that and some of them boggle, because that’s the very subject matter that gets them the most excited for their years of study ahead.
Ultimately, we have to recognize that we are different people, who are motivated by different things, and some things will come easier to some of us and other things will come easier to others of us. Most of us teach a single subject, or have responsibility for a very narrow discipline. Those students who struggle with what we teach will often thrive somewhere else.
Instead of drawing conclusions about our students’ capacities based on a single subject we teach, we need to work off the assumption that we teach talented students and we need to refine how we communicate ideas in order to provoke understanding in as many of those students as possible.
REMEMBERING IT’S NOT JUST ABOUT THE SUBJECT MATTER
There is a broad theme in this patch, and it’s that for our students, there’s so much going on beyond just the experience in our own classrooms. And never has this been more true than in 2017. The economic pressures on our students are immense, and only getting more so. The pressures in the relationships our students have – family, friends, work, even romantic – are constant and constantly changing. I’m still a relatively young faculty member, and the media these students are exposed to bear no resemblance whatsoever to my pre-Facebook and Twitter world, let alone the pre-Snapchat and Instagram world. Many of us were able to pursue our studies in isolated, focused settings that our students literally have no chance of experiencing.
So much of the undergraduate experience I had has no connection to the experience my students have now. There is, and always will be, a core of student who knows exactly how to go away from the world (and, bluntly, who has the resources to ignore all the other pressures and hide away) and learn on their own terms. Frankly, I was never that student myself; there were too many other things that interested me, and that I chased after. The capacity to seek out distractions is only amplified among these students, and the availability of those distractions is all but instantaneous.
And yet, I said it before and I still believe it: we still have interested students. We still are surrounded by people who want to learn.
We have to give up our own experience and do whatever we can to hear our students’ experiences. In many cases, we can even share in those experiences. Do your students play varsity sports? Go to a game and watch them play. Are they involved in campus theater? Go watch a performance. Do they paint or sculpt or photograph? Go to an exhibition of their work. Are they part of a board game group? For crying out loud, board games are fun. Jump in. In every experience, I’ve never heard a student tell me they wished I wouldn’t have come to an event they were involved in; sometimes, I’ve been stunned at just how welcomed and appreciated I was. Again: our students want to be known, and recognized for who they are.
If we don’t listen to and understand our students’ voices, if we don’t recognize the fullness of their lives, we miss all kinds of opportunities to meet them at their point of need – and we miss the chance to welcome those students into the fullness of learning.
We do have plenty to offer our students. Some of that is even knowledge.
Kudos to the people of the Fleming College Learning Design and Support Team for the idea for this project; all gratitude to Terry Greene for kicking me through this. Thanks also to the new friends in the open education community I’ve made over the course of this past year, the names of whom are simply too numerous to mention fairly; if I’ve talked to you for anything more than a few minutes this last year, your ideas have worked their way in here somewhere.
The frustrations about teaching about internal energy and enthalpy were worked out and written down in my physical chemistry classes at Shorter College (of Rome, GA) starting in Fall 2005. There’s a paper in them somewhere.
The LEAP project at Tennessee Tech owes much of its pedagogical thinking to Steve Robinson and Paula Engelhardt; the level of learning that this late-career faculty member took from them made my two years there the equivalent of my second postdoc. I’ll always be grateful not merely to them, but to my colleagues in the Tennessee Tech physics department (especially Adam Holley, Mustafa Rajabali, and Mary Kidd) who put flesh and bones on these ideas not only through conversations, but through their example in the classroom.
Most of all, I’m so grateful for the privilege of the students I’ve taught at Ohio State University, Middle Georgia College, Shorter College, Virginia Intermont College, Tennessee Tech, and now at Tusculum College over the course of the past two decades and change. I hope I’ve listened to you well.
featured image credit: “donkey’s ears” flickr photo by Jeanne Menjoulet https://flickr.com/photos/jmenj/9613683203 shared under a Creative Commons (BY) license