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 and take responsibility for any harm caused.”

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.



Growth is Uncomfortable

Today, in our Claremont Colleges Center for Teaching and Learning Book Club meeting, my colleague Kathy Van Heuvelen shared with us a great analogy relating to the current controversy about “safe spaces” in college classrooms: Good athletes know their bodies well enough to know the difference between soreness and injury. Soreness is a sign that you’ve been working your body hard and that you’re getting stronger and faster. Injury is a sign that you’ve gone too far and need healing.

In a similar vein, our job as instructors is to help students develop the self-awareness to know the difference between feeling uncomfortable with having our ideas and beliefs challenged (a sign that we’re on our way to getting stronger and wiser) and feeling alienated, marginalized, or belittled. I posit that “brave spaces” are classroom environments in which students expect the former and not the latter.

I firmly believe that a good college education should challenge students with ideas and beliefs that are different from their own and should help them to develop the reflective judgment and skills of inquiry to be able to think on their own.

There is a lot of misunderstanding in the popular media about “safe spaces”. I fully agree that we don’t want spaces in which students never encounter any ideas that they find challenging or uncomfortable. I want students to encounter feel challenged (and perhaps even desire it), but in an environment where there is discomfort within a structure that gives them a sense of security. The kind of “safe spaces” that are being described in the media sound like echo chambers where you only hear your own thoughts, and no colleague that I have talked to wants that for our students either.


Some probability problems for your consideration

As I was preparing this tweet on AMS prizes given at the 2016 Joint Mathematics Meetings…


…I checked the AMS Annual Survey of the Mathematical Sciences to determine that in 2015 roughly 30% of full-time faculty in the mathematical sciences were female. Then, I wrote and did the following math problem:

Question #1: Suppose that 20 people are being chosen for various awards. Assume that for each award, there is a committee that narrows the field of candidates down to a set of 10 finalists who are deserving of the award, and 3 of them are female. Assume that each committee independently chooses the winner from this set of finalists in such a way that each of the finalists is equally likely to win the award. What is the probability that none of the 20 people are women?

Answer: (0.7)^20 ≈ 0.0007979

That seems really unlikely.

Some people are going to argue that because women have been excluded from the mathematical sciences to a greater degree in our recent history, the population of senior people who have made big contributions to their fields is going to skew even more male than the general population of full-time faculty.  (BTW, not all of the awards above are for senior people who’ve made big contributions.) OK, so let’s consider another problem.

Question #2: Keep everything from Question #1 the same but this time let’s assume that x (in %) of the finalists for each award are men. What would x have to be so that the probability of not having any women chosen is something more likely, like 25%?

Answer: x^20=0.25 means x ≈ .933 ( or 93.3%)

Is it the case that there are so few women deserving of awards in mathematics?

I assert that we don’t suffer from a lack of talented women and people of color in the mathematical sciences. The problem is that we don’t nurture talented women and people of color, don’t recognize their talent, and don’t take enough steps to make sure our award processes are unbiased, fair, and equitable. (There is plenty of evidence that women are just as implicitly biased against women as men are.)

Look at the dramatic change in the representation of people of color in this year’s Oscar nominations, compared to a mere two years ago when #OscarsSoWhite was trending. Did the field suddenly produce a bunch of new Black artists and producers and directors in those two years? No.  So why can’t those of us in the mathematical sciences also try harder to make sure that we make sure award winners are more broadly representative?

Every time a women or person of color looks at a list of winners like this one, they receive messages that they aren’t welcome in the field.

Important caveats:

  • These two problems are just food for thought. I’m not implying that the actual awarding of the AMS prizes is anything like what is described above.
  • I’m not suggesting that any of the selection committee members were deliberately being racist or sexist.
  • I’m not suggesting that any of the winners of the awards were not deserving and should return their prizes.
  • Also, my tweet and this post is about the underrepresentation of women, and I also recognize that there is an underrepresentation of African-American, Hispanic/Latinx, and Native American people among the award winners.

It would be interesting to go back in history to look at the demographics of all AMS prize winners.

