Thursday, December 16, 2021

Liminal space

 “Honor the space in between no longer and not yet.” 

                          - Nancy Levin.

I’ve written this post a dozen times, and have deleted it a dozen times. I am still processing.  What existed before (pre 2019) is no longer, and what we will be in the future is not yet here. We’re in liminal space. 

Fall 2021 has been the hardest semester that I have ever experienced as an educator by far.  Even though the coronavirus is not done, some people or many people are done with it. I totally understand that it’s been hard, and we want to move on.  Along with covid fatigue I have seen less empathy and kindness, and I learned quite a few very unwelcome things about the systems and societies we live in. Many of us lost loved ones or colleagues, have had to deal with covid, or had to work in unsafe conditions and the stress that goes along with it. 

Team education is about the long game. We are educating today’s youth, as a social responsibility to them, to prepare all of them for their future lives. While some try to spin education as a commodity or individual good, I push back against this “consumer” notion of education and re-center it as a social responsibility. Using the social responsibility lens has helped me understand where we have come from and where I hope we can go.  

Where we were wasn’t all rainbow cupcakes and unicorns. Back in 2019 and before, we know we had major cracks in society from inequality to inequitable systems to classrooms that still were based on the weedout culture. 

I also understand that we want to get back to being able to do some things in person, such as see our friends for lunch. Yes, we want those basic, human parts of normal back and I am all for it. I'm not talking about that part of normal.

The other part of normal is what I hope we don’t go back to. That part of normal, brought us to how we mismanaged the pandemic in the context of a spectrum of inequities. Teachers and nurses quitting or thinking about quitting their jobs, because they were treated in undignified ways. Witnessing a non-expert suddenly in charge of managing how a campus deals with a rapidly evolving infectious disease, despite there being much better qualified people available, without enough safety precautions, and requiring students to sign waivers to release that campus of tort liability, all the while ignoring the concerns of the local community.  It’s like that time when you went to dinner with a friend, who treated the waiter terribly, and you learned that person isn’t someone you wanted to hangout with anymore. It’s that feeling times 1,000,000.

Where do we go from here? I don’t have answers, but I know a direction for the long game.  The striking thing to me as I have observed and watched people and society, is that the lack of collectivist values and empathy are things that desperately need to be addressed.  I don’t know how we accomplish this in college math classes yet, but I do know that it’s not enough to teach math as isolated from humanity. 

Sometimes new beginnings are disguised or start as painful endings. Sometimes we are betwixt and between. This time could be merely a waiting place, where we just sit it out. Liminal space, however, could be a graced period, where we create something special for the next phase.  The active learning movements were not born out of some mythical halcyon days, where students were all learning and succeeding. Thoughtful people noticed that there were shortcomings in education and that we needed to do better for our students.

So I have a direction to travel through this liminal space. That direction is towards humanistic math education.  Humanistic math education has risen in my thinking more and more over the years. Initially it was about inclusion and equity and helping students succeed at math, and I see even more now that it’s also about somehow teaching people to be more collectivist and that education must also be about all of us. Knowing math is not enough to be a moral citizen, and likewise teaching via IBL without the humanistic element is not sufficient. 

Take care and stay safe!

Saturday, October 2, 2021

Resources for Professional Developers (short post)

Note:  I've been backlogged for a few months from moving and starting at a new job. More posts on IBL topics coming. 

Last August, I gave the Leitzel Lecture at MAA MathFest.  In that talk, I shared some resources for professional developers.  Here's a link to a webpage on the AIBL site with a range of resources.

Some items you find are:

  • N things to consider when facilitating a workshop
  • AIBL Handbook for Online Professional Development: Lessons Learned from PRODUCT Workshops
  • AIBL Workshop Modules for course coordinators running department-level workshops on IBL
  • Self-paced course on Race in America
  • Links to blog posts on equity and inclusion
  • Explainers and evaluation reports for about what IBL workshops are and evidence about their effectiveness. 

