Jeff: Reflections and Moving Forward

Jeff Shriner is a graduate student at the University of Colorado at Boulder.

As a reminder, I taught 2 sections of pre-calculus in the Fall semester — one evening class meeting twice weekly for 2 hours, and one online class. I aimed to keep the courses as consistent as possible, but there were some key differences due to the different formats. Please refer to Jeff: The First Inning for some more details about the main methods I implemented in an effort to engage students in each of these classes.

In the weeks since the end of the semester, I’ve spent time reflecting on what went well, and where I would like to grow. I will say that my overall ‘feeling’ about the semester as a whole is very different than previous semesters that I’ve taught. Previously, my sense about a course throughout the semester was more-or-less constant; generally, the semester felt smooth and agreeable. This semester, my sense was much more erratic, filled with peaks and valleys. I think some of this is due to the fact that I was trying many new things. But I think this also illustrates the nature of how we learn, which lecture hides, and IBL techniques emphasize.

In the following, I’ve summarized my reflections on what went well (and what I believe contributed to this), and the areas I’d like to grow in for next semester (and the actions I plan to take to achieve this).

What went well:

  1. Increased student-to-student interaction. Students were talking to each other about the material more, by far, than any other course that I’ve taught. The two strategies that contributed most were think-pair-share questions/exercises which I embedded into lectures, and weekly small group problem solving sessions for assigned homework problems.  The latter was something that I actually was nervous did not go well most of the time, because it felt messy. To my surprise, this activity was mentioned in multiple end of semester feedback forms as a favorite. Students said that they appreciated the space to talk with classmates in a low pressure environment. I also learned about an unintended benefit from one of my international students, who said he appreciated this time because he was able to practice his conversational English skills.
  2. Modified perceptions about what math is and what it looks like. Because our course structure was based on interacting with each other and effectively communicating our ideas, students could see math as a creative process in which we experiment and ask questions. There were students who were noticeably more comfortable at the end of the semester asking questions and attacking a new problem that they didn’t know the answer to right away. One student told me confidently at the end of the semester that he was ready for calculus — he didn’t say this because he aced the final exam, but because he better understands the mathematical process, and is not intimidated to approach a new concept.

Areas for growth:

  1. Providing clear spaces for productive failure. If we tell our students that they learn by making mistakes and that this is part of the mathematical process, we must give them space to do this and not be penalized. I did provide some spaces to make mistakes, but I think I need to provide more, and also make it explicit to my students what these spaces are. Specifically, I plan to
    • Implement a 2 week cycle for written homework. I previously  used a 1 week cycle: homework problems were assigned, due a week later, then returned with a grade/feedback. My intention was that students would take the week to ask questions, struggle with the problems they found difficult, and submit a final version; but this did not happen nearly to the extent I was hoping. I think part of this is because they don’t know what they don’t know. I plan to add an extra week to this cycle, in which they have time to ask questions and correct problems that they misunderstood the first time around.
    • Emphasize group work/presentations as spaces to make mistakes. This is one of those things that sounds really simple, but I think can make a huge impact. I think I need to simply say ‘It’s OK to make mistakes here’ more often, giving them permission to explore their ideas without knowing whether they’re ‘right’ or ‘wrong’.
  2. Moderating full class discussions. I found this extremely difficult to do effectively. It was hard to get more than a small core to participate, and it was also hard to keep them from looking at me whenever anyone asked a question. I plan to
    • Formalize class presentations. Students did get to the board, but it was always informal. Because of this, there wasn’t enough investment in what they were doing, and there wasn’t enough diversity on who went to the board. I plan to make presentations a requirement (something like one presentation per exam) to get everyone involved, and also hopefully make everyone more prepared to have a productive discussion. I will identify specific written homework problems which are candidates for presentations.
    • Improve worksheets and discussion board prompts. One of the contributors to my problems in this area was just bad content. There were certain worksheets and discussion board prompts (for my online course) that just didn’t work the way I envisioned. I plan to do a content review and try to update the activities that didn’t work.

As always, I appreciate feedback and suggestions for improvement!