Recommended reading:

Addressing the underrepresentation of women in mathematics conferences” by Greg Martin

The MAA’s guidelines for award selection committees on how to avoid implicit bias.



Institutional and Personal Roadblocks to Implementing Active Learning

As I posted last October, the evidence in support of the benefits of active learning for student learning is very robust. The CBMS put out a strong statement advocating for “institutions of higher education, mathematics departments and the mathematics faculty, public policy-makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms.”

Active learning has been around a while. Why hasn’t it been more widely adopted? Debbie Gochenaur (Shippensburg University) and Larissa Schroeder (University of Hartford) organized a panel discussion at the 2017 Joint Mathematics Meetings on this subject. Larissa, Kimberly Presser (Shippensburg University), and I spoke.  Here are some of my thoughts on the institutional and personal roadblocks that prevent faculty from implementing active learning in mathematics courses.

Here’s a link to Debbie’s notes on active learning based on her presentations at 2017 JMM.

Roadblock #1: Department/institution culture is often not set up to encourage teaching innovation

Three instances of this roadblock:

  • In our discipline, lecture is still dominant and it is uncomfortable to go against the dominant culture.
  • If departments don’t seem something as needing to be fixed, then they won’t invest the time to fix it. In many institutions, high DFW rates are not seen as a problem. Sometimes, they are even seen as a good thing because of a commitment to upholding “high standards” and seeing Calculus courses (or intro math) as gatekeeper courses.
  • Reappointment/promotion practices and departmental culture often discourages teaching innovation. Many people will say that teaching matters, but when the rubber meets the road, what do senior people in department and on reappointment committees really think about spending time on teaching instead of research? At many schools, especially research-intensive schools, spending time on teaching is a hindrance. Unless we get our institutions to expect faculty to spend on teaching, folks won’t do it.

Some possible strategies to overcome these roadblocks:

  1. Find allies. Are there folks in your department who use active learning? Talk to them. Look for people at your institution in other disciplines. If your institution has a teaching and learning center, find folks there who can support you.
  2. Don’t be naive about your departmental/institutional culture. Be politically savvy. Especially if you’re a junior or pre-tenure person, know who you can trust to tell you the truth about the prevailing attitudes and practices are at your institution. Get clarification from them about what the tenure and promotion expectations are. How is teaching innovation viewed? Is it ok to not get stellar teaching ratings one semester when you try something new as long as you can describe what you did, show evidence of self-reflection and improvement? Most administrators are reasonable and understand that tenure processes are not supposed stifle teaching innovation. If your department is not supportive, seek administrative support.
  3. Have evidence about active learning at your fingertips. There is a ton of research about active learning. Read and use the CBMS statement about active learning. If there are other folks at your institution who have had success with active learning, talk to them and find out how they measured success. Be aware of common myths about active learning and how to rebut them. (Common myths: You can’t “cover” as much material if you use active learning; or you can’t do active learning if you have too many students in a class.)
  4. Sometimes the active learning folks can behave like they’re members of a cult, so be careful about how you talk about active learning with your colleagues who aren’t into it. In your zeal for a particular active learning technique, don’t forget that any particular teaching strategy is not going to be the magic bullet that will solve everyone else’s problems. We should try not to alienate people but to welcome them into dialogue with us about teaching.

Roadblock #2: It’s difficult to find adequate training and support to implement active learning.

The truth is that you can go to a bunch of sessions about about inquiry-based learning (IBL) and still not know how to implement it. In fact, we know that is unlikely that people actually change their teaching practices as a result of attending a one-off workshop or session about a particular teaching strategy.

Learning a new teaching approach requires a lot of direct interaction with other people who are thinking about and working on similar problems. This is why the previous suggestions about finding allies is doubly important. You want to find people who can observe your classes and give feedback. You should also try to visit others classrooms. If you have the opportunity to co-teach with someone that you trust, that is often a great way to really work on your teaching.

Look for more in depth training. There are multi-day institutes during the summer, MAA minicourses, etc. Again, seek out folks in the teaching and learning center to support your efforts.

Roadblock #3: Many students don’t expect to be active in college classes. Change is uncomfortable.

If you spring active learning on your students, sometimes that can back fire.

