Wednesday, November 21, 2018

Nudges as a Teaching Technique

When we think about teaching and discuss teaching, we are usually focused on the framework, teaching methods, how to organize groups, assembling rich mathematical tasks, and more. This post is about thinking in human terms. It's about one specific (seemingly peripheral) action that can potentially have a large impact. It's called the nudge.

The basic idea of the nudge is to check in with students during group work time, before or after class, or via email. A nudge is a way to touch base with students to see how they are doing and to open a dialogue. It gives students opportunities to engage, and is an invitation by the instructor to students to discuss Math.  Here are just a small set of examples.

1. "Hi Sandy! How are you doing with the homework?" as a student settles in before class. Sometimes it'll be that it's going fine. Other times the student will be reminded to ask you a question about one of the problems.

2. When visiting a student who has been quiet... "Hi Amy, show me what you have for #7... That's a nice idea. You know we haven't seen you present in a while, would you be willing to share your ideas with the class later?"  Affirmation and success are great ways to get people more involved.

3. Or sometimes students are stressed about the course, and it isn't right to discuss personal issues in class. Perhaps sending an email is useful. "Dear Matt, I thought I'd follow up and see if you can make office hours this week to discuss your situation..."

4. You notice a group is not talking much. "Hi! I thought I'd come over here and encourage your group to work with each other. Take turns sharing how you did the problem..." Nudges can be used for accountability without raising the stakes, keeping things friendly and focused on the task at hand.

5. A student looks frustrated working on problem. Go over and check in. "Let's see if we can talk this through together..." Usually the student has something you can work with, and then setting them in a fruitful direction via a hint and some structure, can be help. Even just talking through the thought process can help and be calming. Reassurances that the struggle is part of the process also helps.

Teaching is a cultural activity. I've mentioned this repeatedly on this blog. Teaching is much more than following a script or clear presentations or putting people into groups. Beyond the framework are the human interactions and the teacher-as-coach idea, going past cheerleading. (The difference between cheerleading and coaching has been talked about on this blog HERE.)  Nudges (AKA good communication, attentiveness, and building rapport) helps complete the package.

To dig a bit deeper, an instructor could mention in the front of the class for students to email to setup appointments or that making mistakes is okay, and that can have some effect on some students. But following up and nudging students takes this up a notch. Imagine you're a student and there's good advice being mentioned by the instructor up at the front of class. That can be influential. But what if the instructor also comes to visit your group and checks in. That can be a far more impactful experience.

Nudges also send the message via your actions (not words) that you care. Words matter. So do actions. Saying and doing, can then be the proof to the students that their instructor cares and wants them to succeed.

So here's a nudge to readers to try some nudges. And share with us how it goes!

Thursday, October 4, 2018

Guest Post by Dr. Sandra Laursen on Gathering Feedback from Students

SY - Hello colleagues! This is a guest post by Dr. Sandra Laursen, University of Colorado, Boulder.

Gathering feedback from students has several potential benefits for IBL instructors. It can be important for student buy-in — building that reservoir of goodwill that helps them stay with you when the math gets tough.  It shows students that you’re listening and are interested to know about their experience and how (within limits) you might improve it.  It also helps them recognize what they can do differently themselves to improve things too. And the data can help figure out how to get better at how you implement your IBL approaches, or head off a small problem before it becomes a big one.

When you help students recognize what they learning (and indeed that they are learning at all! ), this is a form of metacognition, or thinking about one's thinking. Fostering metacognition is a good learning practice in general, one of the best.  It can help frustrated students to realize they are making progress and gaining some knowledge and skills they may not have recognized until they stopped to write them down or talk about them.  Sometimes their peers' testimony is more powerful than anything you can say.  A few weeks into the term is usually a good time; in rare cases, a second time later in the term too, to see if changes you have made are working.

Here are some student feedback strategies I’ve gathered over time from IBLers and others.  Some are take-home assignments (anonymous feedback will be the most candid) and some are things you can do in class to foster metacognition.

1.  What works?  This open-ended format asks students to write short answers to each of these:
  • What is working for you about the teaching and learning in this class so far?
  • What is not working for you about the teaching and learning in this class so far ?
  • What can you do to improve your learning?
  • What can the instructor to do improve your learning?
2.  Roses, buds and thorns:   Students write half a page about their learning experience which must include at least one rose, one thorn, and one bud.  Roses are positive things, thorns are negative things, and buds are growth-- new understandings or changed attitudes.

3.  Start-stop-continue:  Students write three short sentences:
  • one thing they'd like to stop doing in class to enhance their learning.
  • one thing that they would like to start doing in class to enhance their learning.
  • one thing that they'd like to continue doing in class to enhance their learning.
4.  Plus-delta:  A daily feedback method where students write short responses to two questions:
  • Plus: What helped you learn today?
  • Delta: What should we change together to help you learn better?
5.  Consensogram: Baseline knowledge/emotion check on any topic. If you Google consensogram, there are a bunch of images (mostly with younger students) that show it in use.  I could imagine using this to launch a discussion to help students recognize what they are learning beyond mathematics:  speaking and listening skills, teamwork, logical thinking, appreciation for others’ thinking, and more.