Saturday, April 3, 2021

Umami and Teaching: "Feeling Closer to the Teacher of My Vision"

Umami is a Japanese term from the culinary world described as meaty, savory deliciousness that deepens flavor (Link).  Umami as an idea has other forms. For example, umami can also be the first sip of coffee in the morning.  Ahhh!  Or it can be taking a refreshing hot shower after a long hike on a warm summer day. Ahhh!

We usually talk about IBL teaching in terms of benefits to students, the key features, or the nuances of how to implement it well.  What faculty gain is talked about less, and is often overlooked.  For many of us  teaching is a calling, and it's not only because we love our subjects. The enjoyment of teaching is in meaningful human interactions, students and instructors working together towards to learn, discover, and grow as humans.  

One of the big reasons why instructors should use IBL methods is because it's enjoyable and fulfilling for instructors. A centerpiece of IBL teaching is building community, and when students and instructors work as a team, then the magic happens. Enabling the dreams of students and transforming their lives is a great thought to wake up to in the morning. That's a form of umami within the grasp of every teacher.

The evaluation team (Sandra Laursen, Devan Daly, Tim Archie, Chuck Hayward) for the NSF PRODUCT asked participants, what did you gain personally from employing IBL methods? Below are a some responses from participants about umami and teaching. Enjoy!

“I personally enjoy going to class more each day.  When lecturing I sometimes found myself dragging myself to the classroom with particularly challenging groups. In IBL classrooms, I am generally excited to see what my students will do each day.” 

“Teaching using IBL methods keeps me excited about teaching, helps me see things from different angles and I learn new things from students all the time.” 

“When I can do it, I feel really proud and energized--feel closer to the teacher of my vision.” 

“I feel that the IBL workshop helped me adapt my pedagogy in small ways to try to create equity and make my students feel that this was their classroom and that I believed in them unconditionally. I held those beliefs prior to the workshop, but the workshop opened my creative thinking to all the ways I could adapt small (and large) behaviors to support my goals.”

“I enjoyed my time in class more, was able to interact more with the students and develop deeper relationships with each.” 

“I've learned more about the material than I thought I had left to know.” 

“I found it much more enjoyable designing a course around IBL methods, and implementing these methods in my classroom. There's only so much you can do with a lecture, and it becomes boring after a while. It was exciting when students surprised me with the answers, both correct and incorrect.” 

“I enjoy teaching more, and find my work has much more value. I'm not just teaching students calculus, I'm changing what they think mathematics is and their views of themselves and their own view of their ability to do mathematics.” 

“It was a lot of fun! It felt like my students and I were working together and that they were like mathematicians in training/apprenticeships.” 

Monday, March 1, 2021

The case for virtual conferences and workshops post pandemic

The future is not written. We can secure the prosperity of future generations through our actions today. We can make choices that determine how we ultimately manage the climate and human climate crises, AKA the twin crises, of our time. We need both policy and individual actions to address these crises, and while individual actions are small in terms of contributions to the CO2 footprint, changing norms and influencing the policy requires individuals to take part in the process by raising awareness. We influence the people in our circles. 

Everyone wants to see friends, family, and colleagues in person and enjoy activities we can do together. Conference travel has taken me to places I wouldn’t have traveled to otherwise, and I have been able to meet new people and learn new ideas via work-related travel. No one wants to travel more than I do, and I understand how going virtual impacts people.

But my thinking has drastically changed the past few years, and now I’ve come to the conclusion, where I strongly believe we need to do things differently in higher education.  We should plan virtual meetings and conferences post pandemic as the default (with allowances for regional hubs). More and more faculty are concerned about our role in the climate crisis, and some believe we should do our part to reduce our carbon footprint and set an example for other sectors of society. My individual actions are tiny compared to what professional societies and institutions can do, and purchasing an electric car or reducing my air travel is minuscule in relation to what the math profession or the larger education sector contributes.

How much CO2? For one of the 2019 IBL workshops offered by AIBL, the total flight miles was about 90,000 miles traveled by just 33 participants and facilitators. These flights created about 24 tonnes of CO2, and does not include airport transfers, conference room service, and if family or significant others also traveled. 