Be transparent about why you’re using active learning. Don’t surprise them by it. Talk about why you’re using active learning on the first day of class. Tell them how to prepare for class to engage. Introverted, English language learners, and students with learning differences need heads up and time to prepare.

Roadblock #4: We are our own best and worst critic.

Don’t worry about getting it 100% right the first time. Improving teaching is a lifelong process anyway. I will never be perfect at my teaching. When trying something new, the most important thing is quickly adjust based on feedback. I strongly recommend exit tickets at the end of your class to get feedback. Then in the next class, refer back to specific comments that you received (good and bad) and show students that you’re taking their feedback seriously.

Don’t feel like you have to dive into the deep end. For example, don’t feel like you have to flip all of your classes. That’s one way to do it, but I having done it, I don’t recommend that unless you’re willing to put in the time and you have support. You can gradually develop more active learning strategies in your teaching repertoire over time.

There are lots of different forms of active learning. If one form of active learning doesn’t work for you, there is always something else to try. Not all of them are as time intensive as group work, or project-based learning. You can use clickers in class. You can set aside time for a quick think/pair/share. The key about active learning is that you are not doing all of the intellectual heavy lifting for students–you just have to get them ready to do it. Find ways to get students to prepare for class by doing the reading (or watching videos) so that they are able to take on some of those tasks on their own in class. That way you still “cover” the same material but you involve them actively in some of their own intellectual development.

If you’re pre-tenure or worried about employment security, take time to document your process as you teach. Jot down your thoughts at the end of class before you forget them. Use those in your tenure packet later. Use your exit tickets and teaching evaluations as evidence of self-reflection and improvement.

We often hold up others as models for ourselves. That is great to be inspired by others, but you have to be yourself in the classroom. And in fact, if you aren’t authentically yourself, students will know. So take the time to be introspective and find out what works for you and don’t apologize for being yourself.

What roadblocks have you encountered or observed to implementing active learning? How did you overcome those roadblocks?


Promoting a Culture of Assets Instead of Deficits

There is a pervasive culture of deficit in the education world when it comes to talking about or working with certain groups of students. In this post, I’d like to highlight the ways that deficit thinking enters into our language and institutional efforts to broaden participation. I’ll end with a great activity called the Community Cultural Wealth Walk.

Our Language Choices Reveal our Beliefs 

Let’s be clear about who we’re talking about here. In my experience working in higher education in the United States, we often talk about these students in terms of their deficits:  African-American, Hispanic/Latinx, Native American, Pacific Islander, and certain groups of East Asian students; students who are the first in their families to go to college; students from poor families; students who are recent immigrants to the United States; students with disabilities; students who are not fluent in American English; transgender students and cisgender students who identify as anything other than heterosexual; and women, especially in certain STEM disciplines.

We educators use lots of terms like “underrepresented”, “at-risk”, “underserved”, “marginalized”, “underachieving” to talk about sets of these students when it is not convenient or expedient to be specific, or when we just want to be vague. I am just as guilty of this as anyone else.

I’ve been thinking about this language and how I can be more inclusive, respectful, and at the same time avoid adopting a deficit frame when thinking about these students. I don’t have any answers about this except that I think we should be really cautious about using words like “at-risk”, “underachieving”, “slow/fast” to refer to students. Perhaps there are better words that we should be using, but I think the more important thing is to interrogate our own conscious and unconscious biases, assumptions, and beliefs about students. These biases, assumptions, and beliefs show up in the way that we talk about students.

Please note: I am not suggesting that we need to act like “thought police” because that is not productive. Instead of shaming others for using terms that are taboo or have fallen out of fashion, I think we should strive to believe the best in each other first. Let’s not assume negative intentions of others solely based on their choice of words. It’s difficult enough talking about diversity and inclusion without also feeling like you have to avoid landmines of non-PC words. And, let’s not forget that sometimes the language of inclusion and diversity gets used (ironically) as a tool for excluding others in the conversation.

Institutional Efforts that Can Marginalize

Deficit thinking can creep into the way that we implement programs at our institution to broaden participation in higher education.