6.  The SALG (Student Assessment of their Learning Gains) instrument is a survey instrument developed specifically to address the fact that institutional end-of-course forms often focus more on what students liked rather than what they learned.  It is highly adaptable by instructors; see

The SALG-M is a form of the Student Assessment of their Learning Gains (SALG) survey instrument that is customized for undergraduate mathematics courses. My research colleagues and I have used this survey to examine students' learning gains across a range of cognitive, affective, and social domains and it is available to instructors and researchers. To examine or use the SALG-M, please download these instructions and visit to set up and customize a copy for your own use.    —>  go to Tools item

7.  Your local teaching and learning center may be able to help you.  Many of them offer focus groups and other ways of gathering student feedback.

Whenever you gather feedback from students, in order to get the buy-in benefit, it’s important to do something with it --to respond to their feedback in some way.  Tell them a few key points about what you heard and understood, and how you are taking it on board.  You don’t have to report back on everything students said, just a few key points that may be actionable this term.  This might mean explaining your teaching approach:  if they don’t like presentations, for example, it doesn’t mean you stop doing them. Rather, respond by saying something like, "Many of you responded that you did not like presentations. Here is why I find them valuable.... I do want them to benefit your learning, so please take a few minutes and write on a notecard a few suggestions for how we can make student presentations more beneficial to you."  (thanks to Jess Ellis Hagman for this example)

Learning is a joint effort; it’s always smart to ask students what they can do as well as what you can do. Meet them partway by making an adjustment yourself, even a small one, based on their feedback--and be sure they understand that you’re responding to their input.  This shows them you’re listening!  Recognize too that some of students’ ideas about what to do about a problem are more useful for telling you what the problem is, but not necessarily providing the best possible solution to that problem. So try to treat their suggestions as helping you diagnose their concerns.

Finally, self-reflection and collaboration with colleagues are key tools for improving your practice.  Can you journal for a few minutes after class or at the end of the week?  Annotate assignments or the syllabus with things you’ll change next time? Read a blog post or a book on learning? Swap classroom visits with a colleague? Agree with a colleague to try a specific feedback practice and then discuss what you learn from it?  Join a listserv on teaching and learning or follow fellow educators on twitter?  Paying attention to what your students think and feel is a powerful tool for improvement, and being interested in strengthening your IBL practice is already a great start.

More about metacognition:
Ambrose, S. A., Bridges, M. W., DiPietro, M., Lovett, M. C., & Norman, M. K. (2010). How learning works: Seven research-based principles for smart teaching.  San Francisco: Jossey-Bass.  See Ch. 7, How do students become self-directed learners?  (I recommend the rest of this book too)

More on administering and responding to student feedback, from Prof. Robert Talbert, Grand Valley State University:

More examples of feedback methods and questions:

Monday, September 17, 2018

Cliff's Column on Productive Failure

Note from SY: I'm pleased to announce a new column on The IBL Blog by Cliff Bridges, CU Boulder. This column is going to focus on Cliff's perspectives on productive failure and messages to students. Please share with your students and colleagues! Turning you over to Cliff!


I’m Cliff Bridges, long time math PhD student, first time blogger. I’m here to talk about my experience as a mathematician. The “my experience” part is really the crux of this idea, not the math involved. The math is really just a launching point where lots of folks can grab on and enjoy the ride. I am using “lots” and “enjoy” pretty loosely here… I don’t know how many math folks there are who read blogs, and the ride on which I plan to bring you is pothole-ridden and the only pit stops are on dimly lit backroads. And the background music from “Jaws” is playing. And your cell phone battery is on 1%. But let me get to the point…

Cliff Bridges

This column is intended primarily for math students. As a student, I haven’t felt encouraged to think about my experiences as a mathematician, but rather to focus on the math and assume that the rest will work itself out. But the rest, the interactions with colleagues, the personal doubt, the institutional practices, did not always work itself out. For that matter, that math didn’t always work itself out either! I hope the reflection in this and future posts can reach students and provide the encouragement to sit with their experiences in both math and the rest.

I’ve experienced a lot of failures in my math career. This is a phrase I hear a lot, but I rarely hear details about what those math failures are. This vague sense of “everybody fails, just try and try again” makes it hard for me to relate to any one person’s experience. And that makes it hard to identify how much struggle should be expected on the path to success and how much is too much. Well, this column will be about the details of these struggles, failures, and how I or others get through them. This is my service to the readers: to provide an example of the emotional turmoil failure can instigate in a person, and show how one person identifies this turmoil and works through it. To be very clear, this column will focus on the stumbles through paths to success, not the success itself. To be less clear, this is like an opposite Facebook.

Before I really begin with my stories, I want to do a bit of hedging. If you ask any of the people who know me best, they would be shocked that I am writing about my emotions. Delving into my emotional content is a new practice for me, but it is something I am very interested in. And I’m excited to go through this learning process with all you!

Okay, now for an explanation of how I arrived at the conclusion about writing about failure. I participated in a summer Inquiry Based Learning workshop a few summers ago, and really latched on to the ideas presented there. I had already tried to encourage student engagement in my classroom, but maybe I didn’t have the right verbiage to be able to convince others, or even myself, that IBL was definitely the way I wanted to frame my courses. In any case, this workshop gave me the tools and data to back up my decisions about my teaching philosophy.

