Town Hall: Sept. 17, 2020, 7:30pm
Because coursework is central to students’ experiences, the effort to build a more inclusive and welcoming department must include embracing inclusive pedagogy. Below is a list of strategies generated by math department faculty to promote inclusivity, diversity, and belonging in the classroom. What other strategies have you found successful?
It is well documented that active learning increases student performance and active
learning narrows achievement gaps for underrepresented students. An interactive classroom
also lays the foundation for students to build a vibrant intellectual community and
increase students’ sense of belonging. Below is a list of activities to consider using
in your classroom.
- Think Pair Share-
Give students an opportunity to think independently about a question
or a prompt and then share their ideas in small groups. The following are possible prompts:
- Why is the converse of this not true?
- Come up with an example of a _______ with ______.
- The definition of _____________ precludes ____________. Why?
- One hypothesis of the theorem we just proved was ____________; is this hypothesis necessary? Where did we use it in the proof?
- What are the big picture questions the course is trying to answer in this lesson?
- Circulate an incorrect proof. Where does the argument break down? Can you fix it?
- Muddiest Point--This teaching move helps students develop their metacognitive skills, emphasizing learning as a process, and gives the instructor valuable information about what is challenging for students. At the end of class, every student submits a response to the question “what did you find most confusing or most interesting today?”
- Polling--This active learning strategy helps instructors take the pulse of the students’ understanding in real time.
It is important to think carefully about productive poll questions ahead of time. Here are some quick facts:
- Good poll questions are typically multiple choice or true false questions that target conceptual understanding.
- The real power in polling during class is to leverage a poll that doesn’t have consensus into an opportunity for students to discuss their answers with people sitting near them. After students have a chance to discuss, repoll the class to see how successful students’ discussions were.
Carol Dweck has started a national conversation about students’ mindsets and the importance of encouraging students to adopt a growth mindset. Students with fixed mindsets believe their basic abilities, intelligence, and talents are fixed. Having a fixed mindset shapes the way students respond to setbacks and can short circuit students’ long term success. On the other hand, students with a growth mindset believe their abilities can be improved with deliberate practice, learning from failures, making use of effective study strategies, and quality mentoring. Look at these two studies that show the importance of individual faculty members adopting a growth mindset and reshaping the broader mathematical community’s expectation about brilliance.
- STEM faculty who believe ability is fixed have larger racial achievement gaps and inspire less student motivation in their classes.
- Expectations of brilliance underlie gender distributions across academic disciplines.
- Talk explicitly about a growth mindset and encourage your students to take on a growth mindset.
- Share a personal reflection of how you believe that ability is not fixed and how hard work improved your understanding of something specific. Describe a personal failure and how the experience helped you grow.
- Praise the process instead of the product. To highlight the process consider having some assignments that can be resubmitted. This will help students see the importance of mistakes and feedback in the learning process.
- Many students (and faculty for the matter) experience imposter syndrome. Acknowledge imposter syndrome and address how to overcome imposter syndrome. This can be especially important for students at transition points: e.g. first year students, first year grad students, students in Math 112 or Math 122 etc.
- Avoid language that promotes a fixed mindset and embrace language that promotes a growth mindset.
- Communicate that learning is a process through your course design. Think about ways to fold in formative assessments that promote students’ learning instead of just aim to evaluate learning.
Get to Know Your StudentsStudent-centered education requires you to know your student. Here are a few strategies to get to know your students better:
- Learn your students’ names and pronouns.
- The first day of class sets the tone for the semester. Consider doing an icebreaker that signals to students how important you think community is and that you want to get to know them better.
- Distribute a survey on the first day of class and inquire about their hobbies and interests, mathematical experiences, or the other classes they are taking. Your survey could also ask students when they are free so that you set office hours that are convenient for a majority of them. In upper-level courses you might also ask: What kind of work/questions/approaches most fascinate you in math? What is an interest of yours outside of mathematics? What first got you interested in mathematics? What other math courses have you taken?