Example: Many institutions have bridge programs that aim to give a small set of students some extra support and resources (to accelerate their acclimation to the college environment, to help them develop better study skills, to help them learn some content knowledge, to give them summer research experiences, etc.).  Harvey Mudd College has one of these too, which I directed for several years. Whenever I hear about these programs, I want to know these things:  (1) who is the program for, how are those students invited/chosen, and what is the language used to describe them? (2) what kinds of resources are provided to those students and what is the language that is used to describe those resources?

Deficit thinking can seep into these summer bridge programs because we fall into the trap of thinking that we are remediating students. If these students would not have been accepted to the college or university if they didn’t join the bridge program, then that sends a very clear message that the students are less qualified to be there. (Mudd doesn’t do this.) And honestly, I don’t think there is a whole lot of remediation that you can do in a short amount of time. I worry that these kinds of efforts stigmatize students and hurt them more than they help them.

On the other hand, if the students in the bridge program are accepted to the college or university regardless of their participation in the program, then they deserve to be at that college or university just as much as any other student. Of course, students all have their own strengths and weaknesses.  To create a more level playing field, we want to offer resources to help students grow. And if those resources can’t be deployed to all matriculated students, then we should prioritize those resources to those who could benefit the most–that’s why we have bridge programs. I believe these bridge programs work best when we give students agency. We should focus on helping students self-identify things that they want to work on (study skills, math, writing, etc.) and give them individualized supports to help them achieve their goals. I also strongly believe in setting high bar for that learning so to allow them to be leaders and supports for others.

Community Cultural Wealth Walk Activity

The privilege walk is a powerful activity to help people understand about privilege and reflect on their own privilege. (Click on that link to watch a video if you’re not familiar with this activity.)

One negative aspect of this activity is that if you have marginalized people participating in the activity with more privileged people, it can serve as a reminder to the former about their lack of privilege. In a way, it’s that classic problem of marginalized people bearing the burden of explaining things to others.

However, let’s be clear that whatever privilege walk activity you use, the questions that are asked reveal a set of societal standards for who has cultural capital and advantage. For example, sometimes you’ll see a prompt like “Take a step back if you grew up taking public transportation.” Why is that a negative thing? What if we viewed it as a positive thing? “Take a step forward if you’re comfortable riding public transportation because you rode it consistently for a part of your life.”

Last semester, when I taught “Social Justice and Equity in STEM” with Sumi Pendakur, she introduced me to the Community Cultural Wealth Walk Activity. Here’s how it works: during one of our class sessions, we had students do a standard privilege walk activity. It was familiar to some students, but not all. Some students were in tears. We had a great discussion in which we defined privilege and allowed students to confront their own privileges. As usual, many of our black and brown students and women were at the back of the room.

In the following class session, we used this Community Cultural Wealth Walk Activity instead. Here are some of the prompts in the activity:

  • Take a step forward if you grew up with more than one language or dialect spoken at home.
  • Take a step forward if you have cooked dinner for a family of at least 4 people for less than $5.
  • Take a step forward if you grew up having to negotiate more than one culture.
  • Take a step back if you had very few significant obstacles to overcome to succeed in education.

This time around, many of the students who were at the back of the room were now at the front of the room! It was a really powerful experience for many of them, and it opened up a great conversation about how society and media program us to favor certain forms of cultural wealth and to discount others. This activity doesn’t negate the fact many people have privileges that afford them real advantages in life. The point is not that “Oh! You have your privileges and I have mine so we’re all good.” The point is that our society privileges certain forms of cultural capital over others, and that is why some people have more advantages than others.

(Updated on Nov 28, 2016) María Oropeza Fujimoto, Eugene Fujimoto, and Huang I-Chen have given me permission to share their Community Cultural Wealth Walk Activity here. Many thanks to them!

(Updated on Feb 11, 2017) Jolina Clément shared with me that students at her school created what sounds like an amazing and beautiful piece of performance art. The students participated in a privilege walk, which resulted in a White girl ending up in front of everyone else. The students of color had their faces painted white. After that point, the students continued by doing the community cultural wealth walk and ended up together. At the end they removed the paint from each others’ faces. Sounds like an amazing and moving work of art!

