David: Grace in the Struggle

David Failing is an Assistant Professor at Quincy University

“When every day seems the same, it is because we have stopped noticing the good things that appear in our lives.”

One of my students shared this quote from Paulo Coelho as part of her reflection on “The Lesson of Grace in Teaching,” the MAA Haimo Teaching Award Lecture (subsequently shared as a blog post) given by Francis Su at the AMS/MAA Joint Math Meetings on January 11, 2013. At this point in the semester, it can be easy for faculty and students alike to feel overwhelmed, overworked, and potentially burned out. We may have tried something new in the classroom (a first foray into IBL, or a tweak to an old standby activity) and had it fail miserably. Our students might have bombed their midterm despite feeling like they’ve worked their absolute hardest in the first half of the semester. It might feel like these failures are judgements of our worth, but we shouldn’t lose sight of the good things taking place in our classrooms.

At this same point in the Spring 2016 semester, I thought my students could use a little boost to their morale. Francis’ words had inspired me before, so I hoped the effect would be similar for them. All I asked was that, in exchange for a small boost to their grade on our most recent exam (in all courses I was teaching at the time), they read and reflect on the post. A half page minimum. My post on Facebook, from February 3, 2016:

“Early reflections on Grace coming in from my students, and they are giving me confidence that I’m doing SOMETHING right this semester. Several students have commented that they need to share the post with their friends, because they see them already stressing out over their performance as if it is life or death. Several commented that they personally aren’t worried about if they make an error in class, because it’s okay! One quote from a student below:

‘There were also two specific times in this post that I saw how you use grace when we are in your class, the first time is when they mention names and how you were determined to learn all of our names and probably now know each and every one of us. The second was today in class, even though when they wrote their answers up on the board, instead of straight out saying that they were wrong, you explained to all of us how they got that answer, and then took the time with them to fix it to where they learned it, without making them feel embarrassed, and that meant a lot to me and showed me that I know I can come to you with my questions and I don’t have to be embarrassed.’ “

I was overjoyed that my students (from freshmen on up to seniors) were willing and able to reflect on the semester in a meaningful way. The following day, I got to work on developing the reflection assignments that this series of posts has shared throughout the fall. Since this was originally successful without much guidance, I kept the assignment simple:

Please read the blog post (or listen to the audio version linked at the top of the post) and write a 1.5-2 page reflection responding to it. Have you encountered any situations in your life where someone has given you grace as Francis Su’s advisor did? Have you given grace in a similar fashion? Just respond to the post in whatever way you see fit.

The responses were a lot more varied than I remembered from last time. Some students said that they were very moved by reading or listening. They admitted to things like depression, abuse, homelessness, or divorce, illness or death of a family member, and how someone unexpected stepped in to their life to help them cope when it interfered with their academics. How that person gave them grace,  (or as one student shared) “comfort and stability when they have neither in their lives.” Some students, however, didn’t seem to “get” the point of my sharing the post. In fact, some students were defiant. “I don’t believe in grace. … I believe that everything that I receive is the result of my actions and I somehow deserved it,” one wrote. Others simply summarized Francis’ words, and made no apparent effort to find examples of grace in their own life. Our previous reflection assignments had a purpose I made clear at the outset – the math autobiography was meant to help us understand where they had come from, and where they were heading academically; the growth mindset activity was meant to help them think more clearly about their own learning. But grace? What the heck does that have to do with mathematics?

What was lost, this time around, was that I did not share my own reflection beforehand. In the spring semester, I told my classes how I have several folks in mathematics education that I look up to, Francis being one of them. That who he is (a Christian) informs what he does in the classroom, unashamedly so, and I strive for the same. I’m an educator and an outdoor athlete. I run ultramarathons (races greater than 26.2 miles, often on hiking trails in the woods) as a way to explore the world around me and to explore within. And, when I’m ready to give up, somehow I’ve always been able to dig in and persevere. Like Francis, I was ready to give up on my PhD before it was completed; I also wanted to quit, 50 or so miles in to my first 100 mile race this October. Knowing that the reward for perseverance, for sticking with what I had worked so hard to train for, was so much greater than what I stood to lose by not trying, allowed me to decide “I signed up for this, I’m going to do everything in my power to finish.” What I want to bring to the classroom is an attitude that helps my students keep sight of their goals, even when they face adversity in the interim.

