Jeff Shriner is a Graduate Student at the University of Colorado Continue reading
Nick is an associate professor at Stephen F. Austin State University.
I have a problem with grading. Actually, I have lots of problems with grading, but I do it because student feedback is important. With grading it can be a problem that I tend to focus on all of the stuff that my students get wrong. By this I mean that I notice everything that they miss. The worst part of this is that I tend to not pay attention to all the stuff they do well. We actually have a rule in our house when grading exams; complaints are limited to one minute until the exams have been totaled and reexamined. This phenomenon is a lot like implicit bias, in that recognition and attention to changing conscious attitudes are vital.
The same kind of thing often happens to me when I reflect on my teaching between semesters; I see only the things that I think I can do better. Again I try to combat this with some conscious statements about the things that went well. This past fall semester I had the heaviest teaching load of my time at SFA. I had three sections of freshman level trigonometry (all at capacity) and a section of multivariable calculus. My fall semester is seems at this point like things were either the best or the worst and not much in between. This goes not just for my teaching being split like this course to course but also to each student. More specifically, I feel like one of two things happened: 1) I really reached a student and was able to engage them in meaningful and profound ways about their education or 2) I was unable to connect even at a superficial level.
As a whole, each of my three trig sections was a different story. My first section met MWF, which I point out because I almost exclusively teach on Tuesdays and Thursdays. Having more meeting times ended up being a great help in this section, not because we had more in class meeting time (we didn’t), but because I had more opportunities to make adjustments to the many facets of the course. For instance, students don’t know what they don’t know, so they need lots of opportunities to discuss and ask questions. I think that being able to make these adjustments had a profound effect on the students in this course. In total, this section was the most engaged group of students I have ever taught or observed. It was truly awesome to go to class toward the end of the semester.
A colleague visited this section and was overwhelmed (in a great way) by a many of the things we did in class. Going into this visit, I had mixed feeling about how things were going. After discussing what I was trying to do in my classes and what was actually getting through to students in the post-observation meeting, I had a better picture of just how far the students in this section had come (at least the ones that showed up). It was another success in a course that I was very happy with the outcomes.
Attendance was an issue for me in all of my trig sections, but no more than in traditional classes. I thankfully had another faculty member who was not annoyed by my monthly visits to her office about the various issues that come up in this freshman level course. While she does a traditional lecture course, it was good to know how things like content and attitude compare to the student-centered approach that I took.
In the spirit of not trying to dwell on the places that need improvement, I am only going to talk about one of the things that did not go as well as I wanted. I really missed a lot of opportunities to effectively engage students who are from underrepresented groups in STEM fields. I set that as a goal for my semester and a lot of the student-centered stuff we did not seem to have much of an effect on many of these students and their habits. Let me clarify; when they got past the different learning environment, they flourished, but I was not able to encourage that regularly enough and get them to internalize the habits that would make them more successful in their academic and professional lives. It is not that I didn’t have some cases that I shouldn’t see as having a great impact on my students’ lives, but I had too many misses for me to be happy with how things went. This was especially hard on me because I spent a lot of physical and emotional energy on trying to make improvements in this area.
My multivariable calculus course was a lot of fun and very easy to see the gains that many students made to their habits of mind and their approach to their education. It was especially good to teach this course alongside a young faculty member. With this new faculty member, I found it really helpful to discuss how our students were doing and what we are trying in class. I think I was able to offer more questions that show what our students don’t understand (the notation is always very difficult for students), and he kept me from reverting to mechanical questions about the content and skills. I think it was especially important as a reminder for me to remember that we should not be doing our teaching in isolation, just as we would not expect to do research in isolation.
I am headed to Atlanta right now for the JMM and I look forward to the ideas and energy that I get from interacting and working with some many people who really care about improving the facet of our jobs with the greatest impact, teaching. As always, feel free to let me know if you have any questions or comments.
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:
- 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.
- 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:
- 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’.
- 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!
