Defensiveness is a barrier to equity work

Defensiveness can be a barrier to effective communication, particularly when it involves receiving feedback from others or encountering information that contradicts what we believe about ourselves. For that reason, defensiveness can be a major barrier to becoming a more equitable educator. In this blog post, I’d like to dive deeper into this subject to think more deeply about what I can do to become a more equitable educator and how we can help our field move towards greater equity and justice.

A few months ago, I was teaching multi-variable calculus and drew the following vector field on the board.


When this happened during class, a student mentioned “Oh! It looks like a swastika” and I said that it was unintentional but didn’t change the diagram and just kept going on.

After class, one of my students came to tell me that another student felt uncomfortable with the swastika and with the way that I handled the situation. In that moment, I felt a rush of defensiveness. My initial instinct was to defend myself (to point out that the swastika has actually been used for centuries before the Nazis and the version that appeared in class is actually a different orientation from the Nazi swastika and is closer to the sacred symbol used in many Asian cultures (…and even now as I write this I still feel defensive and feel like I have to explain myself)). I didn’t say any of that. Thankfully, I just paused and apologized, expressed that it wasn’t my intention to be dismissive and didn’t realize that it had that impact, and said that I would be more careful with this example in the future. Later, I removed one of the red arrows above in the online version of the lecture notes.

I share this anecdote not to make any kind of judgment on the student who felt uncomfortable. I don’t want to get into a debate about political correctness or students who are fragile “snowflakes”. All that matters here is that a student felt uncomfortable, I received feedback about it, and that feedback helped me recognize how I will do better in the future. (In the future, I won’t shy away from this example, but I will take 30 seconds to share a bit of history about the symbol.)

What was the source of the defensiveness in that situation? I realize now that the first emotions I felt in that moment had to do with surprise and anger from being misunderstood: “How could anyone think that I would be so insensitive or oblivious as to use such a hateful symbol in my class? Don’t you know all the stuff I’ve done to promote equity and justice?” I really dislike the feelings that come with someone being offended or upset by something I said or did, when that was not my intention–lots of people feel this way. And, that, dear friends, is a common source of tension for many people about talking and thinking about equity. The recognition that our past deeds might have marginalized, discouraged, or discriminated against people of color, women, people with disabilities, LGBTQ people (list goes on…) runs smack into the thought “BUT I DIDN’T MEAN IT”. And yet, while the intent was not there, the impact can still be real.

How does defensiveness lead to undesirable outcomes? When receiving feedback from someone else, defensiveness shifts the focus from the issue at hand to our own emotions. In this situation, if I would have responded defensively, it would have shifted the attention away from the student who was uncomfortable to my own hurt feelings. And the reality here is that I had nothing here to lose except my own stupid ego by listening to and receiving the feedback.

I’m not saying that we instructors should not defend ourselves against baseless accusations. If it is really the case that there is no possible iota of truth in the feedback that I am given, then I can choose to reject the feedback, or perhaps actually defend myself. However, in this situation, there really was something that I could have done differently so the feedback was helpful. And, the power difference in the student-teacher relationship is important here. Because it takes so much more courage to say something to someone who has power over you, I believe that when instructors receive feedback like this we should listen carefully and err on the side of being generous.

Here’s another example of how defensiveness can be an impediment to thinking about and working toward greater equity. An imagined conversation snippet:

Person A: “I think when our department enacts policy X, that is a form of institutional racism.”
Person B: “What are you saying? I’m not racist!”

The words “racist” and “racism” can conjure up strong feelings and sometimes bring conversations about equity to a halt. The historical significance of the word “racist” (that it came into popular use in the 1930s in response to the Nazis) helps to explain why some people react so strongly to that word.

This kind of defensive reaction often stems from the contradiction between unjust outcomes or discriminatory behavior and a belief in oneself as a good and decent person: “How could students possibly suggest that I could be racist/sexist/*-ist? Don’t they know that I have been fighting for [XYZ cause] for longer than they have been alive?” As with the previous swastika anecdote, the defensiveness here has the effect of shifting the conversation away from the topic of discussion (a policy) to a person’s feelings.

To get move past my own defensiveness, I want to work toward having a thick skin but tender heart. I want to become less sensitive to the effects of any feedback and criticism on my ego, or my conceptions of who I am or want to be, and instead be more sensitive to the experiences of others. I would rather err on the side of being misunderstood than to misunderstand others. My problem is how to disrupt the surge of defensive emotions so that I can exercise enough cognitive control to react gracefully in that situation.

And as an educator who tries to help others move toward greater equity too, I think this deeper understanding of my own defensiveness will help in situations when I encounter defensiveness with others. Defensiveness often begets more defensiveness, so having a thick skin and tender heart can help to disrupt that cycle.

(Many thanks to Dylan Kane for encouraging me to think about this topic, and to Robin Wilson and Dagan Karp for their helpful feedback.)