That fall, returning to my campus to teach in a newly invigorated way, I focused on the idea of “Productive Failure”. I hear that in the business world this is called “failing up” or “failing forward”, but the idea is the same: to use one’s mistakes as building blocks for a future success. To me, the idea sounds lovely! I can tell myself that I’ve never really failed, I’ve just discovered what my goal should have been from the start. This always reminds me of that one line in the song “She’s Always a Woman” by Billy Joel. My students, however, seemed to focus on the underlying structure of this idea: failure.

Failure is hard. I don’t want to downplay that. For my students, failure means you have to take the class again, and in college you have to pay for that. There are harsh ramifications of failure. But there are imaginary ramifications as well: failure means your friends will banish and unfollow you from twitter, or Santa will leave coal for you instead of a present. Okay, hopefully these ramifications sound a bit outlandish, but the feelings associated with them are very real and therefore just as harsh. Many of my students honestly believe that failing means they are somehow less deserving of good things. I have had a student tell me straight to my face that their parent would love them less if they failed! With a little coaxing that student dropped the idea as just fearful thinking, but a switch had already been flipped in my mind: I have to get students through the idea of failure in order to get to the idea of productive failure. Blogging about my failures is the best idea I have had that might help students prepare for the emotional expenditure of failing. So here I am, inviting students to walk with me through my failures so that when they face failures alone, the journey may seem less daunting.

Hopefully my students will be able to get something from this blog. They might see for the first time a teacher admit to not knowing everything, which might give courage to pursue teaching. Or mathematics. Or just a life where they aren’t afraid of getting something wrong. Maybe a fellow graduate student will get something from this blog. They’ll read the blog and decide that “it” is worth one more shot. Maybe “it” is their degree. Maybe “it” is just one more job application. I don’t know who will get something out of this blog, but I bet a lot of people can get something out of it. We all fail and none of us fails gracefully every time, but bringing this productive failure idea into everyday conversation might make the prospect of failing a little less scary.

Sunday, September 9, 2018

IBL Video Series on How to Teach via IBL

I'm happy to announce the new AIBL Video Series page. This video series focuses on topics that we cover at IBL Workshops. It's a virtual, self-paced, virtual IBL workshop (a la Khan Academy) for those who cannot attend a workshop (yet). Virtual workshops do not replace intensive summer workshops, but we also recognize that waiting until next summer is waiting too long for some. Scheduling or lack of traveling funding may be issues that prevents a math instructor from attending a summer workshop, and here at AIBL we believe that all students should have access to the latest student-centered, active teaching methods. Cost or logistics should not be a barrier to progress, and we are doing what we can to make things a bit better.

To help bridge the gap, I've created an initial series of videos intended for college math instructors. While K-12 teachers are welcome to use the videos and join the conversation, our focus is in shifting the teaching culture at the college level.

One way to look at this video series is as an expanded IBL Workshop Zero. It'll get you going, if you can put in the time or get you more ready just before a summer workshop. We'll be adding more videos, and please feel free to send us topics you want to learn more about and we'll try and make videos on topics that the community wants.

Lastly, while we don't have the resources now for a mentoring program, we do have an active community on our AIBL Facebook Group. If you have a question, post it there! We are also looking into other venues to host and support online communities for math instructors to help one another.  More on that is forthcoming.

Links AIBL Video Series Page AIBL Facebook Group

Friday, August 31, 2018

Beginning of the Academic Year and the Shokunin Spirit

The beginning of fall is a time when I like to reflect on what my goals are as a teacher. It's time to look at work what worked, what needs improvement, and see if new ideas from the profession can be implemented. The way I taught 10 or 15 years ago is very different than what I do today, because of this continuous effort to move forward.

One of my colleagues who teaches college math was once asked, "Why fix what isn't broken?" in the context of why work on improving classes we have been teaching for many years. Course evaluations are solid, and the instructor is well regarded. The question was meant in the sense of you're doing a good job, so why bother with putting in more effort.

The notion that captures an effective response to this question is the shokunin spirit or the viewpoint of an artisan or craftsman with a deeper sense of social obligation. (Shokunin spirit was highlighted in the movie, Jiro Dreams of Sushi.) In this view, it's not about getting there or making it to some achievement level, but to continually improve, strive for innovation, and give a 100% effort for yourself and the welfare of society. It's like the notion of practice makes perfect combined with running through the finish line. Why not work your hardest? Why let up, before the race is over? Why would you want to be the person who just coasts in?

There is a satisfaction of having tried your best and having found ways to innovate and improve, even if it's small steps that others won't notice.  The notion of hard work is sometimes viewed with a negative connotation in the U.S., where hard work is associated with slog, suffering, dreadful repetition. But that's where the point of view of the artisan comes in to lift things up. Artisans are passionate about their work, and hone, refine, and innovate as part of the process of doing what they do, because their process and work is intrinsically interesting and rewarding to them.

Teaching can be practiced with this same spirit. Yes, we could get away with passing out dittos from the 80s and hitting the play button. Or repeating our lines from the lectures notes we wrote a few years after we got out of grad school. An alternative is to look honestly at issues, read articles from Math Ed research, and collaborate with other professionals. We can learn about the documented issues and go to work on trying to make progress on some of them. Conceptual understanding, problem solving, math anxiety, DFW rates, equity and inclusion are not solved problems in college math, the last time I checked. There's a ton of work to be done. We got some fixin' to do!