I’ll be the first to admit, when a student doesn’t seem to “get” an assignment I’ve given, mathematical or otherwise, I take it personally. I ask myself what I did “wrong” or differently that caused the outcome to be different than expected. In this case, not a single one of my students commented on how they had received grace in our class. I certainly don’t give the assignment to receive pats on the back for doing good things for my students, but I had to wonder. Did I learn my students’ names as well this semester as I have in the past? Did I give them my very best every day? Definitely not. Have I let my own frustration with what’s gone on outside of class bleed in to my own classroom and office hours? Certainly. What I, as an instructor, need at this point in the semester, is to remind myself of the things that prompted me to share Francis’ speech with my students in the first place. That I need to give myself grace now and again. Grace has no regard for accomplishments or titles. My students proved wise in this area. “Pass or fail you’re still a person and you can always try again,” one wrote. Grace is a tool that you can use to help you forgive yourself! While I might not be happy with how the last few reflections have gone, I can try each one again next semester, tweaking them and being sure to give my students the grace of acknowledging the failures I’ve had along the way.


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 gmail.com and let me know how it goes.)

David: Encouraging Introspection

David Failing is an Assistant Professor at Quincy University

Like Liza, I have been absent from blogging for quite some time. After last year’s “Summer of IBL,” where I attended the Legacy of RL Moore Conference, the IBL Workshop, and Mathfest (driving cross-country as I did), this summer I spent more time focused on single-course preparation. In particular, now that I’ve taught a few IBL-based upper division courses, I wanted to add value to the two sections of Applied College Algebra I teach each fall. Susan Crook and I co-organized a Themed Contributed Paper Session (Encouraging Early Career Teaching Innovation) at Mathfest 2016 in Columbus, and several of the talks in our session focused on ideas that could be implemented in one course, one semester at a time. What interested me most was the idea of asking my students to spend more time on activities that aren’t just doing mathematics. A few of the talks I attended at Mathfest focused on student writing, and after I spent some time with Nick discussing his experience with short writing assignments in a summer class, I decided to implement them in Applied College Algebra. Over the course of the semester, my 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 next few posts will focus on the results of making this change, and I will also share the full PDF and TeX files of all five assignments.

Each course I teach now begins with a version of Dana Ernst’s “Setting The Stage” activity, asking students to lay out the necessary features of a course that will allow them to fail productively. Our enrollment at Quincy hovers around 40% athletes, so it usually isn’t difficult to get students to discuss the role of practice in the learning process. As a natural extension of this first day activity, I asked my students to write a math autobiography for their first reflection of the semester, due the second day of class. The assignment I developed was mostly the same as was outlined at the MAA’s Math Ed Matters blog in January 2016, but I also pulled in additional questions from similar assignments by Christopher Reisch and Christine von Renesse. I also made sure to ask my students to include at least one nonacademic obstacle they would face this semester, an idea taken from Francis Su’s “To The Mathematical Beach,” (FOCUS, p. 18-19).

We then spent our second day of class in small groups discussing their answers. I bounced from group to group listening in, but made a point of asking each group their thoughts on what it means to be good at math. Often, students would say that this meant being faster than others, getting things right the first time when solving problems (and with no outside help), and being able to fix errors easily. What surprised me, however, was what they had to say in their essays. A handful suggested that understanding and general problem solving ability, rather than pure number sense, was the key. One student wrote that “My ability in math is only as good as my effort.” Another section of the assignment asks students to describe their learning style, including how they think they learn best, their attitude toward groupwork, and what to do when they get stuck. Some students believed that working with others can be a hindrance, while some shared their belief that this is an advantage because others can be both a source of help and an outlet for us to demonstrate our own understanding by offering assistance.

What I’m not sure of, at this point, is what to do with the information I get from these reflections. Like Nick, I wonder the best way to share the results with the entire class while respecting individual privacy. I have told my students that the reflections will give me insight into what they need when they are struggling – specifically the nonacademic obstacles and their ideas of what makes a good mathematics instructor. I will ask my students to return to these autobiographies at the end of the term, in hopes that they will notice areas of personal growth. Since the course mostly serves first-semester freshmen, I also hope they are encouraged toward introspection in future courses as well.