Conferences create orders of magnitude more carbon footprint than a single, small workshop. One large example is the Fall Meeting of the American Geophysical Union (AGU). “Take the Fall Meeting of the American Geophysical Union (AGU) — the world’s largest Earth- and space-science conference — held in San Francisco, California, last December. We calculate that its 28,000 delegates travelled 285 million kilometres there and back — almost twice the distance between Earth and the Sun. In doing so, they emitted the equivalent of about 80,000 tonnes of CO2 (tCO2e).” (Link).  The Joint Math Meetings or MathFest are much smaller, yet still could account for thousands of tonnes of CO2. 

I think most people understand generally why this matters. David Wallace-Wells wrote about some terrifying studies in his book, “The Uninhabitable Earth.”  Half of all CO2 emitted in history has been during the last 30 years. In one study just the difference between 1.5C and 2.0C and only looking at air pollution (and not other factors) results in an estimated 153 +/- 43 million deaths. This is unconscionable, especially given that poorer, developing regions and BIPOC communities will bear the greatest burden, and they have contributed far less to the crisis (Link to cited article). Not only is climate the largest problem we have faced, it is also the largest social justice problem we have ever faced. What scientists have learned is that we are on the path past +2C, and that climate change is a dial, not a binary on-off switch. The less carbon we emit, the less suffering there will be, and humans control how far we turn this dial. 

Another major reason why I believe in the value and promise of virtual options is equity. There are a handful of groups of people that often are not able to participate in professional development workshops or travel to conferences. These are people with small children or other people in their care, people with health issues or disabilities that prevent them from traveling, non-tenure track faculty, and instructors who do not have access to travel funding, who often work at 2-year colleges and regional institutions. 

Even before the pandemic, people in these categories were not able to travel to conferences or workshops. For those who have been able to travel in the past for work and are looking forward to doing it again, imagine all the people working in our profession who have not had such opportunities. During the pandemic some of them were able to attend virtual JMM or a virtual IBL workshop, and if things open back to the way they were, these groups will once again be locked out. Even if we had the technology to create zero-carbon air travel, equity will persist as an issue. 

One overlooked consequence of going back to 2019 is that it puts the onus on individuals to try and navigate systemic issues. Individuals would have to choose between the climate or attending a conference to advance their careers. Some individuals will not be able to attend, and all they can do it email the organizers, if there will be remote participation options. This is one way systems perpetuate social problems, and hence it is the responsibility of professional societies and institutions of higher ed to work on these issues and develop systemic solutions to system induced, contributed, or created problems. 

One aspect of addressing the climate and equity crises is the essential role of policy. In our small corner of the world of math associations, policies could be crafted that help us do better in both reduction of our carbon footprint and increasing access for all people in the math profession. Otherwise, we will continue to add to climate problems and maintain social inequities.

Biennials, regional hubs and virtual attendance can significantly reduce emissions (Link). Carbon offsets can be purchased to mitigate absolutely necessary travel (and could be built into the cost of registration fees. I personally use Native Energy). I We can also develop virtual events during conferences and workshops to include activities for informal community building, recreating some of the valuable informal time at in-person conferences. We can innovate how we organize these sessions and utilize technology to make these experiences check all the boxes.

One oversimplified mental exercise is to ask, "Would I rather spend part of our carbon budget on work travel or on visiting family once a year?" This is not a real choice. It's an exercise in engaging in defining priorities and attempting to connect to our values.

As a profession we say we care about climate and equity, and if we go back to the way things were in 2019 after the pandemic, then it’s tantamount to looking the other way. Looking the other way normalizes human suffering and inequities, which is exactly the opposite of the collectivist values needed to pull us together to deal sufficiently with the twin crises of our time. So let’s not look the other way and languish in complacency, because we need a more empathic, active response. Let’s look forward and think creatively to recreate better and more inclusive ways to meet and do our work.

Friday, February 26, 2021

IBL Rhythm Changes (IBL-Jazz Analogy)

Rhythm Changes is a common 32-bar chord progression in jazz, originating as the chord progression for George Gershwin's "I Got Rhythm."

Jazz is a useful analogy to some aspects of IBL teaching. You have your big goals and plans for what to do in class, and as the teacher you are the holder of the vision for the course. But what happens in class depends on the people there. Two sections of the same course can often be different on a day-to-day basis. What an instructor does depends on what happened the class before, and being able to "improvise" in the moment to take advantage of what students are saying and doing. That is, be open and able to dance with the spirit. 

