It's a great pleasure to be able to interview of Professor Daniel Reinholz, San Diego State University about a vital issue, gender equity in the academy. As it happens, how we teach using active learning matters very much. This interview is based on a recent 2022 publication, When Active Learning is Inequitable: Women Participation Predicts Gender Inequities in Mathematical Performance, Journal for Research in Math Education, Volume 53, Issue 3.
The authors of this article are Daniel Reinholz,Estrella Johnson, Virginia Tech, Christine Andrews-Larson, Florida State University, Amelia Stone-Johnstone, California State University Fullteron, Jessica Smith, Florida State University, Brooke Mullins, The University of Virginia's College at Wise, Nicholas Fortune, Western Kentucky University, Karen Keene, Embry-Riddle Aeronautical University, Niral Shah, University of Washington-Seattle.
First, tell us a little about yourself.
My name is Daniel Reinholz and I’m an Associate Professor of Mathematics Education at San Diego State University. Broadly, my research focuses on understanding how patterns of inequity arise in mathematics classrooms, developing methods to make these inequities visible, and helping instructors recognize and disrupt these inequities with their teaching. One way that I have done this is through the EQUIP observation tool (https://www.equip.ninja) that I co-develop with Niral Shah (Reinholz & Shah, 2018). EQUIP is free and customizable, and it tracks who gets to participate and how. Because participation is a key part of learning, we want to ensure that all students get to participate in meaningful ways (not just some students who are positively stereotyped in math classrooms). EQUIP automatically generates data visualizations to help instructors rethink their strategies for their next lesson. Most inequities that arise in classrooms are subtle and unintentional, so having extra data to support us to teach better is always helpful.
When not working on math stuff, I’m probably playing with my two young children, or making music on the drums or piano. I love spending time outdoors, enjoying the oceans of San Diego, and traveling when life allows for it.
Active learning by itself isn’t a panacea to issues in equity and inclusion in the classroom. We have known this from earlier work. You and your co-authors recently published a paper in JRME, When Active Learning Is Inequitable: Women’s Participation Predicts Gender Inequities in Mathematical Performance (2022). Why did you study this issue and what are some of the takeaways from your paper?
A number of years ago I was talking with co-authors Estrella Johnson and Christy Andrews-Larson at a conference about some findings from the TIMES project they were running. The TIMES project is an excellent set of inquiry-oriented curricula for upper division mathematics. Christy and Estrella (and others on the project) had developed a robust professional development program that they studied over a few years. Surprisingly, they found gender inequities in the inquiry classes that weren’t present in the lecture classes. (To be clear, the inquiry classes led to greater learning overall, but there were inequities, because men disproportionately benefited compared to women). I suggested that we work together and analyze their data using the EQUIP tool, so that we could get a better sense of what was happening in terms of classroom participation and how that might connect to inequities in student outcomes. As expected, the amount of participation by women was a significant predictor of how well women scored on the performance outcomes.
Tell us about “shared inquiry” and what that looks like?
Although our study was primarily focused on quantitative data, we developed a few qualitative profiles of classrooms to help readers get a better idea of what was happening. The shared inquiry set of classrooms were the ones that had the highest levels of performance for women. What we found is that in these classrooms, students were most likely to respond directly to their peers and build on each other’s ideas. In short, the instructors had created a productive community of learners that could work together to deepen their mathematical understandings. Although the other classes in the study also featured inquiry-oriented teaching strategies, some of those were more centered around the teacher going back and forth with individual students. In other words, the teacher was the center of the conversation, not the students.
There were no classroom observations at the beginning of the semester, so we can’t say exactly how the instructors initially built this positive community. But we can hypothesize that they used a variety of strategies to build their classroom culture, community agreements, participation norms, empower students to share ideas and take risks, and so forth.
As a caveat, I want to mention that these instructors didn’t simply ask the students “who would like to participate?” and have students answer in a free-flow way with no guidance. Our research across hundreds of classrooms shows that if instructors aren’t intentional in setting up the participation dynamics and supporting marginalized students, then white and masculine norms tend to dominate, and so white men talk more than most other students. In short, using a variety of simple strategies like having students raise their hands, using wait time, waiting for multiple hands before calling on someone, stopping conversations with think-pair-share if nobody raises their hands, and setting up students to share work from small groups to the whole class are all useful and we’ve used them in our professional development across settings to great success.
What are the benefits of a shared inquiry classroom?
These classrooms empowered students to learn from another and respond to one another. They helped students deepen their thinking, take risks, and have ownership over their learning. This is quite a wonderful thing to witness in a mathematics classroom. Stereotypical images show stressed out students sitting in desks listening to lectures. In contrast, these classrooms had students engaged with each other and learning from each other.
Why might pairs work better than larger group sizes? Other implications for using groups?
My early research work focused on peer feedback (Reinholz, 2015, 2016). In particular, I had pairs of students provide feedback on in-progress solutions to homework problems, which they later had a chance to revise and turn in. I’m a strong proponent of partner work because it provides more equitable opportunities for students to participate. Because there are two students, in most cases, both of them are able to take turns and share their ideas. In larger groups, group dynamics can take over and one or two students dominate the conversation. Larger groups can also work well when they are set up properly, but they definitely need more support to provide equitable learning opportunities. Variety is a spice of life, and it makes our teaching better too. A variety of different modalities can give students a lot of different ways to learn and engage.
