Split Classroom Teaching

What a great class today! My students have their outline for their paper due today. Their assignment was to bring in two copies of their outline for peer review. They had previously submitted their theses and thus I grouped the students by related topics. This was done so that they might benefit from the ideas and quotes presented by their peers. I then gave them prompts for how I wanted them to give feedback to each other regarding their outlines. Here are the prompts I gave them:

  • Rewrite their thesis in your own words
  • Would you describe the thesis as overly broad? overly specific? vague? controversial?
  • If the answer is yes to any of the previous questions, how can the thesis be improved?
  • Write one sentence per paragraph talking about each paragraph
  • Write briefly about how each paragraph will support the thesis
  • Rank each paragraph on how strongly they support the thesis
  • Are any of the paragraphs superfluous?
  • Can you think of anything missing from the paper? (A good quote for example)
I gave these prompts because the last time we did peer review I found that most of the comments the students gave each other were things like, “good job” and “I like your paper.” Comments that don’t help their peers become better writers.

The students then worked diligently on reading and responding to each others’ theses. This went on for most of the class period. With about 15 or 20 minutes of time left in class I noticed that a number of students were clearly done with the task. I had all of the teams who were finished come to the other side of the room and we had an impromptu discussion. I began by giving them the generic prompt of defining the liberal arts or what it means to get a liberal education. The students discussed this for a bit when one student said something on the order of,

I think school is an inefficient waste of time. Why do we spend four years learning extraneous things when we could finish with what is important in two? The only purpose is the degree anyway.

I immediately refocused our discussion on this comment. I didn’t want the students to think there was a right answer, so I removed myself from the discussion and let them talk on their own. I made it seem like I was going to check on the teams still doing peer review so I had an excuse to leave the discussion. After checking in with the peer review teams, who were working diligently, I sat down and admired my classroom. Half of my students were in small groups diligently peer reviewing outlines of their classmates and having great conversations about how to improve their papers. The other half was in a lively large group discussion about the purpose of higher education. All of this without me present in their conversations. I marveled at how well my students were engaged in their activities and how I could have two completely activities for my students to be doing in class based on their individual needs. To put it nerdily, *ding* I just leveled up as a professor. I always strive to individualize each student’s education as much as I can. Each student has different needs, goals, and interests. The more that I can address on a personal level for each student, the better their education. My next goal will be to attempt to have three simultaneous groups. The difficulty is keeping each group’s engagement in their activity, especially when I am not present.

Some notes that should be made.

  • I have honors students. I don’t know how successful this would be with non-honors students.
  • We have been spending time discussing what makes a good discussion and what are things they can do to improve their discussion techniques.
  • Our FYS topic revolves around education. This made the side discussion very easy to seem “on topic” with what our class is doing and not just something to fill the time.

Adjusting Class Activities from Formative Assessment

My colleague Bret has started a pedagogical discussion group. We meet roughly every other week to read some literature regarding pedagogy. This group’s formation is partially due to working on creating a new general education curriculum last year. A number of us appreciated reading the literature last year and wanted to continue in the process.

This week we met and read Black and William’s paper “Inside the Black Box: Raising Standards Through Classroom Assessment.” One particular idea I wanted to discuss from this paper was that a teacher should adjust the teaching and learning based on formative assessment results. I appreciate and agree with this idea. If I am finding that my class requires more time on a topic, needs a refresher on something, or they just need a break then I should provide that for them. I reflected on my own teaching and thought that I did not engage in this idea. For example, today in probability and statistics we talked about the probability model that describes the distribution of a sampling proportion. Now, we didn’t talk about that today because I deemed the class was ready. We talked about it because that was my plan. The plan was made this summer and I have been sticking to it. We need to cover this material so I am covering it. This troubled me.

What happened in class today? We began as we always do, discussing their daily homework problems that they do to prepare for the class day. I found, though, that they were being overwhelmed with the number of probability distributions they have been hit with lately. We have talked about Bernoulli trials, the geometric model, the binomial model, the normal model, using the normal model to approximate the binomial model, and now sampling distribution models. They were having trouble distinguishing between the models, when to use the models, what we need to use the models, etc. In a moment of clarity I decided to jettison the work I was planning to have them do in class today. Instead, I gave an impromptu mini-lecture summarizing all of the different models, when we use them, what we need in order to use them, essentially everything related to each model. In a sense, I was doing what Black and William were saying that I should do. I am happy that I was able and willing to respond to the needs of my students and provide what (I hope) they needed most. We will see how this plays out and whether it made a difference in their understanding.

