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.

Nick: Some IBL Things For My Summer Class

Nick Long is an Associate Professor at Stephen F. Austin State University

As great as most things have been with my transition to using IBL in my classes, I didn’t expect that future semesters of teaching the same course would be so intensive in preparing materials. With a traditional lecture, you can crank out a set of notes and apply minor tweaks when you use them in future semesters with relative ease. With my IBL materials, I have found I work almost as hard to edit and re-adapt my own materials in future semesters. This is how you get better materials that others can use, through a near constant flow of application and revision. My efforts this summer have been to add some problems in order for us to get more done. That may not sound right but when we prime our students to think more carefully and more deeply, then they can do more in less time. That’s the idea but as most of you know, the correct balance of problems is exceedingly difficult to produce. As many good resources as I got at the IBL Workshop last summer, I have been going over C. Von Renesse’s recent paper “A Path to Designing Inquiry Activities in Mathematics” which is to appear in PRIMUS soon. I have read and re-scanned this paper several times this summer as I have been asking myself “What is it I want my students to get out of these problems?” I have had my own share of productive failure this summer, which I have not hesitated to tell my students about, namely I had to abandon about 3 weeks of work writing materials for a 100-level trig class.When I thought about what I was writing, it turned out to be exercises that don’t really further understanding but rather just asked students to do something without really going anywhere. I hope to write more later about how I am trying to be more explicit with my own productive failures and why I think #pf is valuable to us as faculty.

I have added a couple new writing assignments to my courses this summer as well. Specifically, I am opening the semester by having students write their math autobiographies. While not all of the students took this assignment very seriously, I got a lot of wonderful responses from students which showed both a wide range of experiences and somehow that ~80% of my students thought they were below average. One thing I am trying to figure out how to do is share some of these wonderful ideas with the class, but I’m not sure how to do this while respecting the anonymity of the students. The other new writing assignment I have added was shamelessly borrowed from Francis Su’s article in the June/July issue of the MAA Focus. His assignment is stated as:

One of the luxuries of the internet era is that you can look up the answer to almost any problem you  want- as long as it’s been solved. Yet when you are learning a subject it can be counterproductive. In this class, I have emphasized the importance of struggling in mathematics: that it’s normal and part of the process of learning, and that when you are stuck, you should just “try something.” Describe an instance, so far in this course, where struggling and trying something was valuable to you. 

I really like this assignment as an end of semester reflection that I hope will reinforce a lot of the non-mathematics things that our class has worked on this semester. I’m sure I will get to talk about the responses in the future.

As for the particulars of this summer’s course, I have a great mix of students. One superstar student can’t believe how well doing problems explains all the things she has ever done in math without someone telling her stuff. She even brought her 12 year old son to class when he didn’t have other summer activities and he was able to do a surprising amount of the work in the class because he saw how much math should make sense.There are a bunch of other students who are starting to understand that when something doesn’t make sense, you need to start working: In other words, don’t just say something on your homework and move on… think about what precisely you are stuck on and work to have it make sense. I’m at the point in the semester where they have normalized just about everything they are expected to do with homework, presentations, and respectful behavior. I barely need to be there but to be an administrator (and ask them a lot of questions to see how well they believe their own work). Two areas that I am particularly happy with the progress of this class is how they work and speak to each other effectively and respectfully as well as their persistence in problem solving. They have really been struggling with algebra and simplifying some of our work on conic sections but most students have not gotten over discouraged by the amount of effort they are putting into their work.

As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.