"Why fix what isn't broken?" is not the question we should be asking. We should be asking, "What are we going to work on next?" As I head into my 19th year of college math teaching, my personal goal is to stay fresh, look for opportunities to make improvements to increase student success, and enjoy the daily process of becoming a better teacher.

Best wishes for a successful academic year, and I hope you also find a way to capture and find your own shokunin spirit!

Friday, August 24, 2018

Women Show Up in Math Ed Reform Efforts

In going through our summer 2018 numbers, I was reminded of a ongoing, persistent pattern. Women Show. Up.

Approximately 55% of participants of the three IBL Workshops in summer 2018 are women. Let's put this into context. Yes, women are half the population, but they make up far less than half the math profession. The AMS publishes reports that give us a good snapshot of the demographics of the profession. Only 15% of tenure/tenure-track positions are held by women. Women comprise 29% of non-tenure track positions (including postdocs), and women are conferred about 25-30% of the PhDs in the Mathematical Sciences.

This is of course a good thing. Women benefit from IBL courses in ways such that it *levels the playing field*. (Men benefit too, and the operative notion is level playing, not one that favors one group over the others. See Laursen et al 2014.) And female math instructors who can be mentors, role models and who also use IBL methods can make a positive impact.

Diversity of perspectives is one of the ingredients of creativity, scholarship, and maintaining a robust field. People have made arguments for why diversity in Math (or any field) is a good thing, and I'm not going to repeat those arguments here. I'm going to instead highlight a very simple idea. If a person, any person, male, female, non-binary wants to learn Math, that should be supported. Period.

Allyship isn't just about agreeing in concept. Allyship is about doing the right thing, or at the very least not getting in the way. Using appropriate active-learning methods or supporting others to use them is a doable step for anyone in the profession. Women, men, non-binary math instructors are all welcome to get off the sidelines and be involved in improving math learning for everyone. Active, intentional allyship matters.

This isn't a zero-sum game. If a female student learns more math, it doesn't take anything away from a male student. Or in this case if we note that women are showing up to IBL workshops, that's a good thing, and doesn't take away from the accomplishments of men in the subfield. Hence, let's acknowledge and celebrate the fact that women show up to IBL Workshops!

Friday, July 27, 2018

Student Voices Video: Episode 11

Here's Charlotte. She's a first year student at Cal Poly, majoring in Environmental Earth and Soil Sciences. Charlotte discusses how working on problems and learning other students' perspectives helped her own learning and her classmates' learning. Fruitful engagement and collaboration are two core components of IBL!

Tuesday, July 10, 2018

France's Soccer Program, Professional Development in Math Teaching

The World Cup 2018 is going on as I write this, and I happened to come across this Vox Video that explains why France has far more players in the World Cup than any other.  "France was one of the first European countries to create an academy system for scouting, recruiting, and training talented young soccer players; many grew up in immigrant neighborhoods where their foreign-born parents had settled." 

How did they get to having the most soccers players at the top level? They have a system that invests in their people.

System-level success is intentional work. You could try to rely on luck, “osmosis,” or search for a magic bullet, like the special textbook or school choice that will mythically unlock the learning potential in our students. Or wait for the next generation of talented people to move us forward. Of course good materials and dedicated professionals are needed. I’m not discounting those things. We need those things. But thinking in terms of only books or simple, one-dimensional ideas isn’t a strategy should bet on. It's too passive, and ignores the power we have to act and work together now to harness our ingenuity and passion. Further, if it was that easy, it would have been done already generations ago.

I prefer an intentional, systems approach. Teaching is a human system, and improving education means thinking carefully about solutions on a system level. This includes addressing change as a community building effort. People do the teaching. People, primarily students, do the learning. People write the assessments, publish the textbooks, set the schedules, and so on. Education a human endeavor, and teaching (math) is a cultural activity.

To get at the core things that we need to do to make progress, we shouldn’t think only in mechanistic terms like schedules and books. Education is not a factory, and children are not machines. Yes, math teachers are humans :) Like France’s approach to developing soccer players, we’re developing an approach to professional development to establish a system for math instructors to learn about IBL methods and join a community for continuing, long-term development. We're supporting math instructors. We’re investing in people, and hence the community of practitioners who are key players in system. (We've highlighted our real-world successes so far in this post HERE).

Professional development, therefore, is a vital strategy. It’s how knowledge, skills, and practices of the broader profession can be efficiently shared with and learned by individuals. IBL Workshops are in this sense a framework or structure that can collect or house the community knowledge, and then provide coherent programs for new IBLers to learn quickly the skills and practices of effective IBL teaching.

Professional development is also an opportunity to build new leadership. Developing facilitators is developing community leaders, and this then grows the capacity for the profession to effectively implement improvements to education. Professional development is to faculty as classes are to students. (See our team of IBL workshop facilitators and IBL community leaders!)  This year I am attending exactly zero workshops, so others can learn to do this and own it. In fact, this is one of the main goals of our current project (NSF-PRODUCT).

Some caveats... Professional development does not solve all problems in education, but it's how we get at solving many of those problems. The point I'm making here is that investment in professional development is necessary. People solve problems, and professional development programs bring people together to share, grow, and find new solutions.

Designing a professional development system with intent is our mantra. Not only are we focused on running workshops to disseminate IBL methods, we also have an eye on community building and scalability of our workshop model.