Quiz Retakes

I have taught our introduction to probability and statistics course enough times that I feel very comfortable with where I am with the course. This allows me to focus on fine-tuning small aspects. One aspect of the course is that I give my students weekly conceptual quizzes. One conceptual question that is typically short and sweet. If you understand the concept, then it is easy, if not then it is quite difficult. The problem I have had in the past is that assigning grades to these quizzes has been difficult. Mostly, students either got it or didn’t get it. There was not an in between.

My colleagues here in the HAByss have allowed students the opportunity to retake quizzes and encouraged me to do the same. This has allowed for more freedom in my grading. I now grade the quizzes more in the style of mastery grading: Either you have mastered the concept or you have not. If a student has not mastered the concept then they get a certain number of additional opportunities to demonstrate mastery on similar quizzes in my office. This has the added benefit of generating more foot traffic in my office and having students meet and talk with me more.

Two things I want to think about more. I need to do a better job of explain how this system works for students. My students still don’t quite comprehend how retakes work or how the grading of the quizzes works. I think I need to create a small tutorial or video to help them understand at the beginning of the year.

The second thing I need to think about is what to call the retake quizzes. I want the name to convey the idea and purpose behind this. Retake quizzes or makeup quizzes emphasizes the student’s mistake. I want them to know that these are opportunities, not consolations or mistakes or anything like that. Suggestions welcome.

Bringing Inquiry Based Learning to CSB|SJU

Inquiry Based Learning(IBL) has become the new hot pedagogy in the math community. My colleague, Anne Sinko, went to a workshop years back to get training on IBL. Since then, she has been teaching regularly using IBL. She has also developed her own notes for our linear algebra course. I would like to learn to teach using IBL myself and moreover I would like more of my colleagues in the math department to teach using IBL. Over the last couple of weeks we have had conversations about this in the HAByss. We have come up with some ideas of how we might accomplish this.

Our first thought was to bring in an expert to run a workshop just for us. Potentially apply for an internal grant to bring an expert to the college for about a week and have them teach us. This idea has blossomed in a few different directions.

  • We should invite the rest of our department to this workshop. There may be others who want to do IBL in their courses, or at the very least understand the pedagogy that we will be using.
  • Could we open up this workshops to other disciplines on campus? Maybe focus the workshop to just STEM fields, but there would be a lot to be gained from the expertise in other fields. I recognize that each field has their own version of IBL with different names. We can bring together ideas and collectively benefit from them all. This may mean we need to work with colleagues in other departments to find experts from different fields to bring in, but it also means we could apply for different grants that are more broadly STEM focused.
  • Could we open this workshop to colleagues at other nearby institutions? I believe that in the northeast MAA section there is a group that do IBL together. They are kind of a support group for each other. Occasionally getting together to discuss ideas, get feedback, and improve as a whole. I would like to develop such a thing in central Minnesota or Minnesota as a whole. If we do this, then there are other grants we could apply for that are for multi-institutional ventures. Certainly worth looking into and gauging interest from neighboring institutions.

Here is the catch. We are a small group of heavily worked professors. We do not have the time at the moment to submit grant proposals and organize these grand workshop ideas. Anne suggested that we stick with our original small idea. See if we can get that off the ground first. If that works, then in future years we can look bigger. We will see if we even have the time and will to start that. I hope we do.

Team Teaching without Team Teaching

Last year my colleague Anne and I were slated to teach multivariable calculus at the same time. Here at CSB|SJU, multivariable calculus is not Calc 3. Our sequence is

Calculus 1 -> Calculus 2 -> Linear Algebra -> Upper division

Thus multivariable calculus is an upper division course with a prerequisite of linear algebra. We get a diverse group of students taking multivariable calculus as well, math majors, physics majors, econ majors, even some chem majors. Both Anne and I had taught multivariable calculus prior to this. Both of us had the same concerns from that first time, we don’t use enough linear algebra and the material wasn’t mathematical enough. Essentially, the first time we had taught it, we taught the course as roughly an advanced Calc 3. This doesn’t build on linear algebra and the motivation for a lot of the ideas comes from physics. This frustrated us as well as our non-physics students.