Jeff: The First Inning

Jeff Shriner is a Graduate Student at the University of Colorado

I suppose I should begin by explaining my title. I played baseball for most of my life up through my early 20’s, and have always admired many things about the game. Given that we’re currently in the thick of the post-season and my Chicago Cubs (I was born into Cubs fandom) are still giving me hope, I could not resist a baseball reference. I could probably write a whole post on the lessons we can learn by drawing analogies from the game of baseball, but I’ll spare you and discuss just one.

Pitching has always been my favorite position on the field, and one thing I learned as a pitcher was that in order to be successful, I had to grow with the game. That is, I could study hitters as much as I wanted to before a game began, but I always had to be ready to adapt and change that plan depending on what was actually happening in the game. This has also been my experience with IBL. I spent numerous hours this past summer thinking and talking with experienced instructors about best practices and methods that have been successful for others in the past – I came into this semester with a thoughtful plan. But the moment anything in my plan was not working (or was not working as I had envisioned it should in my head), I was fairly quick to become discouraged. It’s very difficult to leave this mindset that if I don’t get it right the first time, then I must be failing (which is an important reminder as we try to guide our students into a productive failure mindset). This is where my analogy helps me personally – I’m currently in the first inning of my journey. I must give myself space and time to grow into IBL – not just what studying film says should work – but what actually works for me.

Now that you all know where my head’s at, here’s what I’ve been learning so far (I am teaching 2 sections of Pre-calculus):

Like so many others, for my buy-in on day one I used Dana Ernst’s setting the stage activity. Also like so many others, it worked really well! It really is as simple as asking some basic (but important) questions and giving space for students to respond. Our students care about these things, and this is a great conversation starter on day one.

I’ve been trying to make heavy use of group work and think pair share activities. At the end of group work, I try to get a full class discussion as often as possible to summarize main points. Leading an effective classroom conversation in which I am not in the center is very, very hard. Like Jessica, my students still look to me as the expert in the classroom, probably because I have a very hard time shutting my mouth. I have a small core of students that are eager to participate, ask questions, and engage, but I’m having trouble getting everyone in the class to be engaged.

I’ve been assigning weekly writing reflections, in which I ask students to respond to the following:

  • What did you learn this week?
  • Can you think of any connections to previous material, or anything outside of class?
  • Has what you learned created any new questions or topics that you’re curious about?
  • Do you have any general questions or concerns about the course?

My motivation is simple: I want to give students space to stop and think about what they’re doing. I know I’ve gone through classes without doing this at all, and would have benefited greatly by just pausing periodically to paint the larger picture in my head of what’s going on. These have elicited some great responses. But I’m having a similar issue here: a small core of students respond thoughtfully on a consistent basis, while others don’t take it very seriously (or don’t submit a response at all).

One of the main themes we consistently refer back to is that mathematics is roughly “good ideas + effective communication”. We had a discussion recently in class about the millennium prize problems. They were shocked at first that there were actually million dollar prizes on math problems, but seemed to be very intrigued. We talked about how many people submit solutions for these problems but don’t receive the reward – in some cases because they’re wrong, but in some cases because no one knows if they’re right or wrong. They might be very clever, and have some very good ideas, but they cannot communicate them so another person can comprehend them. This tangible example has really helped with the buy-in on why we’re picky on how we communicate, and why it’s important. This has been very helpful in classroom discussions and providing feedback, as we’ll often say things like “all of the good ideas are there, but let’s discuss how we can communicate this more effectively”. I like rewarding their efforts and creativity, while still being able to nudge them to improve something. This is what I consider to be a main success so far in the semester – my students are thinking about the communication aspect of mathematics, and why it’s important.

One of my sections is an online format. In this section, my main efforts to engage students are

  • embedded exercises throughout the lesson (I create Livescribe PDFs with a smartpen) in which I ask them to pause to take some time to struggle with, then come back to the lesson to work through it. They turn in their work ‘portfolio’ (mistakes, corrections, everything) weekly.
  • discussion boards with prompts that are meant to provoke deeper thought on conceptual ideas. This has again created some really good conversation between individual students and I, but I have not been successful at all in getting students to engage with each other. I do think they read each other’s posts, but they never comment or ask questions of each other, which was something I was hoping for.