More Links:
1. A Vision for the Future of Active Learning: Professional Development Centers

2. 2018 IBL Workshop General Info

3. Vox Video "Why France Produces the Most World Cup Players"

Tuesday, June 26, 2018

2018 IBL Workshops in Chicago and Washington DC

This is a short blog post on the IBL Workshops going on right now or just ended. Last week, the Chicago team hosted an IBL Workshop at DePaul University!  This week the DC team is running a workshop at the MAA Carriage House at MAA HQ. More info about our workshops is available at

It's inspiring that about 100 college math instructors are meeting this summer to get better at teaching!

Enjoy a mix of images of faculty and staff working together to improve college math education.

Tuesday, May 22, 2018

Student Voices Video: Episode 10

The student voices series of videos is focused on telling stories from student perspectives. In this episode, Shannon Sheehan is the subject. Shannon is an undergraduate at Cal Poly, majoring in Liberal Studies (Elementary Ed), who was in Professor Champney's IBL Calculus 1 class in winter quarter 2018. She discusses how IBL helped her learn math better, contributed to her success in the course, and perhaps most importantly she will use IBL in her own teaching. Shannon will be an IBLer, not just in math, but in all subjects. See this for yourself!

For more student voices, please visit the Student Voices Playlist.

Wednesday, May 2, 2018

Interview: Professor Stephanie Salomone, University of Portland

Stephanie Anne Salomone, Ph.D.
Associate Professor and Chair, Mathematics Department
University of Portland

Tell us about your institution and what the teaching environment is like, what courses you typically teach.
I teach at the University of Portland, a comprehensive Catholic university in Portland, OR. I started here in 2005, my newly-minted PhD from UCLA in hand. At the time, there were 9 full time mathematics faculty, and four of us were brand new to the department and new to the profession. We were a traditional department, as far as teaching goes.

Things are substantially different now. We have grown to fourteen full-time faculty, with several colleagues who teach using active-learning strategies rather than lecture. We have several practitioners of IBL in classes such as real analysis, modern algebra, discrete structures, topology, modern geometry and number theory. We have people inserting IBL modules into calculus and other lower-division classes, and several faculty have flipped their classrooms.

We are an institution that values teaching and learning, and reflective practice fits within the Mission. Our department is, as well, deeply committed to teaching, and our departmental mission.

As a department, we describe our purpose, vision, and mission in the following way:
Our purpose is to foster belonging and participation in our intellectual community, wherein we model the vitality of teaching and learning by addressing the whole person.
Our vision is to sustain a life-long, collaborative community of mathematical scholars, teachers, and learners, connected globally and locally, in order to empower one another as we engage and transform our world.

Our mission is to evoke curiosity about new ways of thinking, and connect to, collaborate with, and challenge one another as we invite students to contribute to our mathematics community. Through inquiry, creativity, and vital, relevant conversation, we instill habits of abstract and applied mathematical thinking and examine the impact of mathematics on our world.

How how long have you been teaching via IBL and how did you get started?
I started teaching IBL in 2006, the first time I taught Real Analysis. I enrolled in a summer institute in Costa Mesa, and learned from Stan Yoshinobu and Ed Parker. I’ve never taught Real Analysis any other way, and in fact, no matter who has taught the class since 2006 has revised and used the notes that I got from Stan. I don’t think we’ll ever go back to a more traditionally-taught class. Since 2006, I’ve taught IBL versions of topology (using Ed’s notes) and modern geometry (using David Clark’s book), and I added sections to Dana Ernst’s Discrete Math notes so that I could adopt it for our Introduction to Proof course. Several of my colleagues have also taught using IBL in other courses, and we have great support in the department for faculty who want to try new pedagogical techniques.

What are some of the benefits of IBL classes to your students?
I taught Discrete Structures in a traditional lecture format for many years, and always felt disappointed at the end. Students really were not as engaged as I wanted them to be, and finally, a little fed up with my inability to really capture their attention, I realized that I was trying to teach them to write proofs and follow logical arguments by showing them how rather than just having them try, fail, regroup, and try again. The answer was actually obvious to me, and I spent the summer of 2016 writing notes and adopting Dana Ernst’s notes for my classes. I’ve been using them ever since. Yes, it’s true that this change means that I “cover” less material in the class, and I don’t get to “cover” equivalence relations any more. What I found was that even if I went over them in class, students didn’t get them enough to use them in future classes anyway. I made a decision to sacrifice coverage for deep understanding and skill, and I believe it was the right choice. My students can write proofs. They can interpret logical arguments. They can find flaws and offer gentle and constructive criticism to peers. They can talk intelligently about the nuances of mathematical communication. And they can do these things well, far better than most students in my class prior to making this pedagogical switch.

In fact, that is true in all of the IBL classes I’ve taught. If I look at the content we cover, it is definitely less in quantity than what I could do in a traditional course. However, the quality of learning is so much higher, and beyond that, students learn to support one another. They learn to take risks and recover from mistakes. They learn to communicate well orally and in writing. They learn to pace their work around everything else that is going on. They learn to listen, to think on their feet, to work in teams. These are invaluable skills.

Tell us about your current grant-funded projects.
I am currently running two NSF-funded projects.