The Ever-Present Challenges of Group Work

I have written previously about how group work is both great for students and difficult to do well. Today I had a conversation with a student and faculty member that reinforced these ideas again.

Prof. X, a faculty member that that I know, is trying to incorporate more small group work in an upper division mathematics class. Through a set of circumstances that are too complicated to explain here, today I happened to talk to Student S who is in Prof. X’s class. Student S shared some difficult moments that she experienced in the class recently.

(1) In one situation, Student S said that she was in a group of four students. The students were asked to answer questions on the back of a worksheet, which involved parsing some definitions on the front of the worksheet. Three of the students chose to forge ahead on the questions without reading the definitions first, referring to them when they needed them. She wanted to read the definitions first and understand them before moving on. They left her behind and she basically worked on the assignment by herself.

(2) In another situation, Student S was in a group of four and was the only female student. Each person in the group was given a different task to complete and had to explain how to do that task to the rest of the group.  When it was Student S’s turn to explain her task, a student in her group was a bit confused and another student jumped in and explained Student S’s task instead of letting her explain it. And, that student didn’t explain it correctly! But, Student S diplomatically corrected the situation by giving the correct explanation to her group and also helped the student who jumped in realize that it wasn’t right that she wasn’t given the chance to talk about her assigned task. Nevertheless, Student S said that this “mansplaining” happened two more times that day.

Experiences like these caused Student S to feel frustrated in these group work experiences. Student S also shared that she has had a difficult semester full of experiences that have caused her to doubt her mathematical abilities. I don’t know all of the details, but I do know that one of the reasons why active learning (and group work in particular) is so risky is that it puts students at risk of being judged by each other and the instructor as being incapable, slow, unprepared, less than.

I also happened today to talk to Prof. X, who genuinely wants to make his class a more welcoming and inclusive space by using group work. He shared with students some research showing that that group work helps improve student learning overall but also tends to have disproportionately large benefits for women, first-generation students, and students of color. That transparency is very important and most of us could probably benefit from being more transparent about the rationale for our instructional choices. However, there is a slight danger here that I hadn’t considered before: these research studies show positive results of using group work on average, but that research does not guarantee that individual students will always benefit from the effects of group work. In fact, my hunch is that the variance of experiences in active learning settings may be higher than in a more controlled lecture classroom format. So, while transparency is important, I also wonder about whether in sharing evidence for these instructional approaches we also need to be careful to avoid making students that don’t have good experiences as a result of those approaches feel bad about that.

Let no one misinterpret what I’m saying here as a pronouncement against active learning or group work–on the contrary, we should double-down on group work and active learning, recognizing that it is simultaneously beneficial for students and difficult to implement well. We instructors need to think carefully about how we deploy group work and other forms of active learning so as to mitigate any potential negative effects, as much as is possible. Here are three questions to ask ourselves to do so:

  1. Who is likely to benefit (as a result of me using group work or some other form of active learning)? Who is not?
  2. Who is likely to feel included? Who is not?
  3. How would I know if I need to intervene in some way?

To answer questions #1 and #2, I suggest we think of groups of students such as first-generation students, introverted students, students of color, students for whom English is not their first language, students with learning disabilities, students who have had bad experiences in a mathematics classroom, etc. For example, in the case of (1) above, it might be the case that the group work was inadvertently structured in a way that students who needed or wanted more time processing definitions were at a disadvantage. It would then be a good exercise to think about ways to mitigate the difference in experiences caused by the way the activity was structured.

Note about questions #1 and #2: Almost certainly students who come to class prepared are more likely to feel included or to benefit from your class activities compared to students who don’t come to class prepared–that is a difference that is expected and that you may or may not want to mitigate.  It’s those other unintended and unwanted consequences that we need to look for.

Regarding Question #3: Student S is a remarkable person who has enough self-assurance that she was able to have a long conversation with Prof. X about these difficult topics, which led Prof. X to make some changes to the class. But, that leads me to wonder: in the absence of having such thoughtful, well-composed, mature students as Student S, how would we find out about these kinds of problems in our class? We can’t be everywhere all at once in the room when group work is happening. If we don’t have mechanisms to gather student feedback, problems can go unnoticed and result in real harm to students.

These conversations today also remind me the important of setting and maintaining norms of behavior in the classroom. It’s easy to set up good norms. It’s much more difficult to maintain them and creating a culture in your classroom where those norms are pervasive.

The reason these conversations were so poignant for me is that I know Prof. X has the best intentions and is making a strong effort to be inclusive and welcoming and yet Student S experienced these discouraging situations. It made me wonder how ignorant I am about such things happening in my class.


Why should faculty care about diversity, equity and inclusion?