We decided to change how we would teach the course. The new course was based heavily on the book, “Vector Calculus, Linear Algebra, and Differential Forms” by Hubbard and Hubbard. Our course pushed more into the realm of differential geometry in order to ground the ideas in mathematics, instead of physics. Now let’s make it clear. I am an algebraic geometer, heavy on the algebra. Anne is a graph theorist. We’ve each seen differential geometry, but this was not our cup of tea. We would have our work cut out for ourselves.

We decided to essentially run the same course so that we could lean on each other when things got difficult. Same topics, same speed, same assignments, same everything(or most everything). What this meant was that each of our workloads shrank. If she made a video for class, I didn’t have to. When I made a quiz, she didn’t have to. We could spend less time on the tedious and more time on the material. We could spend more time grappling with questions like: What does this mean? What are good examples? How should we present this to the students? Etc.

After each class day we talked about how our classes went. What questions were asked? What is the student understanding? Where do they need more assistance? Sometimes a question would be asked in one class and not the other, but both classes needed help with that question. We would also discuss the upcoming material. A way that I like to describe it is that we better know level 3 understanding of the material because we teach level 1 and they might ask about level 2. Best to be prepared for anything.

So where is this long ramble going(maybe I shouldn’t write these Friday afternoon)? The classes went great! Anne and I ran a new course for us(so to speak) very successfully. What is more, neither of us feels like we needed to put that much work into it. Anne once said, we both put in 75% of the work of creating a course and got out 150% of a course. Each of us had our own strengths to bring to the table that would improve both courses. We both highly recommend doing courses this way. Along those lines, I spoke with another colleague of mine about teaching differential equations. My differential equations sorely lacks applications and his differential equations course has an abundance of applications. He liked the idea of roughly team teaching without team teaching.

One last tangential note. Anne and I discovered that there was a physics lab at the same time as my multivariable calculus course. This meant that all of the physics majors were in her class and I had most everyone else. So we taught the same course until the very end. Her last week focused on connecting manifolds, k-forms, and integrating k-forms into the classic language of physics, things like line integrals and flux. In my last week, we proved the generalized Stokes’ Theorem. By “we,” I mean me. And by “proved,” I mean we only black boxed one small piece.

End of Week One

I want to have a thought provoking post about some new pedagogy or some assessment technique. Unfortunately, I am exhausted. I always forget about how tiring teaching is over the summer and week 1 is always tough. Moreover, I met with every one of my first year seminar students individually. Worth the investment of time and energy, but I am drained. To all of you finishing your first week, cheers. Here is to another successful week next week.

Becoming a Reader

Many math teachers and mathematicians lament comments like, “I’ve never been very good at math.” There has been a lot of commentary about how it seems O.K. in our culture to openly admit to being bad at math, but not necessarily other subjects. You would never say, for example, that you are illiterate or read at a sixth grade level.

I am going to say that I read poorly. Or, maybe instead, I will say that I am not a reader. My earliest memory of my aversion to reading actually comes from kindergarten. We had enumerated books that we could read that would increase in difficulty. Once you finished book n you would turn it in to read book n+1. I remember turning in book 8, or so, at the same time my classmate was turning in book 41, or thereabouts. I was crushed. I remember not wanting to read after that and thinking that I was just a bad reader. Throughout my schooling I would purposefully not do the reading. I was on the fence between majoring in mathematics and history and decided against history simply because you have to read in that major.

Now I am a college professor and admittedly, not very well-read. That is rather oxy-moronic if you think about it. I have decided that I want to change this, however. I want to read more and, more importantly, not scoff at the idea of reading. Reading can be a joy and I want to work to remove the negative connotations that I have built up in my mind.

Here are some things I have done to improve:

  • Over the past couple of years I joined a couple of reading groups on campus geared towards professional development. Through these groups I have read and discussed “Teaching Naked” -Bowen and “In Defense of a Liberal Education” -Zakaria.
  • This year I am teaching a section of our first year seminar. This course has a focus on developing student writing, discussion skills, and presentation skills. This having been said, there is still reading involved. In preparation for this course this summer, I read “Mindset” -Dweck, “The Brief Wondrous Life of Oscar Wao” -Díaz, “What Does it Mean to be Well Educated? And More Essays on Standards, Grading, and Other Follies” -Kohn, “Shop as Soulcraft” -Crawford, and about half of “A History of American Higher Education” -Thelin. I also tried reading “The Republic” -Plato, but I couldn’t get into that nor see the value without a big investment of time.
  • To balance work with pleasure, this summer I also read “Thrawn” -Zahn and listened to the audio books “Ready Player One” -Cline, “Aftermath” -Wendig, and I am almost through “Bloodline” -Gray. What can I say, I am a sucker for Star Wars.