(Updated on Aug 29, 2020) How do we do this activity in a virtual classroom? We’re using a simple Google Sheet, set to “anyone with the link can edit”. Each person picks a row and then they put an “x” in their space (and remove the “x” from the previous space) each time they want to take a step forward or back.


For further reading:

Blake, J. Herman. “Approaching Minority Students as Assets.” Academe 71, no. 6 (1985): 19-21.

Yosso, Tara J. “Whose culture has capital? A critical race theory discussion of community cultural wealth.” Race ethnicity and education 8, no. 1 (2005): 69-91.

The Benefits of Active Learning for Instructors

There are many reasons why active learning is so wonderful:

There is robust evidence that it improves student learning outcomes. One meta-analysis of 225 different studies on active learning found that students in traditional lecture classes were 1.5 times more likely to fail than students in active learning classes.

What’s more, there is growing evidence that there are forms of active learning that improve learning outcomes for all students, but also improve learning outcomes disproportionately for women and underrepresented students. In essence, these teaching strategies have the effect of leveling the playing field.

My main problem with non-active learning–basically, too much on lecturing–is that it’s an extremely frustrating process. When I lecture too much, I don’t get any immediate feedback from students about whether they are learning. I can periodically pause my lecture to allow students to answer questions or ask them if they understand, but that doesn’t tell me much. (And often, I will get false messages that things are going well when they really aren’t for many students.) The best way to really know if students understand is to ask them to do something with the knowledge that you think they’ve just gained. When I lecture too much, I don’t find out about my students’ understanding until they take an exam. That’s too late to make any real changes. (In theory, homework assignments have a quicker turn around time, but they are usually graded by students here and I never see them.) So, teaching via lectures is like driving where you can only see what was in front of your car 5 minutes ago. You wouldn’t drive your car like that, so why would you teach like that? Active learning allows me to make decisions about teaching in real-time, informed by how students demonstrate their mastery in class. And that makes teaching much less frustrating for me.

But, let’s also be honest here. Active learning often takes more time to prepare and is more difficult to pull off well than lecturing. And yet, I find it far more enjoyable than lecturing. Why is that? Dan Ariely (see his TED Talk) reminds us that people are motivated to work hard by seeing the fruits of their labor. So, what motivates me to put in the extra effort for active learning? I do it because I am rewarded by being able to see the immediate results of my efforts–students learn and do right in front of my eyes. What a thrill that is!

Facilitating Whole-Class Discussions on Difficult Topics

I am saddened and frightened by the level of rancor in discussions about gender equity, race, and politics in American society today. What can I do as an educator to make things better?

My job in the classroom is not just to teach mathematics. I see my job as also helping students become responsible members of society. I want them to develop critical thinking, perspective-taking, and respectful discourse skills. I believe that whole-class discussions can be great environments for helping our students develop these skills. But, how can we do so with rigor and civility without censoring dissenting voices? This question is all the more relevant today because of debates about “safe spaces” at colleges and universities.

But before we get to the question of how, let’s first think about why should faculty facilitate whole-class discussions on topics such as racial inequity, gender inequity (and all other forms of inequity), police violence, etc.

(1) Even if these topics don’t directly relate to course material in our courses, our students (especially those who are experience these issues first hand) are hungry for these kinds of conversations to happen in class. By remaining silent, we can convey that we don’t care. There comes a time when silence is betrayal. We cannot avoid difficult conversations with our students only because we feel uncomfortable doing so.

(2) If these topics can connect to our course content, what better way to add relevance and motivation?

(3) And as mentioned above, it is part of my job to help students learn how to engage in respectful discourse with people who disagree with them.

Sumi Pendakur is an awesome friend who has helped me grow in so many ways. One thing that I learned from her (which she got from her brother Vijay Pendakur) is how to set up the right conditions for whole-class discussions on difficult topics. I also learned a lot from reading From Safe Spaces to Brave Spaces by Brian Arao and Kristi Clemens.