Sumi Pendakur and I recently published an article in the Notices of the American Mathematical Society entitled, “Advocating for Diversity and Inclusion in Faculty Hiring,” in which we offer some best practices for faculty searches. Though it was written for people in the mathematical sciences, the strategies and tactics we offer can be used by any faculty search committee.

We wanted to share with you a section of the paper that didn’t make it into the final printed version, due to space constraints. We both consider this section to be an important piece of the puzzle.

I’m going to label this missing text as “Section 0” because it comes before Section 1. (This text will probably make more sense if you read it in the context of the rest of the article.)

Section 0. Why should faculty care about diversity, equity and inclusion?

Ultimately, the degree to which our institutions are successful at increasing diversity, equity and inclusion depends on how our institutions and those connected to it see these things as vital to their mission (Smith, 2009; Taylor, Milem, Coleman, 2016). The more that we can articulate our own reasons for promoting diversity, the better we can share those with others and see how they are connected with the missions of our institutions.

One of the most important steps that departments can take to support diversity in faculty hiring is actually something that takes place long before the position is approved. That step is to come to a shared understanding as a department about what is meant by words like “diversity” and “inclusion” and how those things relate to the mission of the department. If your institution has a strong vision for diversity, that is always a good place to start. Coming up with a department diversity statement can be helpful, but written documents like these are helpful only as much as they are supported and enacted by individuals in the department.

There are many specific reasons why your department or institution might value diversity in the mathematical sciences. The following economic argument is cited by publications such as “Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future”: minority groups are increasing as a percentage of the U.S. population and if these groups are not well-represented in the STEM workforce, we will suffer from a shortage of innovators who will spur economic growth.

Another argument has to do with the quality of work that we produce as a discipline. Without a broad representation of people, we cannot be sure that our work in the mathematical sciences addresses all of the important issues that need to be addressed, or that we are addressing these issues having heard all of the voices that need to be heard. More equitable participation will increase the robustness of our discipline.
Leadership is a common educational goal at many institutions, and that can often be a way to connect the mission of the institution with diversity. In today’s global society, multicultural competence and awareness of the societal impacts of one’s work is an increasingly important component of being a leader.

The student success imperative is also tied to the vision of diversity held by the institution and the search committee. Recruitment, retention, and successful graduation of an increasingly diverse (racially, sexually, and socioeconomically) student body is directly impacted by multiple factors, including quality of faculty interaction and whether students see themselves reflected in the curriculum and in the faculty body. The powerful mentoring relationships of faculty of color and students of color are well-documented in the literature and contribute to the feeling of a welcoming and inclusive learning environment. In addition, critical mass of minoritized communities in both the student and faculty bodies reduces stereotype threat, thereby enhancing academic success.

Then, there are a whole range of arguments for diversity having to do with social justice. If your institution or department has a goal of graduating ethical people who contribute to society, one can make the argument that it is important for our students to understand their mathematical work in a historical context of exclusion and underrepresentation in the mathematical sciences in the U.S. Hiring faculty who have an understanding of the historical and sociological context of patterns of exclusion in our discipline and are able to integrate that knowledge into their teaching benefits ALL students.

If your department can find consensus around a set of arguments for diversity, equity and inclusion, it will be much more likely that its actions, including teaching practices, curricula, and faculty hiring practices, will support these outcomes. It will also make it less likely that a search committee will fall into the trap of making a false dichotomy between excellence and diversity; instead search committees will see that diversity is part of what it means to reach excellence by fulfilling its goals.

References mentioned in this excerpt:

Smith, Daryl. Diversity’s Promise for Higher Education: Making it Work. John Hopkins University Press, 2009.

Taylor, Teresa E., Jeffrey F. Milem, and Arthur F. Coleman (2016). Bridging the research to practice gap: Achieving mission-driven diversity and inclusion goals. New York,
NY: College Board. Available at

Active Learning 2.0: Making it Inclusive

I’ve written several posts (1, 2, 3) about why active learning is a good thing. There is even growing evidence that some forms of active learning seem to raise student learning outcomes and make those outcomes more equitable at the same time.

All of that is great, but I believe strongly that active learning is not a magic bullet and can be implemented well or poorly. It can sometimes alienate students. A few years ago, I asked students to work in groups on a set of problems in complex analysis. I didn’t give any instructions on how to work well with each other and the problems were rather routine ones. That created a situation in which a student felt left behind in her group and she got discouraged. I tried to talk to her after class but it didn’t help and she dropped the class shortly after.  She said that she dropped the class because it didn’t fit into her schedule, but I still suspect that the group work experience had something to do with it.

In this post, I would like to argue that just using active learning is not enough. Because active learning requires students to be more engaged in their own learning and often involves more human-to-human interactions, we must pay attention to how those experiences support or diminish students’ sense of competence and belonging. I believe that in most cases, what’s needed is a little more care and planning in the use of active learning. I’ll try to illustrate that through some examples.

