Susan: #ProfPF

The reason David Failing invited me to join the list of contributors for this blog is because he saw I had written “#profpf blog?” on a to do list I was keeping during the Active Learning Symposium held before the most recent MathFest.  He kindly asked if I had a blog home where I could write this and when I didn’t, he thought it might be a good fit for the Novice IBL Blog.

So what in the world is #profpf ?  Well, first I need to explain #pf which I first learned about from Dana Ernst.  #pf came from the idea that the math world (and really, the world at large) needs to celebrate and encourage productive failure.  Dana was encouraging people to tweet or facebook productive failures and tag them with #pf.

In my math life, I have learned that failure is not only acceptable, but often required to make progress.  I tell my students in Intro Proofs that to pass the class, they are required to fail – often to fail lots!  We spend a lot of time talking about why failure is scary (embarrassment, the idea that someone else can do it better, imposter syndrome!, etc) and what we can do to break those things down.  Often, a lot of that stigma goes away by facing it head on and naming it.  A wonderful professor I had in graduate school used to respond to students asking for clarification or stopping him because they were confused who phrased the question as “This is probably a dumb question, but…” or “Sorry for asking, but….” by saying “That’s right, Mr. SoandSo. You’re definitely the ONLY student in here who didn’t completely understand that as soon as I wrote it.”  His class really helped me realize that I wasn’t the only who had questions and that there is no shame in having questions.  It means I’m trying to learn!  Confusion is often the first step to understanding.

I show my students the picture below from Adventure Time because I love the sentiment.


We often watch the following clip from the Big Bang Theory to see what doing real math looks like – not so many Eureka moments as there are “I got it!!!!  ….. No, wait, I don’t got it.” moments.

I have become very forgiving of myself for failures and mistakes in my math so long as I reflect on them. And to be totally honest, sometimes that reflection consists of “Wow, I really failed hard at that. It was embarrassing. I am embarrassed. I shouldn’t be. I was trying to learn and play with math. It happens. Let’s laugh at it and then let it go and move on.”  It’s not always a life changing reflection, but it works. So, as far as #pf goes, I’m making some strides.

Where I am not making strides and I would like some help is in what I’m terming “#profpf” – those failures that occur in my professorial life.  The times that I am really excited about a new activity that I worked hard on and it just falls flat during class.  The times that I thought we were all doing wonderfully, chugging along, making good insights and understanding, then find out that the majority of the class is lost.  The journals that I thought they were really reflecting on until one student tells me they’re just writing what they think I want to hear, not what they actually think.  I’m still really hard on myself about these failures.  I know they happen to even the best professors, but I still berate myself over them.  If I try a new activity that flops, sometimes it takes me many classes to be willing to try something new again.  One bad student evaluation comment (even a constructive one) can throw me for a loop for weeks.  Well meaning constructive criticism from a colleague who sat in on a class can ruin my confidence in a class.

I do not like this about myself, but by forcing myself to recognize it, I hope I’m on the path to becoming better about it.  I want this feedback. I want improve myself as a professor. I want to be effective and I want to help my students learn and love math like I do.  To do that, I have to be willing to try new things and to accept feedback on what went well and what didn’t.  I have to reflect on failures, make them productive, and move on without feeling paralyzed and embarrassed.  I’ve more than once heard another professor say they tried IBL in a class once, but it didn’t work so they haven’t tried again.  We all need to be more forgiving and encouraging of ourselves in the classroom. So, to that end, I’m hoping you all will join me in sharing and embracing our #profpf s.  Here’s mine for this week.

I am starting to freak out that we aren’t as far through the material as we need to be and I’m getting frustrated by students continuously asking why they can’t just use shortcuts without first deriving them.  As a result, this past week, I just gave them some formulas and did some lectures on material that with my help they could have discovered on their own.  I cheated them out of the ownership of that material and I regret it. I will look over the remaining classes and try to find places where I can do mini lectures if needed so that I do not steal learning opportunities from them. #profpf

I would love to see your #profpf s on Facebook (tag me!) or Twitter (@sbcrook)!


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! 

