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.)

Jessica: Initial Successes and Challenges

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.

Successes:

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.

Challenges:

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.

Jessica: My Path to IBL

Jessica Williams is an Assistant Professor at Converse College.

I completed my undergraduate education at a small, liberal arts college (Transylvania University in Lexington, KY), and this is the type of institution to which I have returned. My undergraduate classes were lecture, for the most part, with the occasional group work. It was only in independent study courses that I found myself presenting problems at the board. I loved all of my math courses, and in them I was a successful student. In fact, I think if I had been placed in an IBL course I would have, at least initially, strongly disliked the idea!

My next move was to the mathematics PhD program at the University of Iowa, and I became passionate about teaching during my first semester as a teaching assistant. The majority of my time as a TA was spent in lecture mode. My teaching evaluations were always very positive; I was praised especially for my enthusiasm, organization, clear explanations, and accounting for all details in the problem solving process. I felt that I developed personal connections with many of my students, and that I was relatively successful as a teacher. There was no moment where I paused and thought, “Gee, maybe I should overhaul my teaching methods.”

In my fifth and final year of graduate school I first became a Section NExT fellow with the Iowa section of the MAA. I attended the sectional meeting that fall (2014) and met many amazing educators who were using IBL in their classrooms. It was at this meeting that I became convinced of IBL as a more effective way to teach mathematics. The classroom experiences many professors spoke of were so much more meaningful and student-centered than those occurring in my classrooms. TJ Hitchman delivered a final address (with IBL flair) that left me unbelievably excited to start down the IBL path. I left this conference inspired and motivated. “I will IBL all the things!” – me, October 2014.

Then, in what felt like the blink of an eye, I applied for dozens of jobs, spent a few weeks flying around the country for interviews, finished a thesis, defended said thesis, moved almost a thousand miles, and began teaching three distinct courses as a newly minted professor. I promptly took out each of my course textbooks and wrote some nice, comfortable lecture notes. I spent the year developing a lot of notes and a handful of activities for six different courses, and before I knew it I had completed my first year as a professor. I had not succeeded in jumping off the IBL cliff (which is exactly how I envisioned it in my mind), but I had survived.

Along the way, I was fortunate enough to be a 2015-2016 national Project NExT fellow, and I continued to hear about the case for IBL. Nay, the imperative need for IBL! As I listened to mounting evidence, I began to feel that I was truly doing my students a disservice by continuing to mostly lecture. Despite the wealth of information I now had at my fingertips from Project NExT, I felt like I needed more resources. I needed some gear, preferably a parachute, in order to make the jump.

The Academy of Inquiry Based Learning’s IBL Workshop provided me with the parachute I felt I needed. I attended one of the June 2016 workshops in San Luis Obispo with the intention to prepare myself to teach in an IBL style. I cannot say enough positive things about this workshop; it was career changing. The week was spent discussing methods, challenges, successes, materials, and worries (of which I had many). In only a few days, but with endless assistance from the fantastic facilitators, I designed my Real Analysis course for Fall 2016. My very first IBL course was ready to launch.

This brings me to the present day. I am currently two weeks into the semester in which I am teaching this IBL course. Simultaneously, I am working hard to crank up active learning techniques in my other two courses (Calculus III, Pre-Calculus). For the most part I am excited and hopeful, but I maintain a healthy dose of fear and skepticism as necessitated by my risk-averse personality. As I continually remind my students of productive failure, I also remind myself. Here we go!

Nick: Preparing for the Fall Semester

 

Nick Long is an associate professor at Stephen F. Austin State University.

When a bank robber was asked by a reporter why he robbed banks, he replied “That’s where the money is.” It wouldn’t make sense to try to harvest wheat from a forest, so why would I ask my students to do work that isn’t suited to them getting what they need. When considering different activities for my fall courses, I tried to ask myself , “Is this where the learning/growth/effective feedback is?”

This fall I am teaching several sections of a freshman level trigonometry and multi-variable calculus. I haven’t taught either class in a while, so it was nice to look at them through the IBL lens. One of the new (to me) things I will be doing is using a traditional textbook. Last year, I wrote my own notes for my classes, which was a great way to show students just what they needed, exactly when they needed it. I couldn’t be happier about how that went from my end. That isn’t to say that significant changes don’t still need to be made, but I really enjoyed the experience of making the course and materials purpose-built.

One of my meta-goals for the fall semester is to help my students become better readers of mathematical content, their traditional texts in particular. In this vein, I am trying to require the first exposure to new material to be through reading appropriate passages in the textbook. The way I am I am measuring/incentivizing this is different for each of my courses. In my trig classes, I have been writing short reading quizzes and reading guides to be completed a couple hours before class. An example of the kind of question I am using is:

“Write a sentence to explain what the mnemonic “All Students Take Calculus” helps describe.”

The final question on every reading quiz is:

“What question do you have after reading these sections?”

The reason I ask this last question is also the reason that I have these done a couple hours before class, namely that I will read and grade these quizzes right before class so that I can address some of the ideas that students did not understand from the reading. I am cautiously optimistic that this reading quiz idea will also supplement some the the student buy-in work that I am doing to combat the feeling that students are supposed to teach themselves. I’m hoping that I can convince and show students that with a little pre-class work and reading, I will be able to more appropriately introduce new ideas in class. I picked up these ideas and many more from a session on encouraging teaching innovation in early career faculty at Mathfest (run by David Failing and Susan Crook).