Example #1: Think-Pair-Share

A common active learning strategy is “think-pair-share“. Unfortunately, I often find that instructors skip the “think” step and skip to “pair and share.” And more generally, I find that most speakers/facilitators/instructors don’t give any (or sufficient) independent think time before asking participants/students to talk with one another.

In many situations, independent think time is so important because it gives time for people who process information in different ways to put together their thoughts before talking. Some people are great at “talking while thinking”: putting together their ideas while talking it out. It can work out well if you’re like this and you’re around other people who are similar–the process of building off of each others’ ideas mid-sentence is fun to watch. Unfortunately, I’m not one of those people. I prefer to have some time to think before I just start talking and I don’t like it when other people interrupt me when I’m talking.

By giving students independent think time before asking them to discuss, instructors can give students more equitable access to the opportunity to think. Students with learning differences, students whose first language is not English, students who are introverted will appreciate having more time to think before speaking. Even those students who like to “talk while thinking” will probably have more refined ideas to share before they start talking. Therefore, the independent think time makes discussions far more productive and less awkward.  I dislike those moments when I’m in a room of people and the speaker/instructor asks us to talk to each other and there’s this awkward period when people are trying to figure out what to say and who should start, etc.

Example #2: Open-Ended Projects

Do you assign open-ended projects in your classes? For example, in our introductory differential equations course, we often ask students create a model involving differential equations for some phenomena in their lives, then give a short presentation on it. It’s an assignment that spans several weeks and involves teams of three students working together.

These kinds of open-ended projects have all sorts of wonderful benefits: increased agency allows students to take more ownership over their learning; the open-ended nature of the task allow them to connect the course content with their own lived experiences; the chance to be creative makes the learning more memorable, fun, and motivating.

However, it is important to look at how these open-ended projects are structured for students. In particular, I am thinking of the work by Mary-Ann Winkelmes and others on the Transparency in Teaching and Learning (TILT) Project. If our instructions for these kinds of assignments don’t clearly convey to students why they should be personally invested, how to carry out the work, and how the work will be evaluated, we run the risk of making students bewildered and discouraged. That’s where it becomes helpful to be transparent about the purpose, tasks, and criteria for these open-ended projects. Of course, the tricky part is to balance being clear about processes and criteria while still maintaining high cognitive demand and room for creativity.

The reason this issue connects with equity is that not all students have had the benefit of having similar kinds of experiences in their previous education. Those that have often run with these kinds of open-ended tasks. Those that haven’t are likely to find the task so open-ended to be unsettling.

Here’s a nice way to see if your open-ended projects are written up in a way that students might find confusing: show your project instructions to a colleague in a different content area. Ask them what questions they might have as they read the instructions for your open-ended project. That will help to reveal some of the hidden assumptions that you might be making about what students know about these kinds of tasks. Being more transparent helps to put students on a more level playing field.

Example #3: Group Work

I saved this topic for last because I think it’s tricky to do well. The rewards and risks that accompany it are great.

If you assign students to work in heterogeneous ability groups (i.e., creating groups in which struggling students work with “more capable” students), there is always the risk of the groupings themselves to discourage students. Students aren’t dumb–they know that we sometimes group them in this way. If you are struggling in the class and you see that you’re always the one in the group that is struggling, and you’re not really getting the support you need from your peers, you might begin to wonder whether you really belong in the group and the class.  Students also don’t know how to help each other, especially in math classes–their understanding of what it means to help someone else usually involves telling someone a procedure or answer without providing any of the rationale.

But even if you group students in other ways, because you can’t be in all places at all times in the classroom, there is always the risk that one of your groups has negative interactions that spoil the learning for the group, or worse, cause some students to feel marginalized or excluded.

The example that I mentioned at the top of the post suggests a second reason why group work can go badly. When you ask students to work together on a task that really doesn’t require multiple brains, then you’re setting students up for to compare themselves with each other to see who can do it faster/better, or to zone out and copy the work of the “smart” student. If you’re going to have groups of students work together, then the task should really take advantage of the fact that multiple brains working together can accomplish more than those brains working in parallel but separately. In other words, you should use group worthy tasks.

Third, group work can go awry because we all have biases. The small groups in the classroom become microcosms of inequities that exist in the broader society. For example, if you have a group of three men and one woman working together, you might find that the three men ignore the contributions of the woman. Students need to learn how to work well with each other. Scan the classroom frequently for status issues (for example, by looking at each student’s body language and how much they are talking/contributing).

Finally, there is the challenge of establish and maintaining norms and expectations for group work (you have them, right?). If students aren’t familiar with your norms and expectations, you might want to find ways for students to practice working in groups before doing it in class on course content.

What other strategies do you use to ensure that active learning in your classroom supports the learning for all students? Please add your comments below.