Susan: My Back Story

Susan Crook is an assistant professor at Loras College.

Hi everyone! I’m Susan Crook and I’m delighted to be joining my esteemed colleagues as a contributor to the novice IBL blog.  I’m in my 5th year as an assistant professor at Loras College in scenic Dubuque, IA.  Before I delve into the IBL things, both new and old, I’m doing in my current courses this semester, I want to introduce myself.

I was born and raised in Oak Ridge, TN, a town created to help build the atomic bomb during WWII, a counterpart to Los Alamos, so to say that I grew up steeped in a community that loved and prioritized math and science would be an understatement.  My dad had an MD and a PhD in pharmacokinetics and my mom had a degree in art education.  My high school offered myriad Advanced Placement and for college credit courses.  When I began my undergraduate education at the University of South Carolina, my first math class was Math 574: Discrete Mathematics.

I tell you this not to brag about my family, though I am proud of them and my hometown, but to give you a context for me.  I grew up knowing that I would go to graduate school for something because it was expected. I never doubted that women could be just as good and better than men in math and science fields because I saw it all around me.  The thought that women didn’t do math and science never crossed my radar.  I never saw myself as an outstanding math student.  I was good among the best, but I wasn’t the best by any means.  In the long run, I think this helped me in graduate school because I had no illusions to be broken.  As a professor, I think it helps me to understand my students because I struggled with math and had doubts in my ability too.

After completing degrees in Math and French at USC (the South Carolina one!), I went on to North Carolina State University for my MS and PhD in Applied Mathematics.  In all of this education, I’ve had some wonderful teachers, many of them interactive lecturers, but somehow it took me until my junior year of college to have my math epiphany.  USC didn’t offer an intro proofs course, so my first introduction to proofs was the fall semester I took honors Real Analysis and honors Abstract Algebra.  After struggling with both courses for half a semester, I was studying for a test in Real Analysis when it finally hit me that it would be much easier to just understand the proof I was working on rather than memorize the steps.  It was like a switch in my brain flipped!  I started thinking about math as wholly understanding rather than a little understanding with memorization.  It changed my entire attitude toward math and likely why I pursued math grad school.

When I started teaching as a TA at NCSU, I was frustrated that I could not figure out an effective way to get my students to see that math is about problem solving and that understanding why a method works and how it was developed is more useful than just memorizing the algorithm.  Not only does it make things easier, it makes them more fun! Math changes from something we have to do into something that we want to do.  I started talking about this with other TAs, but none of us had a good solution.

The spring of my third year at NCSU, a friend forwarded me an email invitation to an IBL Workshop to be held before The Legacy of R.L. Moore Conference in Austin that summer. My friend couldn’t go due to an internship, but encouraged me to consider going.  The application was short enough, I’d never been to Austin, and the idea of a workshop and conference on teaching intrigued me, so I applied and was happy to be accepted.  I went thinking I’d learn some new teaching skills, but left having had the most transformative and influential experience in my teaching life.  This method proposed a solution to my quandary.  I still struggle to break students of their feeling that math is algorithms to be memorized, but IBL provides me with tools to help. I met so many IBL rockstars who have become mentors and friends to me.  I left that conference (and every IBL conference I’ve attended since) feeling excited and knowing that I could make a change in how my students view mathematics.

That spring as part of a fellowship at NCSU I had the opportunity to teach my own section of their intro proofs course.   During the IBL workshop, I decided I was going to teach it IBL style and since I wasn’t sure I could get approval from the course director to do this, I was going to fly under the radar and hope no one got mad at me.  That class turned out better than I could ever have imagined.  I was randomly assigned to an active learning classroom on campus with wheelie chairs with desks and white boards galore (thanks, classroom assignment gods!).  The moment that I decided that I was team IBL for life occurred in the math tutoring center which was staffed by grad students.  A few of my students were in there studying for an upcoming test.  They commandeered the whiteboard and each had a marker in hand.  They were arguing and debating over a proof and obviously enjoying the process. I had gone over once or twice to see if I could help and was shooed away as they assured me they could do it on their own.  A student I often helped asked me why there were graduate students working in the lab.  Seeing their enjoyment and confidence, so similar to mine when I worked on math, I knew IBL was for me.