In my multivariable calculus class, we start each class meeting with student presentations on some of the problems we worked on previously. As the transition to the new material, I have been asking students to summarize in a couple of sentences what the big ideas are from the reading I assigned. Since this class is much smaller (11 students) and some of the students have had courses from me before, we are able to have a short low-pressure discussion of the concepts before we start working on new problems.

One thing that I have continually struggled with is writing problems that have the appropriate balance of conceptual versus computational versus discovery. The habit of writing exercises similar to what you would see in a textbook is so ingrained that I find myself writing doing just that unless have some explicit reminder of what the problem is really supposed to help the students see. That explicit goal, not just some implicit idea that I am modeling, has made the biggest difference in how much I am able to reframe the efforts that I am putting into my teaching.

Another slight change in my student buy-in plan has been in my explanation to students about why they have what seems to be three or four different kinds of work. For instance, I am using WebWork to allow students practice with computational problems, and I have been very conscious to remind students that the feedback they need on these kind of problems is best  given immediately by a system like WebWork. I am also quick to mention that this kind of work is best done after the conceptual work on these topics is completed. The best way to get good feedback on the conceptual work is to see how convincing your work is. I explain to my students that the best forum to get this kind of feedback is to have students present and discuss their work in class. In other words, the venue for the work should be selected based on what kind of feedback they need. I think convincing students about how important these ideas are will need to be something that happens with regular reminders through the semester.

We have had a few new writers on the blog and we will have a few more coming on board soon, so check back for more posts over the next few weeks. As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.

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.)

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!

Liza: Treating our (young adult) college students like we treat adults

Liza Cope is an Assistant Professor at Delta State University

It has been quite awhile since my last post on the activity “Which One Does Not Belong.” Over the past several months I have been doing quite a bit of work with inservice math teachers through a Math Science Partnership (MSP) grant and through my experiences with Math Teachers’ Circles (MTC).

I’ll start with the latter. I was introduced to MTC by fellow IBL professor, Dr. Judith Covington at the LA/MS Section of MAA meeting in 2014. If you have never attended a circle meeting, see if there is a circle in your area, and go check it out! If there is not a circle in your area, start one (as I did). The MTC site has tons of helpful resources that you can use to start and maintain a circle. I joined the MTC network and started the Mississippi Delta MTC in 2014. This year before the NCTM Annual Meeting I was asked to run a circle at the conference. I was blessed to be paired up with a creative genius and all around wonderful human, Henri Picciotto. Henri said that he had an idea for an activity that would work with the diverse audience that attends the conference. We emailed and talked a bit before the event, but I was not 100% sure how things would go. I was worried about the space… would it be big enough? too noisy? too many distractions? furniture… would it be conducive to collaboration? logistics… how would folks find out about it? content… appropriately challenging? what probing questions to ask? what if there was a question that I could not answer, etc… . Well, I am happy to report that it could not have gone better. Reflecting on the experience on my way home from San Francisco, I thought, that is how I want my college classes to go… the participants were all engaged, most worked collaboratively, but those who worked alone did so by choice, participants asked and answered each others’ questions, openly shared “ah-has” and “wonderments”- it was beautiful! At this juncture I thought, well I can aim for such an experience in my college classes, but I will probably not reach such an ideal, because my students are not as mature or experienced as the NCTM participants. I will return to this.

The other major project that I have been working on is a MSP grant at my institution. Through this project I had the opportunity to teach two graduate classes to 40 math teachers this summer. Similar to my experience with the MTC at NCTM, my classes with these teachers seemed to organically possess many of the key IBL characteristics we learned about at AIBL. Once again, I chalked it up to the class consisting of more mature and experienced participants than the undergraduate students in my college classes.

While planning for my fall classes this past week, I reflected back on my experiences with the MTC  at NCTM and the MSP participants, but this time I dug a little deeper… What made them work? Was it really just the participants? True, they are more mature, have chosen to be math teachers (although many of my college students have chosen teach math too), and have more experiences… but what did I do differently with them? If I am honest with myself, I have to admit that I treated these students differently than I treat my college students. For example: I was more comfortable giving them completely uninterrupted work time, I was better at resisting the temptation to “help” (a.k.a. provide answers), and I was less controlling of the structure of the class. Additionally, I  used activities with them that were more conducive to IBL learning. These activities were more open ended and challenging than the activities I typically use with my college students. I am happy to have had the time to reflect on these experiences.

My goal for this year is going to be to get my college classes to run more like my MTC and MSP classes ran. Although it might not be possible to reach this ideal, it does not mean that I should settle for the status quo. Nick and I agree that one of the arguments that professors make against implementing IBL is, “I can’t make it work perfectly, so I don’t want to try it.” Contrary to this misconception, I remember Dr. Yoshinobu describing IBL as a continuum. I know that in order to move closer to the IBL end of this continuum, I must start treating my college students like adults. Please look for follow-up posts in the coming months on specific changes that I have made and their impact in my classes.