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.

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.

 

Nick: How Things Went This Semester

Linear Algebra: In previous semesters, students who put forth a good and legitimate effort were not just able to pass the course, but make great progress in how they were working. I had three students who were really trying to do well, and while they made progress, they did not pass the class. I am trying to figure out what more I could have done, but I think there was too significant of a gap in their ability to get work done in timely manner. After I let students know that I want them to come talk to me about how they did in the class (individual feedback other than their grade), I had a lot of students recognize how far they came in terms of problem solving and understanding the importance of sense making. I think I will keep sending out that email at the end of the semester because it really reinforces the idea that this is about more than a grad

Geometry: This semester has been a struggle for many different reasons. I feel like I need to find a better way to get students going at the beginning of the semester. As part of this I am going to be evaluating how I do Buy-in in my 100 level classes. I will probably be bothering some of you about ideas.

In reexamining the activities I used this semester, I found that I was just covering topics with some of the problems in my notes. But this, I mean that I talked about a topic just to talk about it, rather than building towards something. Stan’s post about ways to get students to learn what your really care about is something that I am trying to take to heart as I rewrite a good bit of my materials this summer.

Another difficulty I had was that I was not able to build persistence in my students this semester. The final stretch of problems includes many that can not be done (even by the best students) in 15 minutes. Students were able to do these in small groups but it took a long time. Even after congratulating them, they just saw it as a bunch of algebra they did rather than they had a great new tool to solve the next set of problems.

Differential Equations: About half the class was able to make great progress in understanding the whys of the class but I don’t feel like I made much of a difference in the students who were either ill prepared or unmotivated. This was a difficult class to teach because I only had about 50% attendance in many class meetings. Since I did not have time to prepare much active learning for this class, I would usually introduce a new topic and then start students working on problems. I would usually try to pull things back together after most students were able to finish the first few problems. This really seemed to work well since homework scores and exam scores significantly improved over the course of the semester.

I will also be preparing to teach a freshman level trigonometry course and a multi-variable calculus course in the fall. I have decided to use a traditional text for each and to supplement with my own problems and projects. I am hoping that this will mitigate some of the complaints that I need to do more example problems for students in the future.

And finally, I will be heading to Mathfest this summer (my first one), so come out and see my talks in sessions on building a problem solving culture and teaching tips for early career faculty.

Nick: Old Habits Die Hard

Anyone who has children knows that telling them once is not enough, even if you explain things to them and answer all of the many times they ask “Why?”. In fact, you often find yourself saying things you would never have thought any person anywhere would have to say. I’m talking about things like “Toes do not go in your drinks” and “You need to keep your pants on at the grocery store”. This works as a great analogue for how lecturing about a topic for a few minutes will not really foster a transformative experience. A lot has been written about how to help students break their old habits, but what I want to talk about for a little bit is how we as faculty often need to break some of our old habits. Sometimes we need to be told the same thing many times before it really sinks in.

The particular instance that brought these ideas to my mind was when a few trusted colleagues started chuckling as I was lamenting how many times each semester I have to give students a pep-talk and remind them about the reasons we are doing things differently than they are accustomed to. The reason they were laughing is that they had to give me the same kind of pep-talk about this time in the semester several times in the past year. One of them had already talked to me about this challenge this semester. The meta-ness of needing a reminder about why it’s reasonable and necessary to give students reminders struck me as something to write about.

Of course this is not the only time that I have found old habits of teaching hard to break. One of the biggest changes, but happened quite slowly over the course of the past decade for me, is the realization that we need to be explicit to our students in what we are trying to do. For some people, this means writing out all the algebra steps in a problem, but lately, I have found that it means that modeling behavior is not enough. I will go a step further and say that modeling the behavior that I want in students is impossible. I can’t model a transformative experience because that is a ridiculous thing to try to do in hour long chunks a couple times a week. I can’t model how to dissect my thoughts internally. I usually couch this discussion to students by the following analogy: “I can’t teach you how to be clever. I can be clever in front of you, and I can show you how I incorporate other people’s ideas to seem even more clever. But I just don’t know how to teach you to be clever.” Expecting others to pick up what is going on will not reliably work. It will work for some, but it will not reliably work.

One of the best things that my incorporation of inquiry based methods has done for me is the normalization of thinking deeply about what I am doing in the classroom. Meaningful change for me does not come in the form of radical changes. I am far too much a creature of habit. I am incredibly jealous of my wife and son because they have made significant changes, in which they did not later regress, by acting quickly. I know that the most effective way for me to change something is to incorporate the evolution I want into my habits and routines. The preparation needed to use inquiry based methods has incorporated this deep thinking of why I do particular actions into my daily/weekly routine.