I am the PI of the NSF Noyce Scholars and Interns program at UP. We are finishing up our 5th year, and are heading into an extension year to spend the remainder of our funds. We have been offering scholarships and internships to undergraduate STEM majors and to career-changing STEM professionals who want to become teachers in high-needs schools. It has been interesting to partner with faculty from other disciplines, including biology, engineering, and education, as we attempt to address a national need for highly-trained K-12 STEM teachers. In addition to our original Noyce project, I’ve submitted a proposal as part of the Western Regional Noyce Alliance to fund a series of conferences and meetings for in-service, pre-service, and post-secondary educators involved in Noyce programs.  I am working with several faculty members from a variety of universities in the Western region of the United States.

I am also the PI of the NSF IUSE program at UP, which is a professional development program for UP STEM faculty. We’re in the pilot phase of this program, called REFLECT. The goal of the proposed project, Redesigning Education For Learning through Evidence and Collaborative Teaching (REFLECT), is to increase significantly the use of highly effective, evidence-based STEM teaching methods at the University of Portland using peer observation. The proposal team from science, engineering, mathematics, and education is testing an innovative method of teacher change based on faculty peer observation that leads to reflective teaching. The REFLECT framework is organized to support adopters by providing an alternative form of assessing teaching through peer evaluation and reflection, going beyond student evaluations. The REFLECT project will develop and facilitate training workshops to expose faculty to highly effective evidence-based teaching methods and assist faculty in implementing them. The on-going professional development (PD) will be designed to foster support within a cohort of faculty using evidence-based methods. The workshop and PD will also provide training on faculty peer observation and the process of reflective teaching. Over time, this peer observation and reflection process will provide a support network that helps STEM faculty to continue to implement evidence-based teaching methods in the future, ensuring sustainability of the REFLECT program. The project structure aligns with the incentive system for teaching-focused universities, where teaching performance is highly valued and may not be well characterized in student evaluations. Our first cohort of eleven will participate in a four-day institute this May on evidence-based practices, including IBL. We’ll have a second cohort next summer, and then at the end of the three-year grant, we will host an evidence-based practices symposium for the campus and community.

Tuesday, April 10, 2018

Interview: Professor David Failing, Lewis University

This post is a Q&A interview with Professor David Failing, Lewis University.

Professor David Failing has been using IBL methods for the past few years, and recently posted on instagram a nice letter he received from a student about learning to be more comfortable presenting math to classmates and how that impacts their level of engagement. Professor Failing is an avid runner of ultra marathons, and one of the bloggers on A Novice IBL Blog

Thanks for joining us today on the IBL Blog! We’d really like to hear about a positive note you had with a student from your fall Linear Algebra class. Could you share what your student wrote and tell us more about how this student got to this point?
Just one week in to the spring 2018 semester, I received an email from a student who is currently taking Discrete Mathematics with me, and had taken my Linear Algebra course in the past fall semester. The student is a graduating senior in computer science, and while they are an A student, expressed some concerns in the fall about how the material was being presented, and how at times they didn’t “get it” right away when examples were shared in class without a lot of time for discussion.
Hi Dr. Failing,
I just wanted to take a second to say how much better I think this semester is going to be with the presentation-style course! I was hesitant with the idea at first, but I think everyone in the class is much more alert during class and open to learning this way. In addition, it's nice to have notes that are not too overwhelming in the amount of information given to us each day. 
Also, if the peanut gallery of us who haven't presented yet are getting another chance, I'd like to attempt at presenting tomorrow :)
Fall 2017 Linear Algebra Student
How did you teach your fall Linear Algebra class?
My Linear Algebra course in the fall was one of the largest I’ve ever taught - starting with 38 students. Previously, I had used David Clark’s Linear Algebra notes from the Journal of Inquiry Based Learning in Mathematics with a 2-person course I taught for math majors. This time around, my course had to meet the needs of several constituencies - mathematics, computer science, chemistry, and physics. I chose to conduct the course “interactive lecture” style, building Beamer slide decks for each of the sections we covered from David Lay’s “Linear Algebra and Its Applications,” anticipating that I would record YouTube lectures in the future to conduct a flipped class. I peppered the slides with lots of “Think-Pair-Share” activities and examples we would work out on the board as a class, aside from the usual selection of definitions, examples, and major theorems. Students did some online homework in MyMathLab after I lectured, and once a week they'd turn in 2 problems per section as written work. The online HW was computational, the written would be more "proofy."The classroom dynamic was high energy, even at a 9am time slot, and student evaluations were high at the end of the term. The approach worked out in the end, but largely because the students were attentive, stayed on top of the online HW, and asked lots of insightful questions in class. 
You just started at Lewis University. Tell us what some of the factors you considered
I left my previous institution, where I was ultimately the only tenure-track faculty member by my third year, with the intent of joining a larger department at another liberal arts university, to find more support and time for work outside the classroom. At Lewis, I saw a growing department, joint with computer science, where innovative pedagogies were supported, and the curriculum was being retooled to be more research- and project-driven. I also grew up in the Chicagoland area, so returning home was a big motivator.
What are you teaching this spring term (2018) and how are you teaching the course?
This spring, I’m teaching Applied Probability and Statistics, Advanced Linear Algebra, and two sections of Discrete Mathematics (meeting 4 days a week, with about 20 students apiece). I’m viewing Discrete as an “introduction to proof” type course for computer science majors, who are the majority of my students both sections. Ellie Kennedy (Northern Arizona University) shared a set of IBL course notes for discrete mathematics with me after the 2015 IBL Conference in Austin (which I was able to attend due, in part, to a small grant from AIBL). They had been passed down to her through Ted Mahavier, Jackie Jensen-Vallin and a few others. I was impressed with the problem sequence, but hadn’t had a place to use it until now. This semester, my students are working 2-5 problems from the sequence for class each day, and volunteering to present them at the board. I collect their write-ups at the end of the hour for a completion grade, and we are also having three “Proof Workshops” throughout the semester that will lead to their producing a drafted and revised Proof Portfolio representative of the techniques and topics we encounter this semester. It’s my first full-on IBL course at Lewis, and I look forward to iterating it in the future.
What are your future plans related to teaching and IBL?
I plan to continue teaching with “big tent” IBL throughout the rest of my career, focusing on full blown proof-and-presentation courses at the upper level, but adapting to include more “traditional” lecturing when the course merits. I actually could use a more experienced practitioner as a mentor - it would be good to have regular meetings with someone to talk about the particular difficulties that one encounters in selecting “teacher moves.” What happens if the students have nothing to present one day? What happens if the class is low energy? What happens if it looks like you won’t cover the full set of materials by the end of the term? I am slated to teach Linear Algebra again in the fall, and I have a good idea of how I’ll modify the course further to make it more rewarding for the students. However, I’ve also got a few new preparations - Theories of Geometry and Abstract Algebra. Both have some good materials out there (David Clark’s text for Euclidean Geometry and Dana Ernst’s notes for Abstract are my target materials at this point), but I’ll need to adapt or supplement them to meet our own learning outcomes at Lewis.