The word improvisation sometimes has the connotation that things are just made up on the spot. That's not the case in Jazz improvisation or teaching, and we can unpack what improvisation means. In Jazz improvisation is a studied, practiced, musical art form. Improvisation is within a context, a set chord progression, and there are standard practices and key notes. From these "ingredients" comes the creative artistic part, which I cannot explain and merely enjoy as a fan of Jazz. 

The connection to teaching is that we have our plans for the days and weeks of the course. What happens in a lesson or a specific activity depends on what students do and where they are at. This is where teaching improvisation (or flexibility) comes in. Depending on what a student says, we adapt to maximize the learning opportunities present. Mistakes, half starts, full solutions, alternative takes, are all valued discoveries and items for discussion. The students respond to the teacher, and the teacher adapts to the students. The whole group tries to do math and create learning.

    "In music, silence is more important than sound." - Miles Davis

We can teach using silence, and teaching using silence can mean several different things. One is to ensure students have time to think for themselves. Another is to let students to discuss with one another, where the teacher is not talking and instead listening to student thinking.  A third meaning of teaching with silence is letting problems do the talking. This is when a rich task has the imbedded learning through engagement in the problem-solving process. Rather than the teacher explaining it all, the process of working through a problem can be a way knowledge and skills are learned.

Silence can go too far, of course. A song with 3 minutes of pure silence isn't music. I'm arguing for a balance of saying enough to keep things going or set the stage, but not too much that I'm doing all the playing and students are sitting on the side.  

So what about our detailed plans?  Miles Davis might say, "So what." Plans are preparation, and we should expect to be flexible and present in the moment. Plans are the practice, the setup, the choices about what we're working on, and how we're going to work together. If things go well, our students have the time and space to comp and solo in class, and we learn to work together as an ensemble be more creative, thoughtful, and respectful.

IBL is like Jazz, and one of our jobs as teachers is to be prepared for rhythm changes.

Thursday, January 28, 2021

IBL Workshops Work! Validating Our Theory of Change with the Theory of Planned Behavior (Preliminary)

This blog post is co-written with Dr. Tim Archie, CU Boulder, Ethnography and Evaluation Research, Tim.Archie@Colorado.EDU, and this is work done by him and Dr. Sandra Laursen, Devan Daly, Chuck Hayward, CU Boulder. This effort is funded by collaborative NSF grants DUE-1525077, DUE 1525058.


“A lever is a simple machine used to move an object at one location by applying a force somewhere else. When we try something and see that it is working, we have gained leverage on the problem.” -Levers for Change, AAAS Link

In this piece, we look at one of the key levers for change, professional development workshops in higher education. We'll start with our theory of change, and then share results from our research team. Specifically the data is based on participants, who attended intensive 4-day IBL workshops. These workshops provided intensive training to more than 500 college math instructors, impacting hundreds of courses and thousands of students per year. Peer-reviewed articles will be published separately, and if you have questions about technical aspects of this work, please contact Tim. In this piece, we focus on the broad story about how professional development can change instructor behavior in the classroom.

Our Theory of Change is that instructors need professional development to make the switch from passive instructional methods to creating active, student-centered, inquiry-based learning environments.  This professional development must address instructors’ knowledge and skills to carry out IBL in their own classrooms, but also their beliefs about instruction, and must mesh with their own identities as teachers and understanding of their own students and teaching contexts.  Achieving substantive change in teaching can be addressed via intensive summer workshops that provide these resources and a strong, steady support system that follows each instructor through the evolution of their professional career.  Yet we also need to find ways to build the pipeline of instructors who are aware of and receptive to IBL methods.  To widely offer these varied forms of professional development will require a larger, more flexible group of skilled professional developers than is now available.  Building capacity to design and deliver effective professional development is necessary for increasing uptake in college mathematics.