What have you done to bring reflective writing into your courses? Have you used a math autobiography or similar assignment? What did you learn about your students, and how (if at all) did you act on that information? Please share your thoughts in the comments – IBL is nothing if not a community of practice, and I hope my posts this semester provide a forum for learning from our collective experience.

(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 gmail.com and let me know how it goes.)


The Checklist – Setting Up Your IBL Course

The ChecklistIn the latter half of the IBL Workshop at Cal Poly, the organizers guided each participant toward having a few takeaways from that week’s work. Stan simply referred to this as “The Checklist” (pictured) and Liza, Nick and myself think this will be a good theme for our next series of posts. As you can see, the topics are some that we have touched on in our introductions (Nick referred to writing some of his own materials, Liza to assessment techniques), but these are some of the issues a novice IBL-er must contend with as they set up their first courses. I’ll split my own posts as one for each of these topics, though others may divide up the checklist differently. Look for the series to continue over the next few weeks.

I said once before that IBL is a community, and this blog is to be an extension of that community into the virtual space. As with any of our posts, I hope to see others chime in below in the comments section. Do you have an idea for a new post? A response to one of the ideas broached? An experience to share? Please do!

David: An IBLer is Born

Every good blog needs an origin story. So, before I start sharing my struggles and successes in adopting an Inquiry Based Learning approach to my courses, I thought it best to back up a little.

I began to consider an IBL approach as a graduate student (in early 2013) when Ron Taylor presented a colloquium at Iowa State University on Active Learning strategies. I had always been under the impression that such approaches sacrificed the all-important “coverage.” Too many of my colleagues, however, had taken an interest in the approach for me to ignore it. Ron’s talk emphasized that IBL in particular is a commitment to teaching by letting students discover the power of their own minds, paced by student progress. Perhaps most importantly, we (as instructors) get real-time feedback from the students about how they are doing.

Fast forward to MathFest 2014 in Portland, OR. I was just starting my first full time teaching position at Quincy University, and was in Portland to kick off my Project NExT fellowship (I’m a Gold ’14 dot). I ran into Ron for the first time since we’d met in Iowa, and we started talking about IBL, as well as the TeXas Style Introduction to Proof notes that he had coauthored with Patrick Rault. Ron mentioned that there were small grants available through the Academy for Inquiry Based Learning to help novice instructors generate the “activation energy” necessary for a successful IBL classroom. Category 1 small grant applicants are required to select a target course (and IBL materials) for their first foray into IBL, as well as a mentor to guide them through the startup process. Since students are already told that Introduction to Proof is a course where things will be done “differently” than they are used to, this seemed a natural choice for a novice IBLer’s first attempt. Applications were due 4 weeks after I returned from MathFest, and 2 weeks in to my very young teaching career. At the closing talk for our Project NExT workshop, Joe Gallian urged us to “Just say yes.” And so that’s exactly what I did.

My grant application was successful, and as Stan Yoshinobu will tell you, this led to my planning a “Summer of IBL” (cue the Bryan Adams background music). After a year of teaching by the “traditional” lecture approach, I attended (in short succession) the Legacy of RL Moore conference in Austin, the IBL Workshop in San Luis Obispo, and MathFest 2015 in Washington, D.C.. Each conference provided me with opportunities to network with experienced IBLers, discuss startup issues with other novice instructors, and to see a different part of the country. The IBL Workshop, in particular, was an important week, intensely focused on getting one-on-one time with practitioners who had taught our target course. The NSF has just awarded a $2.8 million grant, called PRODUCT, for Cal Poly to expand and continue the IBL Workshop program, and I strongly encourage interested faculty (and high school teachers!) to attend future workshops. I’ll share more in a future post about my specific takeaways from the 2015 edition, but it was, above all else, instrumental in giving me the confidence and courage to take my courses in a new direction. For me, IBL is more than a pedagogical style. It is a supportive community of like-minded individuals focused on doing what we believe is best for our students, and sharing freely the resources that make this possible.

-David Failing