Tuesday, March 27, 2018

Interview: Professor Gulden Karakok

This blog post is an interview of Professor Gulden Karakok, University of Northern Colorado. Professor Karakok works in math education and also facilitates IBL Workshops. Thank you, Prof. Karakok for sharing your insights!

Tell us about your institution and what the teaching environment is like, what courses you typically teach.
I work at the University of Northern Colorado at the School of Mathematical Sciences. Our university started as a State Normal School to train teachers in the area, in 1890s. Since then it is known for educating future teachers in the area, especially the future elementary teachers.  (Here is a short history, if interested:

Our department offers a Bachelor of Science degree in mathematics in three different emphasis areas: a Secondary Teaching, a Liberal Arts, and an Applied Mathematics, and most of our undergraduate students are part of the secondary teaching emphasis. We also offer a Ph.D. in Educational Mathematics, but different from many other math departments that offer Ph.D in Math Ed., we do not have a competing Ph.D. program in Mathematics. We have 6 mathematics education professors in the department (the ratio of math educators to other faculty members is 1:2). I guess the point I’m trying to make is our department focuses a lot on good teaching and our programs are geared towards that aim. 

The courses that I typical teach are mathematics content courses for preservice elementary majors, introductory linear algebra course (we have only one linear algebra course) and graduate level mathematics education courses. I was the course coordinator for the first two mathematics content courses for elementary majors for six years overseeing 10 to 12 sections each semester. Together with course instructors (i.e., faculty members and many graduate students) each semester, we designed and/or revised many activities; which was a great collaborative process. In addition to teaching such courses, I also run Math Circles for middle school teachers and local 4th-8th grade students monthly. 

How do you implement IBL?
Let’s say you walked in to my classroom at a given day, you will see students working on a task in small groups. I typically have students work on a problem or a set of questions in small groups and then present or discuss ideas/approaches/solutions etc. We usually end with a wrap-up whole class discussion, which can look very different each day. As students work on tasks in their groups, I walk around to assess what students are thinking, check to see if they are stuck, challenge their thinking by posing questions and make sure that each individual student is “doing” mathematics. Also, I make decisions on if we need to have a whole-class discussion on certain problematic ideas or if we need to present approaches that are seemingly different to make connections among ideas. I do not necessarily have all students present the same solution/answer, rather try to orchestrate presentations to tease out important mathematical ideas and make connections to the learning objectives of the activity or the course, in general. This working in small groups requires attending to your students’ thinking and progression as well as  decision making on your feet in the moment. It can be very exhausting, especially when you are teaching a new course. 

What are some of the benefits of IBL to your students?
I think the most important benefit for the students is that they “do” mathematics instead of watching some else do it for them. They get their hands “dirty”. On the first day I tell my students that I’m not a selfish person and won’t take away the joy of doing mathematics from them- they laugh, but they slowly understand what I mean as the semester progress. I think having them actively work on mathematics empowers them and gives them the ownership in their learning.  Here is a quote from one of my students:

“I thought it was so funny cause after my meeting yesterday with Dr. G. I went back to my dorm room and all my suitemates were like, ‘How did it go?’ And I was like, ‘My life has changed. I understand math.’ And I was just like freaking out and I busted out the three pages of the portfolio…We worked on stuff and it was weird that I understood because she didn't even tell me what to do, she made me do it myself and figure it out myself. And I thought that was weird because usually, like teachers in high school would be like ‘Oh, yeah, this is how you do it. Now go work on it yourself.’ But she was pushing me to think and try to find the process of how it works. And when I did it... I think that was why I was like so excited, because I figured it out myself, with help obviously, but it was my own thinking.”