When talking to students about the importance of effective communication, I often ask
“How great or useful is an idea if you are the only one who understands it?” As someone who loves to travel and give math talks, I understand the importance of tailoring your argument to your audience. I often ask myself how convincing an argument am I making to my students? Too often I rest on the old belief that students should listen to my ideas on the importance of modifying their perspective or attitude because my name is on the syllabus or because I am at the front of the room. Right now, I feel like I  am persuasive to my junior levels students, and not just because I’m the professor. One of my greatest struggles right now is finding a convincing argument for my freshmen students that would be just as persuasive if I wasn’t the person who puts their final grades into the computer.

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

Nick: Trying for Earlier Ah-ha Moments

A few years ago, my wife bought me a yoga mat and a membership at an awesome studio in town. While I had done some yoga-ish things before, I had never really had a yoga practice. After doing a foundations course, I regularly attended different classes at different levels. One of the things I enjoyed about yoga was how different it was from almost any other athletic activity. In other words, the difficulty was the draw. About six months later, I was in a more advanced class. I had done the poses many times and heard the instructions about how to move into the positions just as many. I don’t remember what I was working on in particular but I finally heard what my instructor was saying about the movements. It was a revelatory moment; I finally understood the poses and motions were more than just lift your leg and extend your arm type things. I also understood that those other little modifications weren’t always apparent to someone watching from across the room. They were very personal modifications. I know I had an excellent teacher when after I started to try to find those personal adjustments, she gave me even more comments during class. I’m pretty sure she saw things she wanted me to change for those six months (and sometimes she did comment), but I wasn’t ready for those small but personal changes yet.

Those revelatory moments are impossible to predict but monumental in their effect. One of the big things I am trying for this semester is get more of those moments as early as possible for my students. This spring I have three different courses: a freshman level analytic geometry class, a junior level linear algebra, and a section of junior level differential equations.

Since I have done the geometry class and linear algebra several times before, I am making relatively minor changes to both classes. The biggest changes I am trying to make in my geometry class is a shift in the early problems. I am spending a couple of weeks doing some problems that I would expect students to know before coming into this course. Since many of the students know how to find the answers (and thus have an early success), I get to use this time to acclimate students to focusing on the whys of the problem. One of the important algebra skills in the course is taking the algebraic expression you are given and making it fit a very specific form (think of skills like completing the square). Students rarely have an idea of why they do the algebra they do. In fact, they are usually told by a teacher that the algebra will make the problem easier, but they don’t often see it that way. Students have had about a dozen Ah-ha moments already with the following two problems:

Question 14.

a) For what values of A and q will the expression 3x+2 be of the form A(x+q)?
b) For what values of A and q will the expression 3+2x be of the form A(x􀀀-q)?
Question 15.

a) Expand (x􀀀-a)².
b) What value should ♦ be so that x􀀀² -4x+ ♦ is of the form (x􀀀-a)²?
What is a for your expression?
c) What about for x􀀀² +9x+ ♦?
d) Or 2x􀀀² -2/3 x+ ♦?
e) For what value of ♦ will 2x􀀀² -2/3 x+ ♦ be of the form B(x􀀀-a)²?

I don’t really know why we have had so many Ah-ha moments with what seems to me to basic problems, but I’m thrilled to have them.

In my linear algebra class, I am using my own set of problems that have worked out pretty well for students the last couple of semesters. One difference that I think will make this semester interesting is that I only have 1 student in the class who has seen this material. In previous semesters, there were at least three students repeating this course. I’m not sure how this will effect the level of work the students present but I’m interested to see how this is different than previous iterations.

I last taught our junior level differential equations course three years ago and only found out that I would be teaching this class the Friday before classes began. I have to thank everyone who sent me information about active learning activities in an ODE class. I am using a great traditional text (Blanchard, Devaney, and Hall) but I didn’t feel like I had time to prepare much in the way of activities. As of now I am introducing new topics and having students work on problems as a class or in small groups. I’m hoping that I will incentivize reading before class enough that we can work up to a minimal discussion lead by me followed by students working in class with homework presentations at the start of the next class.

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

 

Liza: Which One Doesn’t Belong

I was first introduced to Which One Doesn’t Belong (WODB) at a talk given by Dr. Skip Fennell at NCTM Regional. I was very impressed with the engaging discussion that WODB inspired among the participants of Dr. Fennell’s session. I also loved how the focus was not on the correct answer, but rather developing participants ability to explain their thinking and justify their answers. Unfortunately, I was unable to use WODB with my students after the conference, because the semester was over (except for final exams). However, ironically a couple of weeks after the conference at a meeting of our local Math Teachers’ Circle one of the participants shared WODB . The circle members (all math teachers) absolutely loved it! Now that the spring semester has started, I am looking forward to incorporating WODB into my classes. I think that it will fit well with IBL methods. More specifically, I plan on assigning WODB items to students and having them present their problem solving processes and answers to the class. I also think it would be beneficial to ask students (particularly my preservice teachers) to create their own WODB. I am looking forward to using WODB this semester and will be sure to follow up on the blog with how things go.