College math instructors are not fully trained in teaching. We may receive some training as TAs, and then we are off to start our teaching careers. Active, student-centered teaching methods, such as IBL, require skills and practices for maximizing effectiveness. While some instructors are able to learn and develop these skills on their own or by attending conferences, professional development workshops can provide a big boost to help instructors new (or newish) to IBL teaching.

The IBL workshop is a 4-strand model. The fours strands are (1) analyzing video of IBL classes, (2) discussing the nuts and bolts of running an IBL class, (3) developing a target IBL course, and (4) studying articles from the mathematics education literature.  The four strands were designed to address specific obstacles instructors face in their classrooms.

How do we know a workshop works? To answer this question, we need to define two terms, IBL capacity, and IBL intensity.

IBL capacity is an aggregate of several variables. It includes a participant’s beliefs about the effectiveness of IBL, knowledge of IBL, and skill in using IBL. What the evaluation team did is ask participants to self-rate their capacity before the workshop, immediately after the workshop and one year after the workshop.

Our data show in the figure below that workshops increase IBL capacity. We see a statistically significant increase in capacity measures from pre to post workshop and that these gains are sustained through to the one year follow-up.

(The slight drop from post-workshop to follow-up is not statistically significant.)

IBL intensity is a way to measure how much or how intensely an instructor is using IBL. We know the workshops are effective because a large percentage of participants, 94%, reported using IBL methods after attending the workshop.  We also asked participants about the frequency of use of a range of teaching practices (e.g. group work, student presentations, lectures, etc.) before they attended the workshop and again one year after they attended the workshop. Higher scores indicate more intensive use of IBL and lower scores indicate lower IBL use.  Based on their responses, we created an IBL intensity scale shown on the y-axis of the chart below. We see a statistically significant increase in IBL intensity from pre-workshop to follow-up.

Crucially there is more to the story on top of the increases to IBL capacity and intensity. The evaluation team also conducted additional analysis to explain more precisely how the workshops work, using the theory of planned behavior (Ajzen 1991). The theory of planned behavior path model explains how the IBL workshops are influential in changing teaching practices and the relationships between IBL capacity, IBL intensity, and some other key factors.

Let's go down the left side of the model. Belief that IBL is effective is a factor that influences teaching. Simply put, the stronger your belief is in the effectiveness of IBL, the more likely you intend to implement IBL, which in turn affects IBL intensity. The IBL workshop has a strand that provides an opportunity to learn about the research supporting the use of IBL, see successful examples of IBL, and learn about real-world stories of student success. 

Subjective norms include factors such as department or institutional support and supportive colleagues.  For instance, the more supportive your department chair is, the higher your intent to implement is, which then affects IBL intensity. Generally, the more supportive the environment is, the more instructors use IBL. Subjective norms can also be a barrier. If you lack support, then you are less likely to implement. Norms matter, because teaching is a cultural activity, and local environments play a role.

The last factor on the left side is perceived behavior control.  This is the perception of how much you control your behavior, which is highly dependent on IBL capacity. If you feel confident in your skills and knowledge how to implement IBL, then this directly impacts both intent and IBL use. This is where IBL workshops play a direct role. Skills and practices are central topics of the workshops, and as shown we have data supporting participant gains in IBL capacity. 

There are other contextual factors that play a role. These factors are prior IBL experience, whether a course is coordinated (in a way that is supportive of IBL), and class size. All of these factors can potentially be barriers, such as coordination that steers instructors away from IBL or large class sizes.  

Factors such as gender, career stage, rank and position, and institutional type do not influence IBL capacity or IBL intensity (i.e. were controlled for).  This is a striking result, because what this means is that anyone can teach via IBL anywhere! While individuals do face different challenges in the field due to their identity, group differences are not detected in the data. Of course identity matters in teaching, but what we know from experience and from data that no matter what group you are in, it is possible to teach via IBL in whatever setting. This means that the challenges we face are surmountable, and the focus should be on finding ways to support instructors.