Building Evidence Connecting Teaching Practices and More Equitable Student Outcomes (Continuously Updated)

In their 2014 paper “Active learning increases student performance in science, engineering, and mathematics,” Freeman, et al., suggest that we are seeing a new wave of “second-generation research” in the education literature that explores “which aspects of instructor behavior are most important for achieving the greatest gains with active learning, and elaborate on recent work indicating that underprepared and underrepresented students may benefit most from active [learning instructional] methods.”

Indeed, a growing body of research shows that there are specific teaching strategies that (on average) improve learning outcomes for all students and also (on average) improve learning outcomes disproportionately for students who have been historically excluded from STEM: women, African American, Hispanic/Latinx, Native American, first-generation, low-income students.

In this continuously updated blog post, I will try to maintain an annotated bibliography of such research. My goal is to provide higher education faculty and faculty developers with evidence to support teaching strategies that produce more equitable learning outcomes for all students, but particularly those who have been historically left out of STEM fields.

It must noted, however, that these learning gains from active learning pedagogies are not automatic. Much more research is needed to tease apart the nuances and conditions under which students who have been historically underrepresented in STEM benefit from active learning pedagogies. And in fact, please read this other post about research that provides more nuance on how active learning pedagogies don’t always lead to more equitable outcomes.

(Papers are listed in chronological order.)

Lorenzo, M., Crouch, C.H. and Mazur, E., 2006. Reducing the gender gap in the physics classroom. American Journal of Physics, 74(2), pp.118-122.

Multiple versions of an introductory calculus-based physics course for non-majors at Harvard were compared over a period of 8 years: (1) traditional lecture and recitation sections, (2) Peer Instruction with traditional recitation sections, and (3) Peer Instruction with cooperative problem solving activities during recitation sections. (It seems that there was continuous evolution of instructional practices throughout those 8 years, but the researchers groups students in these three buckets.) In Peer Instruction, the instructor alternates between giving short mini-lectures and facilitating small group student discussions on conceptual questions. Student learning gains were measured using the Force Concept Inventory. Learning gains increased with the uptake of more active learning pedagogies. In addition, performance differences between men and women decreased with the uptake of more active learning pedagogies. In version 3 of the course, there was no statistically significant difference in normalized learning gains between men and women, despite there being a difference in pre-test knowledge between men and women.

Beichner, R.J., Saul, J.M., Abbott, D.S., Morse, J.J., Deardorff, D., Allain, R.J., Bonham, S.W., Dancy, M.H. and Risley, J.S., 2007. The student-centered activities for large enrollment undergraduate programs (SCALE-UP) project. Research-Based Reform of University Physics, 1(1), pp.2-39.

This report details the efforts of several groups of faculty to show that active learning pedagogies can be used in introductory physics classes with up to 100 students. The SCALE-UP approach involves using the bulk of class time for students in groups of 3-4 to work cooperatively on rich, computer-based activities and class discussions. Lecture is limited to 10-15 minute segments, mostly to introduce course material. Learning gains were measured using the Force Concept Inventory and Force and Motion Conceptual Evaluation. Student groups were regularly rearranged so that each group had students “from the top, middle, and bottom thirds of the class ranking” and that any women and minority students were not the only ones in their group. They found that when compared to traditional versions of introductory physics, SCALE-UP versions led to greater conceptual understanding, improved attitudes, drastically reduced course failure rates “especially for women and minorities” (pg 37), performance in second semester physics improved.

Huber, Bettina J., 2010. “Does Participation in Multiple High Impact Practices Affect Student Success at Cal State Northridge? Some Preliminary Insights” Northridge, CA: California State University-Northridge Office of Institutional Research.

National Survey of Student Engagement (NSSE) results from 863 graduating seniors at CSUN showed a correlation between HIP participation and higher GPA at exit and increased likelihood of graduating on time. Low-income students (Pell Grant recipients) and Latinx students had even higher GPA bump. Exit GPAs of Latinx and Pell students who didn’t participate in HIPs were lower than those of other students but if they participated in three or more HIPs their GPAs slightly exceeded other students.

Haak, D.C., HilleRisLambers, J., Pitre, E. and Freeman, S., 2011. Increased structure and active learning reduce the achievement gap in introductory biologyScience, 332(6034), pp.1213-1216.

“Highly structured” (daily and weekly practice with problem-solving, data analysis, higher-order cognitive skills) large-enrollment intro biology course for undergraduate majors at University of Washington improved learning for all students compared to low-structure (lecture intensive) version. There were disproportionately large benefits for students in their Educational Opportunity Program (many of whom are first-gen and from minority groups historically underrepresented in STEM).

Eddy, S.L. and Hogan, K.A., 2014. Getting under the hood: how and for whom does increasing course structure work?CBE-Life Sciences Education, 13(3), pp.453-468.