Since that initial course, I have taught Real Analysis, Discrete/Intro Proofs (twice), and Calculus (twice) IBL at Loras.  These classes have had varying success and I’ve adjusted them as I’ve gone.  This semester I have two sections of Calculus I (4 credits each) and I’m using an IBL variant for the course.  I wouldn’t say it’s full IBL, but there are definitely heavy components in the course.  I’m excited to tell you about the things I’m doing in that course and to hear your advice and suggestions on how to make it better!

David: Having the right Mindset

David Failing is an Assistant Professor at Quincy University

Over the course of the Fall 2016 semester, my Applied College Algebra students will write five short (1-3 page) reflections, each worth 3% of the overall grade (replacing the 15% I used to allot for attendance). Most of these reflections will ask students to read an article or blog post, or watch a YouTube video, and then respond to a writing prompt. My posts this semester will focus on the results of making this change, and I will also share the full PDF and TeX files of all five assignments.

We began the semester by setting the stage, outlining as a group the features required of a course to allow productive failure to happen. With that completed, our first reflection was a math autobiography that helped my students identify their own attitudes and behaviors with respect to mathematics. As the first month of our semester wound down, I tasked them with a bit of a meta-reflection, adapted from a mindset activity created by Laurie Zack at High Point University: Watch a TED talk about growth mindset, and read a short article (“I’m Not A Math Person” Is No Longer A Valid Excuse), then reflect on the role of mindsets in their lives. My hope was to help them think more clearly about their own thinking, and to empower them to make small changes in attitude that could have a big impact on their future early in their college careers.

As is often the case, my students provided some unexpected insights – some presented the difference between a fixed and a growth mindset as a contrast of “am I smart” versus “how can I become smarter?” Others, though, explained that a fixed mindset was a belief that they were “good enough as is,” while growth was a willingness to improve. Is it possible to be willing to improve while not actually believing you have the capacity? Largely, my students related that the fixed mindset results from judgement, a worry about looking smart, and a stubborn unwillingness to change; a growth mindset, on the other hand, they said required their striving to improve, willingly enter a state of discomfort, and work hard to reach their maximum potential. Another gem that one student presented was a view of “regular failure” versus “productive failure.” Regular failure is, as they put it “one and done,” where you give up and move on. Productive failure, on the other hand, occurs “when we spin failure and make the mishap into a positive.” While I don’t expect to use #rf in place of #pf anytime soon, it made me smile to see that at least one student “got it.”

There seemed to be some misunderstanding on what exactly the mindsets were applied towards (ability to affect change in themselves versus actual knowledge they possessed), and I wondered if I should have explicitly told them in the assignment instructions what the growth and fixed mindsets were defined as. The “I’m Not A Math Person” article refers to incremental and entity orientations, and while the connection to mindsets was obvious to me, I don’t believe the connection was apparent to my students. The entire exercise made it clear to me that as an instructor, I need to re-read Carol Dweck’s book before attempting a more detailed discussion of mindsets with my students. Perhaps, too, a pre-reflection (but post-viewing) discussion designed to come up with a “class definition” of the mindsets would help.

In addition to providing opportunities for reflection to my students, my hope with these writing assignments was that throughout the semester I would gain insight into my own teaching style. What I have been repeatedly reminded of in recent semesters is that active learning, IBL, writing assignments, and other “non-computational” activities are not magic. Student buy-in is required (which is why I use the Setting The Stage activity each semester), as is a lot of continued energy and effort on my part to maintain that buy-in. Goals (both content-related and “big picture”) need to be set, and activities carefully designed to move toward those goals. Where I could do better as an instructor, I feel, is with that continued buy-in piece. Other than showing them videos about productive failure and such throughout the semester (Stan Yoshinobu has a good list here), what else can I do?

(Feel free to download and modify the TeX and PDF of this reflection as you see fit. If you use it in your courses, send me an email at david.failing at and let me know how it goes.)