Well, this approach of teaching is beneficial to me as the teacher because I can know where my students are in their development of mathematical ideas sooner than later. This (information) allows me to adjust my lessons and provide better learning opportunities for students.  We can skip some materials and focus on other areas as needed.

How did you learn to teach via IBL?
My first IBL teaching method was through the Emergent Scholars Program training that I attended one summer at the UT Austin. When I was a graduate student at Oregon State University, I was selected to run a recitation section for Calc 3 course in this ESP format. With a couple of other graduate students we attended the training during one summer.  I believe the ESP was created by Uri Treisman, connecting to his research work at UC Berkeley in calculus courses. So, the main idea was to create different, challenging tasks for students in our recitation sections for students to work on in small groups. Overall, I got excited to create tasks that were different from the textbook end of the chapter ones. Students were also excited because these tasks were allowing them inquiry into deeper mathematical ideas. After that experience, I worked in another project to create STEM activities and also run sessions using these activities. During this project and in many other projects, my advisor Dr. Barbara Edwards, Dr. Corinne Manogue (in physics) and Dr. Tevian Dray provided me opportunities to develop my teaching style. I’ve been so lucky that they allowed me to develop activities, observed me teach and gave me very helpful suggestions. 

What are your future teaching plans? Aspirations?
As a course coordinator, I have been trying to work with graduate students to give them similar opportunities that I had in my teaching as a graduate student. However, I was doing so many different things as the course coordinator and I did not spend enough time in coaching graduate students in their teaching. Hence, this is my future teaching plan - providing support to graduate students in teaching. This semester I’m teaching one credit seminar course for graduate students on teaching. We have been reading the MAA IP Guide, and discussing what they can implement or are already implementing in their classrooms. Their first assignment for the first week of classes was to read blog posts (e.g., Dana Ernst’s blog and the Discovering Art of Mathematics blog) about what to do during first week/first day and implement one idea in their class and reflect on how it went. I’m so excited that they are enjoying this experience and I love observing their class to see how great they are in their teaching. 

Anything else you want to add?
I’m not sure if such a teaching scholarship exists, but it would be great to spend a semester or a year to observe and/or co-teach with others to learn more about others’ great teaching practices. Such scholarships or fellowships would be great to spread what others are doing their classrooms to improve the learning of mathematics for others.

Tuesday, January 23, 2018

Iceberg Diagram: Fixed-Mindset, Math Anxiety

When students say something like, "I don't learn this way...", it may be the tip of an iceberg. A sign that math anxiety and/or fixed mindsets about learning math lurks underneath the surface. Unless you know the student really well, you may not know the size and depth of the issue. Most people don't go around campus telling others about their math anxiety and fear of failure. Instructors often learn about these things indirectly through more subtle ways.

Here's the Iceberg Diagram

"I don't learn this way..." and "I need to be shown the steps..." are two commons ways to detect an iceberg. Some students may not verbalize these things at all, which highlights why it is important to visit with students regularly and discuss with students about how they are doing with the math task at hand. The more comfortable students are at asking you questions, the better you can hone in on this issue.

Stereotype threat, poor attitudes that do not support learning (i.e. non-availing beliefs), believing mistakes are bad, not realizing hard work is an ingredient of success, and so on. These are things that students have picked up along the way, possibly starting as early as elementary school or perhaps from their homes or elsewhere, and they bring them to your class. These beliefs lie beneath the surface, and ultimately hold some students back.

What can we do? 
There isn’t an easy fix, but we can do something to help melt the iceberg. A broad approach provides the most options and angles of attack. First, problems that are pegged at the right level are necessary, including problems that ask students to explain why things work. Second, instructors need to be ready to coach students through being stuck, pointing out the advantages of productive struggle, including spending time on student buy-in. Third, assessments should also measure process, not just getting the right answer. Fourth, active learning environments that allow all students to ask questions (not just the vocal 3 to 5 in each class), and also regular opportunities to discuss with one another rich mathematical topics. Fifth, readings and/or videos about effective thinking and growth mindset are needed to provide other expert insight, who weigh in on growth mindset. If you, the instructor, are the only one saying these things, it might seem to students like you are making things up. But if growth mindset is presented as a widely accepted emergent truth from research across disciplines, then that's a entirely different framing.

With all that you have a set of strategies that hits at the issue from multiple angles.  Let's get back to the main point. We have a model and a way to see the iceberg, and we have a set of teaching strategies that can address the core issues, which is like applying gentle heat to slowly and surely melt the cold ice.

Here's a quote at the end of the term from a first-year student. This is what melted icebergs sound like.
One big thing I learned from the... assignments was how productive failure can be. Your brain actually grows and develops when you fail. This proved to me that it is more about the process of arriving at the answer than it is about actually getting the right answer right away.

Monday, January 15, 2018

Setting the Stage by Dana Ernst, Northern Arizona University

Hello IBL community. Here's a short post linking you to Dana's great piece, "Setting the Stage." It's a good way to get started at the beginning of the term thinking about what to do to get your students to be more engaged and build buy-in.

Another thing I like to do at the beginning of the term is watch Ken Robinson's Ted talk, "How to Escape Education's Death Valley". It's a nice way to feel a bit more inspired so that you're encouraged to take that next step.

So take a look at some ways to get started on day 1 and on getting pumped up for the rest of the term.

Happy 2018 everyone!