When we taught our “Social Justice and Equity: STEM and Beyond” course last semester, Sumi started out the course by going over these five ground rules for discussions:

(1) Agree to make this room a “brave space.”
Like it or not, the term “safe space” has taken on a negative connotation–it is associated with spaces in which dominant (usually liberal) viewpoints are the only ones that can be safely discussed while dissenting views are censored. What we need to create are not intellectually sterile environments that are devoid of dissent and where students won’t run into viewpoints other than their own. We need spaces in which people are brave enough to talk about difficult subjects while being mindful of others, listening actively, thinking critically, taking on the perspectives of others, consciously questioning of one’s own beliefs and assumptions, and not automatically blaming and assigning negative intentions to others.

(2) Make “I statements” not “you statements.”
Avoid blanket statements about groups of people. Using “I statements” instead of “you statements” can help others not feel blamed, but keep in mind that “I statements” can still cause people to feel defensive. It has to do with the tone of voice and nuance in which things are said.

(3) Know when to step forward or step backward.
If you sense yourself talking too much, pull back. If you haven’t been brave enough to speak, try taking a risk.

(4) What’s said here stays here, what’s learned here leaves here. (“Modified Las Vegas rule”)
We will keep who said what in confidence when we leave this room. But, what we learn we will share with others.

(5) Say “Oops” and “Ouch.”
Acknowledge when you’ve been hurt by something someone says. Take responsibility if you’ve said something that hurt someone. Recognize the difference between intent and impact.

After explaining these norms, Sumi then allowed for other suggestions from participants. I like this strategy better than taking suggestions from the beginning because it is more efficient, avoids awkward floundering, and sets the stage that the instructor is not going to let the conversation go out of control.

It is good to be aware some other common norms that participants might bring up and reasons why you might want to be cautious about using them:

“agree to disagree” – It’s important to be civil, but I don’t like how this norm can encourage people to retreat the moment there is disagreement.

“don’t take things personally” – This norm sometimes has the effect of shifting the emotional responsibility of what is said to the person who is affected instead of the person who said it.

“be respectful/be civil” – This is clearly an important norm, but it might be worthwhile to also spend time to tease out what it looks like. Be aware that for some, “being respectful” means silencing yourself so as to preserve the dominant view. You will need to draw out what it looks/sounds like to disagree with someone while “being respectful”. You could even provide students with some sentence frames for this.

“no attacks” – Make sure to draw a distinction between personal attacks and challenges to an individual’s idea or belief or statement that makes that person feel uncomfortable. “You’re a jerk” and “Your ideas is worthless” vs “What you said made me feel angry” or “I find that idea to be heterosexist”.

If you like these norms, here is a PowerPoint file (based on the original by Vijay) that you might find useful.

If you facilitate discussions like these, I would be interested to know what strategies you use to create a healthy space for conversation. Also, what are some common issues that you run into and how do you deal with them?


Grandfather’s Gift

I was trying to figure out why a flashlight wasn’t working tonight. I changed the batteries, but that didn’t seem to help. I realized that the little light bulb was busted. Then I remembered that somewhere in my drawer I had a collection of those little light bulbs.

I looked in a cupboard and found this:

It was an old 35mm film container that my grandfather had filled with light bulbs, each meticulously labeled, along with a handy guide. I think he used these to test batteries.

I cried in that moment because I miss him so much. But I was also overwhelmed with gratitude for all the things that my grandfather did for me and gave to me.

I definitely inherited his attention to detail. He was supremely organized: all the light bulbs in a little container, all the nails kept in one jar, all the flathead screws kept in another jar, all the batteries organized by size, news clippings filed into folders. And he took notes about everything: when he bought those batteries and for how much. I do that too: recording every expenditure to the penny in a big spreadsheet.

Sometimes I wonder if I became a mathematician because he shared his curiosity and love of learning with me. He loved building and making things, like his own automatic fish feeder (which overfed the fish once and kill them all). Here are some old photos of me having fun with my grandfather. I think he was testing out his new camera and roped me into being his little helper to change the numbers. In the photos, you can see how he was testing out different lighting conditions.

I got that flashlight working. My grandfather had saved just the right light bulb that fit and worked.

Thank you, 爷爷 and 奶奶, for both the little things and the big things. I miss you so much.