Essentially a replication of the 2011 study above except that the researchers studied differences between a “low structure” (lecture intensive), “moderate structure” (weekly ungraded preparatory assignments, 15-40% of each class for in-class activities on questions that were similar to previous exam problems) and “high structure” (even more prep assignments and in-class activities) for at the University of North Carolina. The same instructor taught all of the different versions of this course. Total of about 2400 students over 4 years of the study. Failure rate went down for all students in the more structured courses compared to lecture intensive version. Students also reported a greater sense of classroom community. Black students participated in the lecture intensive class far less than other students did, but in the more structured course, they spoke in class as much as other students. Exam grades improved for everyone in the moderate structure course, but it increased even more for Black students. In fact, Black students in the structured course outperformed the majority students in the lecture version of the course. And, a similar thing was observed for first-generation students.

Laursen, S.L., Hassi, M.L., Kogan, M. and Weston, T.J., 2014. Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution studyJournal for Research in Mathematics Education, 45(4), pp.406-418.

Over 3000 students across 100 different course sections in four colleges and universities were included in this study of “inquiry-based learning” (IBL) in mathematics classrooms. The students were all in a math or science major, excluding students who were preservice elementary or secondary teachers. Even though there was a range of different implementations of IBL, researchers found that students in IBL courses on average performed as well as or better than their non-IBL peers. IBL students also took as many or more math courses than non-IBL students, which seems to indicate that their interest in mathematics increased as well. Pre- and post-surveys of cognitive skills in mathematics, attitudes toward mathematics, and attitudes about collaboration in a math class. Women in non-IBL courses reported significant decreases in their confidence to pursue higher mathematics, whereas men in non-IBL courses reported an increase in their confidence. In contrast, women in IBL courses reported an increase in their confidence similar to that of men in non-IBL courses.

Winkelmes, M.A., Bernacki, M., Butler, J., Zochowski, M., Golanics, J. and Weavil, K.H., 2016. A Teaching Intervention that Increases Underserved College Students’ SuccessPeer Review18(1/2).

These researchers set out to measure the effect of teachers providing two transparently designed, problem-based take-home assignments (as compared to their original versions) on first-year college students. (“Transparently designed” here means something specific to the training that the faculty received. They were trained to revise their assignments to be clearer about the purpose, tasks, and criteria for the assignments.) About 1,180 students taught by 35 faculty, 61 courses, 7 institutions were involved in the study. Because the courses spanned many different disciplines, the researchers relied mostly on self-report data from the students. “Students who received more transparency reported gains in three areas that are important predictors of students’ success: academic confidence, sense of belonging, and mastery of the skills that employers value most when hiring.” And what’s more, for first-generation, low-income, and underrepresented students, those reported benefits were larger.

Ballen, C.J., Wieman, C., Salehi, S., Searle, J.B. and Zamudio, K.R., 2017. Enhancing diversity in undergraduate science: Self-efficacy drives performance gains with active learning. CBE—Life Sciences Education, 16(4), 6 pages.

One of the first papers I’ve read that attempts to uncover why students historically underrepresented in STEM seem to benefit disproportionately from active learning pedagogies. Instructors compared traditional lecture and active learning versions of introductory evolutionary biology and biodiversity course by measured learning gains on course content, and students’ self-report of science self-efficacy and sense of social belonging. Historical performance differences between groups of students was erased in the active learning version of the course. All treatment students reported higher science self-efficacy, but structural equation modeling revealed that the increase in self-efficacy mediated the effect of active learning pedagogies on learning outcomes for underrepresented students only. In other words, one mechanism by which active learning pedagogies might help to produce more equitable outcomes is by helping historically underrepresented students experience more self-efficacy for learning STEM content.

Lape, N.K., Clark, C., Bassman, L., Spencer, M., Lee, A., Spjut, E. R., Dato, A. M., Palucki Blake, L., and Tsai, T. J., 2018. Erasing a Gender Gap in Performance in a Multidisciplinary Introductory Engineering Course. ASEE Collaborative Network for Engineering and Computing Diversity Conference, Paper ID #24241.

The Department of Engineering at Harvey Mudd College transformed an introductory engineering course from a lecture-based format to one incorporating best practices in engineering education: integration of theory and hands-on practice around a theme of underwater robotics, small-group in-class activities, content delivery via videos (flipped instruction). Mastery of course content was measured in both the original lecture-based course and the revised course via a pre/post content test; student attitudes were also measured using pre/post instruments. The results show a significant increase in learning and affective gains for all students. Furthermore, a gender disparity in final course grades disappeared in the revised course.

Casper, A.M., Eddy, S.L. and Freeman, S., 2019. True Grit: Passion and persistence make an innovative course design work. PLoS Biology, 17(7), p.e3000359.