I gave a talk October 28th at a NCTM Regional Conference in Phoenix, Arizona. The focus of my talk was how using IBL and Team Based Learning (TBL) has transformed my math classes. The talk was going really well until about ten minutes before it was scheduled to end. A teacher raised his hand and commented that IBL and TBL would never work with his students. The justification that he provided for his argument is that his students are way behind grade level (he was a high school remedial math teacher) and are unmotivated to do anything. He said that they don’t care about their grades or whether they graduate. He felt that his students would actually refuse to participate in IBL or TBL activities. My immediate response was to ask the teacher what a typical day looks like in his classroom. He responded that he lectures on a topic at the board and then gives the students an assignment related to his lecture. He said that the students will not complete the assignment on their own and that he typically has to spoon feed them the answers. At this point I realized that there was not enough time left in the session for me to “solve” the teacher’s conundrum. I told him and the others that I would share helpful reading and planning resources with them through email after the session and be available to answer questions in the future. I was very thankful for a teacher who raised their hand at the end of the session and commented that IBL and TBL would be worth the teacher’s effort to try, because the alternative was not working for him or his students. After the session I sifted through our AIBL dropbox for helpful resources and forwarded them to the participants. My main take-away from this experience was the extreme importance of BUY-IN. My goals of the session were to expose the teachers to an alternative to traditional chalk and talk, plant some seeds, wet their appetites, and provide resources. I think that I accomplished these goals.
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.
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 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 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 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?
Jessica Williams is an Assistant Professor at Converse College.
The upcoming week will be the fourth of my semester. I am currently operating IBL style (but with a textbook) in my Real Analysis class, and I have Calculus III and Pre-Calculus doing much more activity-based work or presentation of problems at the board, though I am still lecturing.
So far… things are going pretty well! I am lucky to have only 11 students in Real Analysis and I know most of them from previous semesters, so that they trust me (sort of) and are comfortable talking to each other and me.
1) In Real Analysis I am modifying Annalisa Crannell’s IBL worksheets for my own use. The worksheets are wonderful and follow the book Understanding Analysis by Stephen Abbott, which is what I learned out of as an undergraduate and what I had committed to using before ever attending the IBL workshop. The students seem to be really enjoying working together on them, and in the first couple of weeks I had no shortage of volunteers to go to the board to present. One student exclaimed on the very first day, “This class is going to be awesome, I’m so excited!”
2) I modified Dana Ernst’s Setting the Stage activity in different ways and used in all of my classes on the first day, and this was a total success. (Thanks, Dana!) My students were in groups, discussing, engaging, and sharing with the class right away because of this activity, and I think that has significantly improved my classroom environments. In addition to my math courses, I’m teaching a class called Student Success Seminar (which I jokingly call “Intro to College 101”). The Setting the Stage activity went so well in there that my teaching partner shared it with other colleagues, and I have received praise all around for how well I’m doing teaching this class for the first time.
1) Made a student cry on the very first day! I made the first week of Analysis a series of worksheets called “Proofs Bootcamp,” since some of the students have never had a proofs class before, whereas others have had many (this is ongoing challenge and common in my department since we offer upper level courses mostly on a two-year rotation). This was intended to help get everyone a little closer to being on the same playing field. A notoriously tender-hearted student who is enrolled in both Calculus III and Analysis with me burst into tears while working with her group on the proofs bootcamp packet. A week later she came to me and said she had started to really enjoy the class. In particular, she claimed to like getting to see other students’ solutions on the board because it helped her understand how to think through the problems. Win! However, we soon hopped back on the roller coaster, as she came to my office in tears again before class on Thursday. She felt she couldn’t understand most of the recently assigned problems and communicated the fear of “getting a bad grade.” I have tried to set up assessment in this course so that homework is very much an opportunity to try and fail without penalty, so I’m wondering how to better assuage the fear of the bad grade (at least until exam time).
2) I feel like I’m moving at an absolute snail’s pace in all three of my classes. I was warned about feeling this way by basically everyone, so I’m not stressing too hard about it.
3) I find myself still functioning as the “expert” in the room, so this week I’m going to make a real attempt to only let other students comment/correct for the majority of the class. In class this past Thursday there was a huge decrease in volunteers to present the problems they were supposed to have worked on since Tuesday. There seemed to be a general fog around the definitions, which prohibited them from even starting. I ended up at the board for several minutes to dissect the definitions of maximum, upper bound, and supremum. I hope to pass on such a task to the students next time. I’m thinking of handing each student in the room a colored marker and telling them I’m not going to allow myself to have one at all. Until Tuesday’s class, to help with their fear of starting on problems they have no idea how to solve and to convince them how important it is to really engage with the definitions first, I told them to read the Medium post Habits of Highly Mathematical People. This appeared on my Facebook feed recently, and I really enjoyed the read.