The online format has just been challenging in general, so if anyone has experience or ideas about this, I’d love to hear them! 

Jeff: My IBL Story

Jeff Shriner is a Graduate Student at the University of Colorado

My story as an instructor begins with my story as a student. I completed my undergraduate degree through Hope College – a small, liberal arts institution – and my Master’s degree through Purdue University. I am currently a doctoral candidate at the University of Colorado Boulder. As a student, my class sizes were typically small (< 30 students), and none of my professors used IBL methods. I was OK with that, because I learned how to be successful in lecture-based courses. In fact I have several fond memories of these traditional classes that were led by (mostly math) instructors that I looked up to. Naturally, when I began teaching in 2008 (during my Master’s program), I also used traditional lecture-based teaching methods. As general background, I have been fortunate that all of my teaching experiences have been with smaller class sizes (< 35 students).

Overall, using traditional teaching methods has gone very well for me. Certainly I was a bit rough around the edges my first semester or two, but I remember from the very beginning obtaining a natural energy from teaching and interacting with students.  I quickly became passionate about attacking the stigma of mathematics that burdens many of our students, seeking to help them better understand what the mathematical process actually looks like and appreciate the benefits of becoming independent problem solvers. By most external measures, I could argue I’ve been succeeding in that – I receive above average student evaluations, have good relationships and discussions with many of my students throughout the semester, and have won teaching awards in my graduate program. So why am I writing this right now? Why am I interested in changing anything, when most of the feedback I get from students tells me I’m achieving my goals?

I first genuinely started questioning my lecturing ways about a year ago, when I was teaching Calculus 2. We were probably a little over half-way through the semester, and were just beginning to discuss Taylor Series. I had just finished delivering, by my account, a beautiful and organized introduction to the topic. At the end of the lecture, one of my students (one of my best students) approached me with a question: “So, what exactly is a Taylor Series?” A teacher’s worst nightmare! The very point of my lecture had been missed by this student, which means it was likely missed by every other student. I think my first reaction was typical of a lecture-minded person: this student must have been having a bad day.

Or was he? It didn’t take long for all of my walls to come crumbling down. Was I really achieving what I thought I was achieving? Did student perception of what they were gaining in my courses match reality? By this point, I’d heard a lot about ‘active learning’, and was actually doing my best to implement what I thought ‘active learning’ meant alongside my lectures. It was time for me to dig deeper into what this meant, and actually feel confident that the way I ran my class matched my desired outcomes for my students.

I gained a lot of closure around this topic earlier this summer, when I attended the AIBL workshop hosted at Cal Poly. I gained so much at the workshop by hearing from and watching seasoned, talented instructors. Most importantly, though, I was able to finally verbalize a focal point of growth for me as an instructor that I actually believe, if achieved, will affect my students (in reality, not just in perception) in the ways I’ve wanted to from the very beginning: increase positive student-to-student engagement around the core material of the course.

This is what ‘active learning’ means to me now. Paralleling my experience with some math problems, the answer seemed obvious once I figured it out; this, after all, is how I have really learned most of what I know about mathematics – through productive interactions with my peers – and it actually fits the goals I have for my students:

  1. IBL methods make the mathematical process transparent. Lectures are clean and organized. If this is all we show our students, they think something is wrong with them when they start the homework and end up with scribbles, scratches, and mistakes on their paper. Real math is messy, and lecture fails at illustrating this.
  2. IBL methods encourage students to grow into independent problem solvers.  Francis SU spoke at a conference earlier this month, and described this as giving students freedom in the classroom.

‘Increasing student-to-student engagement’ is a simple description of what IBL is to me currently, but as a novice IBLer, I think it is a good pillar to focus on as I grow as an instructor. I’m also not abandoning lecture; I’m just trying to view it as a tool instead of the main vehicle that’s driving my courses. I’m excited to have a new focus for growth, and look forward to sharing successes, as well as ‘productive failures’ (thanks to Dana Ernst for the terminology), in future posts!