I would say that I have made some serious positive strides. This having been said, even today I had a tensing up moment at the thought of reading. One of my librarian friends is planning an event to bring author John Scalzi to campus and asked for advice for what to do with his visit. In the conversation I remember thinking, I should read some of his work before he comes. Immediately I felt defeated. I won’t read it. I don’t read anything. But this has to change! I will read. The first step is access. I have successfully just ordered “Redshirts” and “Old Man’s War.” They will arrive on Monday.

One thing that has helped me make a positive change is Dweck’s book “Mindset.” I am going to have to paraphrase, but one of her ideas is that if you want to change you have to think about the actions necessary to do so. Let me explain with an example. If you tell yourself you need to get into better shape and go to the gym more, you probably won’t go. Or you will quit soon. If, however, you carve out specific time in your schedule that you specifically will be exercising, then you are more likely to be successful. I have specifically put in my calendar that I am going to swim every morning from 7:30-8:30. So, if you want to make a change, make specific plans on what you will do to change. I don’t just want to become more well-read, I will specifically read “Redshirts” and “Old Man’s War” this term.

How Much Feedback to Give

Is there the perfect amount of feedback to give a student? Probably not. Is this because “more feedback is better” in which case there does not exist a finite amount of feedback that is best? I do not think so. If anything, I often think that less can be more in regards to feedback. I am not saying this to try and convince myself that I don’t need to write as much feedback. We should, however, keep in mind logistical constraints. We do not have the time and willpower to give all of the feedback we would like to every student.

I would like to propose a philosophy for feedback that I just discussed with my colleague, Anne. The amount of feedback to give an assignment is directly related to the quality of the assignment. For the purpose of this philosophy, I am considering an assignment to be sufficiently complex to merit such feedback, for example an essay. Let me elaborate, a student who receives one line of feedback on an assignment did worse than a student who receives a paragraph. This having been said, the student who receives less feedback is being given bigger picture feedback, e.g. “There is no thesis in this paper.” In comparison, a student who receives more feedback is being given more fine grained feedback, e.g. “The second point in paragraph three is not as well developed as it could be.”

A goal in giving feedback would be to give an amount of information to the student to learn and improve their work without overwhelming them. I want my students to be receptive to the feedback I give. This means that the critiques need to be manageable and often I need to offer suggestions of how the student can improve their understanding. Last year, I was assisting a number of different students in their abstract algebra and analysis proofs. Students from both classes were struggling with developing proofs for general properties, i.e. a cyclic group is abelian or a closed and bounded set is compact. Their attempts at proofs were riddled with errors of all sorts with little to no substance. The feedback I gave them was to play with more examples. That was it. I did not critique their proof structure, logical reasoning, grammar, or anything else. The students were not ready to work on those ideas yet and I did not want to discourage them with an avalanche of things they needed to work on.

Last year I inadvertently used this system in my own class. I was teaching multivariable calculus, an upper division course in my department. As part of my course I had assigned regular paper assignments focused on big picture reflection of the material. One particular paper I received stands out in my mind. It stood above every other paper I had received that term which became clear about halfway through reading the paper. I shifted my mentality on reviewing the paper from providing feedback to editing. After I finished, I looked over the paper, aghast. There were more red marks on this paper than the rest of the class combined. I couldn’t give this back to the student, she would be devastated. To ensure that didn’t happen I wrote up a cover sheet for her paper where I explained that the reason her paper was covered in red was because it was beyond the realm of big feedback. The paper did not require any major work, in which case we could focus on the small things (and there are always a ton of small things). I also talked with her before the following class to make sure that she understood. She did. I intend to make a policy in my writing course this year that more feedback means a better paper.

Where does this leave us? The proper amount of feedback varies based not only on the student but the individual assignment? That is the idea. How does this fit in our limited time as educators? Most students will only need one or two comments on their work. Make sure you focus on one or two big things that the student could work on. Less often will more feedback be necessary. How do I decide how much feedback to give to particular work, then? Think about the student and what they will perceive is within their grasp. Remember, the goal is for them to learn and often this is done through revision. Don’t give so much feedback that they don’t revise.