This paper is a replication of the 2011 and 2014 studies above involving a “high-structure” course model in an introductory biology course. This time, the study was conducted at an open-access institution: Eastern Michigan University, a regional, public university that “admits almost all applicants to its undergraduate program.” After several course iterations, the researchers found a course structure that significantly lowered DFW rates from 48% to 25% and had a disproportionately beneficial impact on historically marginalized students–in this case, 85% of the students in the class self-identify as African American. This paper also demonstrates how important educational context is in this kind of research and that details really do matter.

Elli J. Theobald, Mariah J. Hill, Elisa Tran, Sweta Agrawal, E. Nicole Arroyo, Shawn Behling, Nyasha Chambwe, Dianne Laboy Cintrón, Jacob D. Cooper, Gideon Dunster, Jared A. Grummer, Kelly Hennessey, Jennifer Hsiao, Nicole Iranon, Leonard Jones, Hannah Jordt, Marlowe Keller, Melissa E. Lacey, Caitlin E. Littlefield, Alexander Lowe, Shannon Newman, Vera Okolo, Savannah Olroyd, Brandon R. Peecook, Sarah B. Pickett, David L. Slager, Itzue W. Caviedes-Solis, Kathryn E. Stanchak, Vasudha Sundaravardan, Camila Valdebenito, Claire R. Williams, Kaitlin Zinsli, Scott Freeman, 2020. Active learning narrows achievement gaps for underrepresented students in undergraduate science, technology, engineering, and math. Proceedings of the National Academy of Sciences, DOI: 10.1073/pnas.1916903117.

AFAIK, this is the first meta-analysis of the effect of active learning pedagogies on existing achievement gaps between over-represented and under-represented students. This paper includes 41 separate studies involving 53,844 students. To achieve greater statistical power, they combined students with underrepresented racial or ethnic identities in STEM with low-income students into one group they call “minoritized groups in STEM” (MGS). On average, compared to traditional lecture courses, active learning pedagogies reduced achievement gaps between MGS and non-MGS students in examination scores by 33% and narrowed gaps in passing rates by 45%. Class size, course level, and discipline did not appear to be important factors. However, there were some variations among the studies: in some cases, active learning pedagogies exacerbated achievement gaps–the amount of active learning in STEM classes seems to be positively correlated with narrower achievement gaps. Additionally, the authors begin to theorize for why certain teaching practices seem to disproportionately benefit students from MGS. This is likely to be a paper that many of us will refer to for years to come, in addition to the previous 2014 meta-analysis led by Freeman. (Focus on achievement gaps is still a bit problematic, but I totally understand the need to do something within the current paradigm of STEM education.)

Please let me know if you encounter other research articles that provide evidence for specific teaching strategies having disproportionately positive outcomes for women and/or students historically exclude from STEM. I will add it to this list.

Growth Mindset and Learning about Equity, Diversity, and Inclusion

Why is it so hard for people to talk and learn about equity, diversity, and inclusion? In this post I argue that part of the answer is that many people have a fixed mindset when it comes to learning about these things.

Carol Dweck’s work on fixed and growth mindset helps to explain why people react differently to challenging situations. In broad strokes, people with a growth mindset believe that ability (as it relates to that situation) can be developed, even when one fails to overcome that challenging situation; people with a fixed mindset approach the same challenging situation with doubt about their ability to overcome the situation despite hard work and they withdraw from the situation to avoid failing.

Mindset changes over time. And, mindset can vary by domain of knowledge–in other words, my self-concept as a learner of mathematics is high and I have a growth mindset about learning mathematics but my self-concept as an athlete is low and I have a fixed mindset about learning sports. (Sidenote: it is important to remember that growth mindset is not a silver bullet–most school-based interventions involving growth mindset have been shown to yield modest effects–and that growth mindset doesn’t make up for inequities in educational opportunities in our society.)

All of us need to learn more about equity, diversity, and inclusion, especially those of us who are teachers. We need to learn about the difference between race and ethnicity, sex and gender identity. We need to learn about our own implicit biases. We need to learn about racism, sexism, ableism, and all other forms of discrimination and bias, at the personal, institutional, and societal levels.

Learning about equity, diversity, and inclusion can be scary, especially for progressive, liberal-minded folks who want to believe that we are fair and good. The thought of being labeled as a racist, sexist, *-ist person can be frightening. However, the truth is that we all carry unconscious biases that cause us to exhibit prejudice despite our best intentions. Instead of thinking of being racist as a binary state, I posit that it is more meaningful and accurate to think of ourselves as being on a journey toward ever more equitable, inclusive, and caring words and actions. We’ll never fully get there, but we still work toward that goal.

There are interesting parallels between ways that people think about learning mathematics and ways that people think about equity, diversity, and inclusion. These parallels have to do with the beliefs that people have about their abilities and the ways that they approach challenging situations. Being racist is not an innate character trait in the same way that having the ability to learn math is not a product of one’s genes.