Technical Question: What does r = 0.18 mean in the relationship between attitudes that IBL works and intent to use IBL? These are standardized regression coefficients which describe the relative strength of association between an independent and dependent variable. Standardized coefficients have standard deviations as their units, making the coefficients comparable when variables have different levels of measurement.  Please also see “An Effect Size Primer: A Guide for Clinicians and Researchers”

Summary of key findings

  1. The theory of planned behavior model explains 21% of the variability of behavior change (IBL intensity). (Note: R^2 equal to 21% is a significant result for social science. For more see this Link
  2. Workshops increase IBL capacity. 
  3. Workshops increase IBL intensity.
  4. Department norms and institutional support matter for better or worse.
  5. Other factors like class size, course coordination, environment, course coordination, beliefs, play a role influencing IBL intensity. 
  6. Anyone can teach IBL anywhere (under the right conditions)

Consequently, we can confidently say that IBL workshops work. Instructors change practices in meaningful ways. We can measure IBL capacity and intensity, and further we can see more clearly how the pieces fit together in a coherent story. Some policy implications include increased and sustained investment in professional development workshops, providing more support for faculty to access training, conducting outreach by individuals and professional societies, targeted efforts to inform and train department chairs and course coordinators, and investing in addressing institutional barriers to adoption of IBL methods (e.g reducing class size, mitigating the effects of large class sizes).


Ajzen, I. (1991). The theory of planned behavior. Organizational Behavior and Human Decision Processes, 50(2), 179-211.

Archie, T., Laursen, S., Hayward, C. N., Yoshinobu, S., & Daly, D. (2020, November 5-7). Findings from 10 years of math instructor teaching professional development [Link to Poster]. This Changes Everything, AAC&U Virtual Conference on Transforming STEM Higher Education.

Ferguson, C. J. (2016). An effect size primer: A guide for clinicians and researchers. In A. E. Kazdin (Ed.), Methodological issues and strategies in clinical research (p. 301–310). American Psychological Association.

Friday, January 8, 2021

Why I Use Dr. Y or Professor Y When I Teach

When I started teaching, I was given some advice to use my first name with my students. The idea was to be more friendly and make things more comfortable in class. Many of us, perhaps nearly off of us, got that message. I didn’t think about it too hard then, and I did that for many years, all the while not knowing that what I was doing was making things harder for women in academia.

Last month Dr. Jill Biden was the target of a disdainful WSJ op ed, basically saying she’s not a real doctor and full of sexism and anti-intellectual tones. It’s one example of a long history of sexist put down of successful, smart women in the academy.

Men get to be Dr. ___, even if they use Stan or Paul in class, but women get called Ms.___ or Alice, and it’s not always respected or assumed that the woman is a Dr. ___ and an expert.

This is how systemic biases can work. We do things without knowing that it undermines a group of people. A well intended suggestion I received early in my career, which sounded like good advice at the time, actually had some hidden( to me) negative aspects that oppresses women in higher education. Later I learned about the biases that make it so that women have to work harder and deal with more, and the extra challenges and burdens women have to deal with.

Consequently, I decided years ago to use Dr. Y or professor Y with my students. It’s out of solidarity with women and minoritized groups, and it’s with the long-term goal of contributing to shifting norms towards equity and social justice. If we all did it, then that’d be the standard way students would address *all* faculty.

In countries like Japan, all teachers in elementary and secondary schools, professors, medical doctors, other leaders are given the title, “sensei.” It is an honorable title for those who teach or help others in society. Japan is not a society that earns high marks for gender equity, so I’m not trying to say that the term is some magic bullet. Thinking about what sensei means in Japan, however, does provide useful insights. Doctor can mean more than one thing, and we generally lack norms that could help our education system be more inclusive and equitable for women.

The closest thing we have to sensei is professor, although professor has been earmarked as a rank. For those who are lecturers and without a Ph.D., we do not have a professional title. Given all this, I argue that it is appropriate for all college instructors to use the title “professor” in classes, just as sensei is used by K-college instructors in Japan. Words and titles can mean more than one thing, and their meaning can be easily understood in context.

Thus, I invite all my colleagues to consider using Dr. or professor with our students, if you haven’t done so already, because it contributes to shifting norms in a decisively positive direction. We could explain to our students why we are using our titles, and why it’s important to respect all educators for gender equity. Where possible, we can use our titles, identities, and positions at our institutions to level the playing field for women in higher education.