- Have everyone in the course make Google Slides introducing themselves. Model building a slide by making one yourself. (Example).
- Arrange short one-on-one or small group meetings at the top of the semester to get to know your students. To help facilitate the logistics consider using youcanbook.me
- Listen carefully to what students are saying. Never deny their experience.
- Arrive to class early and build relationships with students by asking about other courses they are taking, events on campus, extracurricular activities, etc.
- Frequently advertise office hours and describe what the purpose of office hours are. Faculty across the university structure office hours very differently. Be explicit about what your office hours are like. For more information about students’ how students build successful strategies look at The Unwritten Rules Of Engagement: Social Class Differences in Undergraduates’ Academic Strategies.
- Treat students as individuals. Be curious about who your students are. As you get to know your students you will see them as a very interesting group of undergraduates who have surprising and eclectic interests.
- Harvard has a few different ways to share a meal with a group of students. First year faculty dinners, classroom to table, etc.
Build Opportunities for Work Outside the ClassroomBuilding opportunities to work together outside of class helps build relationships between students. Here are some suggestions to pull this off successfully.
- Encourage your students to attend Math Night. Think about when your PSETs are due in relationship to Math Night.
- Advertise Math Table, Open Neighborhood Seminar, and other undergraduate math events in the department.
- Explicitly encourage students to find groups to work on their problem sets with and set a course collaboration policy that promotes community. Give time for students to exchange contact information.
- Seriously consider assigning formal study groups or PSET groups. This will make sure that everyone feels included in the community.
Group Expectations and GuidelinesThe first day of class and the syllabus set the tone for the semester. Consider how you will explicitly signal to students the expectations you have for the course. Establish expectations with students about how to have productive class discussion. Look here for a list of 10 classroom practices that might help you set expectations.
- Consider including students in setting the expectations.
- Include the dates of major assessments/assignments in your syllabus so that students can make plans for the entire semester.
- Explicitly spell out the policy for late work.
- Include an ADA statement.
- Bok Center for Teaching and Learning: Inclusive Teaching
- Inclusive teaching involves cultivating awareness of the dynamics that shape classroom experiences and impact learning. It also involves being responsive to these dynamics and intentional about using strategies, or inclusive moves, that foster a productive learning environment. Sometimes there will be difficulty; inclusive teaching empowers students and teachers to navigate this together. Ultimately, inclusive teaching is good teaching.
- Presidential Task Force Call to Action
- We each have the opportunity — and the responsibility — to create a greater sense of inclusion and belonging throughout our campus communities. Consider the various communities to which you belong — your department, your section, your School, your extracurricular organizations, your lab, or simply the people who live and work beside you. Each of us should think about the numerous roles we occupy within the broader Harvard context and their connection to other parts of the University. Identify the communities in which you have the power to create change and the communities where you can support efforts of those who are already engaged in creating a more inclusive Harvard. How can we each play a part in shaping our own experience and the experiences of those around us through our actions? How can we engage in the activities of our School or department and Harvard more broadly to further the goals, tools, and recommendations within this Task Force report?
- Harvard HR: Simple Inclusive Practices
- Cultivate bonds and bridges that enable all to grow with and learn from one another
- Practicing acts of inclusion each day to foster a welcoming environment for all — say hello and welcome newcomers; learn and use people’s names; share stories
- Engaging with groups who might have different views or interests
- Making time to actively participate in more events and initiatives across Harvard, beyond our School or business unit
- Seeking opportunities to collaborate with people from a different School or business unit toward greater inclusive excellence
- Listening, caring, and supporting — ask someone about his, her, or their personal story and share our own
- Pick one book/article to read and discuss each month to deepen understanding
- Engage in town halls and feedback processes
- Consider how inclusion and belonging concepts connect to our field or profession and develop pathways to further learnings
- Learn about diversity and inclusion efforts underway now
- Harvard Culture Lab
- Do you have an idea that could advance a culture of belonging that would require funding? The Culture Lab is an incubator for innovative ideas that seek to advance a culture of belonging at Harvard. Grants available for $200 to $1,000 for supplementing costs associated with hosting conferences, meetings, events, and trainings and supporting projects and programs on campus. An innovation fund that awards competitive grants of up to $15,000 or more to project teams to pilot and scale ideas that seek to strengthen Harvard’s capacity to advance a culture of belonging.