What an instructor says when visiting groups matters (e.g. “Show me what you tried…”) In your prior work, how instructors prompted students that positively or negative affected women and non-binary students?
In this study we were focused on coding whole-class contributions, so we can’t speak to what happened in small groups. However, in prior work we have observed gendered interactions in small groups (Ernest et al., 2019). What we find there is that a lot goes on behind the scenes that instructors aren’t always aware of, and some of it can be very sexist and problematic. As instructors, the ways that we interact with students both explicitly (e.g., community building and norm setting to disrupt oppressive ideas) and implicitly (e.g., valuing student contributions, seeing student strengths rather than criticizing them) can help move away from that type of environment.
Most importantly, our work showed that women and non-binary students tended to participate more in the small groups and less in whole-class discussions, if there was an overarching masculinized environment in the classroom. As instructors, we should be listening to the interesting things our students are saying in small groups, and helping support them to successfully share them publicly (e.g., “Kayla, that was a really interesting observation about the group axioms. Can you share that with the class when we come back together? I think it’s really important for them to hear your insight.”). Using statements like this, we can help get minoritized students into the whole-class discussion in a way that showcases their brilliance. Although the studies I’m focusing on here attend to gender, we’ve found similar results for race in other settings.
We know there is quite a strong literature in support of active learning from the past several decades. How might this paper or a paper like this be misinterpreted or used for misinformation?
To be clear, our main finding was that overall students learned more in the active learning classrooms when compared to lecture. However, because men disproportionately took up the learning opportunities made available in class (leaving less opportunities for women), they benefited even more from the inquiry teaching. To say it again – on the whole students learned more in the active classes. This work doesn’t provide any evidence in favor of pure lecture. Of course, we all use direct instruction at times, and there’s nothing wrong with that, but students also benefit when they have chances to try problems, talk to their peers, and so forth.
I think it is pretty easy for someone to take this paper as evidence that active learning is problematic, but that would be a misinterpretation. More accurately, I would argue that this paper shows how we need to be intentional about creating equitable learning environments, so that all of our students are able to benefit from the rich learning opportunities available in our inquiry-oriented and inquiry-based classrooms. We shouldn’t assume that it will happen automatically. The very same inequities that exist in society tend to reproduce themselves in our classrooms, unless we explicitly disrupt them.
One challenge for many instructors is using an equity lens during the planning phase of teaching. When instructors plan, it’s mostly thinking about the content and how to organize activities in class. False cultural frames, implicit bias, and other factors are not usually considered intentionally. What are some specific areas where instructors can use an equity lens with intent and hopefully good outcomes?
For the last eight years I’ve had a laser focus on classroom participation. Having observed hundreds of math classrooms (and other disciplines too), essentially every classroom that I’ve observed has some sort of inequity (e.g., Reinholz & Wilhelm, 2022). These inequities are exactly what you would predict based on gender and racial stereotypes in mathematics. Typically, classrooms have 1-2 dominant students from dominant groups (often white men), who will take up a large proportion of the conversational space, and not allow for other students to participate as well. Knowing this, instructors should be intentionally planning how they are going to support women, non-binary folx, racially minoritized students, disabled students, and so forth. Strategies for controlling the flow of discussions and who gets to participate (like the ones I described above), can go a long way to disrupting long standing inequities in our society that manifest in our math classrooms.
Another area that instructors don’t often think about is access. In mathematics, we assume that there is a single, best way to communicate (through formal mathematical proof), and we look down upon other ways of expression (through our bodies, or drawings, or more informal language). However, students bring a wealth of lived experiences and cultural resources that we can draw upon to help them understand math better. One way to approach this is by opening up conversations around access. Rather than creating a rigid classroom structure, ask students what they need to do their best work. Rather than only allowing one way to complete an assignment, give students a wide variety of options to engage and express their learning.
I’ve recently written an article about creating access in the classroom that I’d love to share with the community (Reinholz & Ridgway, 2021).
Currently, I’m working on two books that describe both mathematics teaching strategies and the EQUIP method in detail. Stay tuned, and I’ll be excited to share these resources with our community.
Any other advice for instructors?
I have a few pieces of advice. First, don’t try to do it alone. There are so many incredible mathematicians and non-mathematicians doing really fantastic work, and we should learn from each other. Most of what I know about effective and equitable teaching has come from watching others do it and learning from them. You could create a learning community with peers. Most important, there’s a lot to learn from our colleagues outside of mathematics. Even though they are working in different disciplines, they have a wide variety of strategies and teaching methods that we might not think to use because they are not as common in math, but they are actually very effective.
Second, there’s so much information out there–from the Academy of Inquiry Based Learning, The MAA Instructional Practices guide, research articles, and so forth–that we’re in a really great place to learn more. When I work with instructors, I don’t recommend trying to change too much at once. I usually have folks work on about one new practice every month, so that they can get used to using it, incorporate it into their teaching, and learn how to do it effectively. If you change everything at once, it probably won’t work very well, and it’s easy to conclude that the new strategies aren’t effective (even though that’s not true). Slow and steady is best from my view.
Third, have fun! Getting to know our students, building relationships, and having fun is the foundation for building a happy, productive, exciting, and equitable classroom.
Resources
- MAA Instructional Practices Guide
- AIBL Equity and Inclusion page.
- Future Picture a Mathematician workshops will be posted here.
- Building Gender Equity in the Academy, Laursen and Austin.
- Advance Institutional Transformation, Evaluation and Ethnography Research, University of Colorado Boulder.
References