A few last thoughts on feedback:

  • Grades distract from feedback. Try to separate grades from feedback as much as you can.
  • Feedback should be focused on the work and not the student. “There is no thesis in this paper” vs “You did not include a thesis in your paper.”
  • Feedback should focus on how the work would be improved and not whether the work is good or not.
  • Feedback should be given when there is opportunity to improve. My colleague, Sunil, emphasizes to his students that his exams are not a single chance, but a process to show mastery and develop. He allows his students to come to his office after exams to review and revise their exams. The feedback he gives on the first attempt is appropriate since there is an obvious and emphasized developmental learning process.

Planning a First Year Seminar

There are three weeks between now and the start of term. This year, I am slated to teach our First Year Seminar(FYS). This is an intensive year long course intended to serve as the course that teaches students writing, discussion, critical thinking, critical reading, presentation skills, and all-around introduction to college. Talk about an important course!

As a mathematician, I feel like a fish out of water teaching what is essentially a humanities course. This having been said, I have bought into the liberal arts ideals. Writing is an important skill for students to develop. Reading is an important skill for students to develop. Just like mathematics is an important skill for students to develop. So I will take on this monumental task of preparing these students for college through an intro writing course.

The first step in preparing for FYS was selecting a topic. Most people who teach FYS choose a topic in their wheelhouse. Historians pick topics related to their historical research interests. My colleagues in theater have done theatrical themes. What can a mathematician do, though? There are not a lot of approachable books on the subject of algebraic geometry. I have worked heavily with the director of the FYS program so I can regularly ask him for assistance. His joking suggestion for my topic was calculus. Not very helpful, however, we had worked together on developing a new curriculum for the school over the past year and it hit me that education would make for a nice theme. I already have one foot in the door of education with my interests in curricular development and the scholarship of teaching and learning. Kyhl, the director of the FYS program, did help me pick a title, “What’s all this book-learnin’ good for anyway?”

I spent the summer reading voraciously to build a fuller understanding of the subject and determine texts I would want my students to read. I should say, I read as much as I could. In May my wife gave birth to our son, Finley, so I have been quite busy with learning how to be a father.

Fast-forward to now. I am happy with the four books I have selected for the Fall term: “Mindset” – Dweck, “The Brief Wondrous Life of Oscar Wao” – Díaz, “In Defense of a Liberal Education” – Zakaria, and “What Does it Mean to be Well Educated?” – Kohn. I have a rough idea for the four papers I want my students to write, two reflective papers and two argumentative papers (one with extra sources they will find on their own). The rest of my course seems to be coming together as well: homework assignments, presentation topics, discussion questions, etc. What helped me get here is the immense support I have received from a large number of friends and colleagues. A million thanks to all of them.

What is left to do? I am going to have the FYS director go through what I have so far to make sure everything seems appropriate. One of the most difficult parts of planning this course is determining the appropriate level. How much reading do I assign? How many papers? How long? Etc. The other big task to work on is the day-to-day nitty-gritty details that I need to start hammering out. Ideally(though I know it will not happen), the course will be all planned out on day one and I essentially take the course with my students. I won’t exactly get there, but I want to develop as much as I can. The most important thing, though, is that I still have my other class to prep for: Introduction to Probability and Statistics.

Three weeks… I can do it.

Welcome to the HAByss

There is a building at the College of St. Benedict called the Henrita Academic Building(HAB). The HAB used to be the academic building of the old St. Benedict’s High School, which closed in 1973. Through a few renovations, the building was given a number of classrooms and faculty offices. The original design can still be seen, mainly in the basement. The round cement gym’s walls are now the walls of subterranean classrooms. The locker room was used by duplicating and is now a room for MapCores women to hang out. My personal favorite relic is the old Fallout Shelter sign on the northwest stairwell. Located in this cold war era labyrinthine basement is half of the math department at the College of St. Benedict and St. John’s University(CSBSJU). We have lovingly and aptly named this space, the HAByss.

The HAByss is home to the “New Kids on the Block” NKOTB members of the math department, Drs. Bret Benesh, Anne Sinko, Sunil Chetty, and myself: Robert Campbell. The four of us regularly engage in pedagogical discussion in the HAByss. The goal of this blog is to synthesize and publicize these conversations. I hope to receive feedback and advice as well as spread wisdom. Each of the NKOTB have our own style of teaching, but collectively have experience with many pedagogies and assessment strategies.

I want to close with a wonderfully cheesy line I included in a letter of recommendation I wrote for Bret, “The basement of the HAB is a hive of pedagogical discussion.”