- Project Implicit Bias
- Professor Mahzarin Banaji runs Project Implicit, a non-profit organization and international collaboration between researchers who are interested in implicit social cognition - thoughts and feelings outside of conscious awareness and control. The goal of the organization is to educate the public about hidden biases and to provide a “virtual laboratory” for collecting data on the Internet.
Resources from Teaching and Learning Centers
- Georgetown: Center for New Designs in Learnings & Scholarship
- A great resource for universal design for learning, teaching well-being, handling implicit bias, and difficult conversations.
- Stanford Center Teaching and Learning
- Suggestions and strategies focused on growth mindset, student identities, implicit bias and microaggressions, and difficult conversations.
- Yale: Poorvu Center for Teaching and Learning
- Lots of great suggestions on a range of inclusive pedagogy topics.
Math Specific Resources
- inclusion/exclusion - An AMS Blog
- This is a blog about underrepresented groups in mathematics. The main goal of this blog is to discuss issues pertaining to marginalized and underrepresented groups in mathematics. We hope that by increasing awareness of these issues, we will help develop a more inclusive, supportive, and diverse community of mathematicians. Topics may include: conferences targeted at underrepresented groups, inclusive teaching strategies, summaries of current educational research, features about inspiring and successful underrepresented mathematicians, and advice for students, faculty, and researchers at all levels.
- AMS Blog on Teaching and Learning
- The goal for this blog is to stimulate reflection and dialogue by providing mathematicians with high-quality commentary and resources regarding teaching and learning. Because there is no simple solution to the challenges facing mathematics education, this blog will serve as a big tent, giving voice to multiple contributors representing a wide range of ideas.
- MAA Posts on Inclusivity
- A series of posts from the Mathematical Association of America on Inclusivity.
- Franics Su’s Writings
- A collection of writings on inclusivity and math instruction from Francis Su, former President of the MAA and Professor at Harvey Mudd.
- Empowering Whom? The Challenge of Diversifying the Mathematical Community
- A talk on the importance of inquiry in mathematics classrooms by David Kung, the Director of Project NExT and Professor at Saint Mary’s College.
- AMS Blog: Six Ways Mathematics Instructors can Support Diversity and Inclusivity
- Use students’ interest in contextualized tasks
- Expose students to a diverse group of mathematicians
- Design assessments and assignments with a variety of response types
- Use systematic grading and participation methods
- Consider your course logistics
- Encourage students to embrace a growth mindset
- The Role of Failure and Struggle in the Mathematics Classroom
- A blog post about promoting productive struggle and growth mindset in a mathematics classroom by Dana Ernst
- 5 Ways to Respond When Students Offer Incorrect Answers
- The way we answer these questions impacts the learning environment in our classes, according to a study in the American Educational Research Journal. Conversations with colleagues Darryl Yong and Lelia Hawkins generated these five suggestions for constructive responses to misconceptions. A blog post from Rachel Levy, Deputy Director of the MAA.
- Social Justice Mathematics and Science Curricular Resources for K-12 Teachers
- A curated list of resources from Dr. Kari Kokka, Assistant Professor of Math Education at University of Pittsburgh.
- Axioms proposed by Federico Ardila
- Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
- Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
- Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
- Axiom 4. Every student deserves to be treated with dignity and respect.
- Dweck, C. (2007) Mindset: The New Psychology of Success. Ballantine Books
- Jack, A.A. (2019) The Privileged Poor: How Elite Colleges are Failing Disadvantaged Students. Harvard University Press.