Fixed Mindset Growth Mindset
Learning math “I’m not good at math. My sister has the math brain in the family.” (implying that there is some sort of “math gene” that they lack and that math skill is a binary trait) “I can learn math with effort and persistence.”
Learning about equity, diversity, and inclusion “I’m a good person. I’m not racist.” (denying the existence of implicit bias, and implying that being racist is a binary trait) “I can learn more about these things with effort and persistence.”
Learning math “I don’t want to attempt this mathematical task because I’m likely to fail and I don’t want to be seen as dumb.” “I will try to learn what is needed for me to attempt this and if I mess up I will learn from that experience.”
Learning about equity, diversity, and inclusion “I can’t raise any controversial topics in my class because I might say the wrong thing and I don’t want to be seen as racist.” “I will try to learn what is needed for me to attempt this and if I mess up I will learn from that experience.”

I draw these parallels because I suspect that appealing to growth mindset might help some educators be more willing to talk about equity, diversity, and inclusion. Many educators are already familiar with the idea of a growth mindset and actively think about how to use it in their own teaching, so they might be able to see how it also applies to learning about equity, diversity, and inclusion. Most educators I know are trying to do the right thing and aren’t overtly racist and sexist. And yet, we still need to work harder to help more folks see equity, diversity, and inclusion as central to their work.

But a growth mindset approach is not enough. For folks who train others on topics relating to equity, diversity, and inclusion, it is important to set a tone of compassion and humility. Shame and guilt often cause people to withdraw from the conversation and put up defenses.

It doesn’t help that we seem to live in an age when people’s mistakes can be captured on video and shared around the world instantly. Call-out culture makes people nervous about saying or doing the wrong thing. And, our human nature is to want to discredit a person or organization entirely once we’ve found some flaw in them/it. The pressure to be perfect is so great–I understand why some faculty want to just sit on the sidelines and avoid saying anything that could be used against them.

We desperately need to transform classrooms and schools into spaces in which instructors and students can be brave with each other and at the same time offer grace to each other when mistakes occur. Part of the solution is to establish classroom norms that foster these things. (See previous post about some possible norms to use.) Part of the solution might also be to use the growth/fixed mindset framework to help debunk myths about ourselves. I invite you to share other things that could also help in the comment section below.

The Necessity of Encouragement and Positive Feedback

According to John Gottman, professor emeritus of psychology at the University of Washington, couples in a close relationship need to have 5 times as many positive interactions than negative ones for the relationship to remain stable. Couples for whom this ratio of positive to negative interactions is less than 5 are more likely to split up compared to those whose ratio is higher than 5. Apparently, 5:1 is the “magic” ratio that strongly discriminates between couples who stay versus split.

(Side note: I’m not a psychologist, but I suspect that one reason that so many more positive interactions are required compared to negative ones is negativity bias.)

That got me thinking…is there an equivalent idea that applies to our job satisfaction as teachers and the likelihood that we will remain teachers?

We teachers receive all sorts of messages every day about our work. We receive positive ones: successes when students learn something challenging, happy smiles from students, thank you notes from family members. We receive negative ones: those lessons in which you’ve poured your heart and soul that doesn’t seem to get results, students who are rude and hostile to you, parents who don’t notice your effort, administrators that stymie your ideas, an education system that is broken, a society that doesn’t honor and value teachers.

Oh wait… I have seem to have many more negative ones than positive ones….

That year I spent teaching high school in 2009-10 was one of the hardest in my life because I received so little positive affirmation about my work as a teacher. Many of my close friends prepared me before I started teaching high school not to take mean things that students say and do personally. It took a while, but I eventually learned to do that. But still, after learning to ignore those negative messages, the positive messages were too few and far between.

Perhaps, with time I could have become a more effective high school teacher such that I could have received more positive affirmations than negative messages about my work as a teacher. But, I still strongly suspect that many of my teacher friends struggle with the brutal reality of what it means to teach in challenging situations.

So, here are some suggestions for how to invert this balance and keep ourselves sane.

Cultivate a practice of looking for successes, no matter how small. I noticed that the practice of blogging during that year of teaching helped me be more aware about the successes that I had in my teaching. I didn’t blog every day, and in retrospect, blogging more frequently could have helped. Other ideas: keeping a journal, sharing those successes with a loved one every night, meditating regularly.

Savor those positive affirmations. I keep a folder of thank you notes and other mementos. I actually do this more because I can’t bear to throw those things away, but I sometimes return to that folder on a day when I’m down on my job as a teacher. This memento has lifted me up many times.

Encourage each otherFind people around you that will support you and get in the practice of encouraging each other.

What other strategies do you employ to persist in your work as teachers? What do you think your positive/negative ratio is right now and where do you think it should be for you to feel good about your work? I’d love to hear your comments.