- Karaali, G. and Khadjavi, L. (2019) Mathematics for Social Justice: Resources for the College Classroom, MAA Press
- McGuire, S. (2015) Teach Students How to Learn: Strategies You Can Incorporate Into Any Course to Improve Student Metacognition, Study Skills, and Motivation. Stylus Publishing
- Nunn, J. (2018) 33 Simple Strategies for Faculty: A Week-By-Week Resource for Teaching First-Year and First-Generation Students. Rutgers University Press
- Su, F. ( 2020) Mathematics for Human Flourishing. Yale University Press
Hear From Our Teachers
Physicist and Nobel laureate I. I. Rabi once said that his mother made him a scientist, because each day after school she would ask him not, "Did you learn anything today?" but rather, "Did you ask a good question today?" To nurture those same scientific impulses in my students, I want to ensure that my classroom is a place where students feel safe and encouraged to ask questions. I request that my students post a question on a shared discussion board before each class, and I also periodically pause classes until I receive questions from my students, or to encourage discussions about questions students have already posted. Breaking students into smaller groups to discuss questions is also helpful. By the end of the semester, I hope for my students to feel that they are not just individual learners but a community of scientists, engaged collectively and collaboratively in a shared quest for new understanding.
I am also planning to assess the students' sense of community and inclusion, among several other points of feedback, in weekly surveys (worth a small nominal amount of credit to encourage participation). If the need arises, backup plans include embedding some teamwork activities into the live lectures or into the homework assignments, or hosting a social get-together event (on Zoom or on gather.town; at a time that works for the students who can't attend lecture). Important considerations in these efforts include making sure that students who are shy or reluctant to interact in a particular way (text chat vs. video, live vs. asynchronous, etc.) or in a faraway time zone find some way of fitting in and interacting with the others; while promoting and modelling a culture of respect and inclusiveness, where students cooperate and help each other rather than show off and compete (for some of the students in Math 55 this will require adjustment).
One thing I always keep in mind is that the students in calculus courses are mostly not math concentrators. They often wonder how the theorems and concepts taught in class can be applied in their disciplines. Therefore I mention some applications whenever I can. It is also useful to involve the CAs in lesson planning occasionally, as they are usually upperclassmen in the disciplines the students are interested in. For example, when I taught least squares approximation, I asked during weekly meetings with the CAs if they had encountered any applications, and the CA suggested a very cool project on the correlation between upward mobility and a bunch of socioeconomic factors, and the students were very interested.
I also often include some facts about the mathematicians involved, some history about the theory (which I find really lacking in any math course), or some fun trivia/history about the Harvard math department. I feel like these fun tidbits of information gives a “human” aspect of the concepts and theories we are learning, and it’s a very effective way of generating interests and fun in a class that might be quite dry.
Instead of a midterm and/or final exam, I assign writing projects. These ask the student to write up a lecture that the student would give the class about some topic from the textbook or other source that I either didn’t cover during the regular class meetings or only touched on. (I suggest the topic; but I do allow on occasion a student to pick a topic that I didn’t suggest.) The assignment asks the student to explain the background to the topic at hand, the main notions and theorems, and then the main ideas, insights, strategies and steps in any proofs. (But all line-after-line derivations have to be in an appendix, not in the body of the lecture.) These are typically 6-9 pages long. After the students turn in their lectures, I then read them over and send them back with corrections and suggestions for improvement (unless the lecture is perfect). The students then have the opportunity to revise their lectures based on my comments so as to produce an admirable piece of exposition. Depending on the size of the class, this back-and-forth with my comments and suggestions might happen more than once. In essence, I work with each student to guide their understanding and writing so that the end result is something to be proud of. (Also, some of the homework assignments during the course are mini-writing projects that are meant to get the students acclimated to the writing process. They ask the student to write in their own words various small theorems and proofs from the weekly reading.)