*By *__Natalie LF Hobson__*, Graduate Student, University of Georgia*

What teaching practices support a diverse student body in your mathematics classroom? In this post, I suggest six concrete teaching practices you can implement today to help make your classroom a more inclusive environment for your students:

- 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

I hope these strategies can spark conversation with colleagues on how we, as educators, can support a diverse and inclusive mathematics classroom.

**1. Use students’ interest in contextualized tasks. **

What communities and interests are represented in the problems you assign students? How do these backgrounds align with those of your students? Researchers have shown that students are more motivated in material when it is applicable to their own interests and communities (Carlone & Johnson, 2007; Jones, Howe, & Rua, 2000). In order to identify the interests of our students, consider giving your students a survey to ask for their hobbies, motivations for taking the course, and career goals (for example, a form I made for my own students is available here). Use what you learn about your students while framing the mathematical tasks and problems. Be sure to consider if the tasks you assign represent *all* of those interests in your classroom and which students might be left out.

In a traditional calculus course, for example, a common topic is related rates. Some typical related rates problems involve falling ladders, hemispherical reservoirs, and cars and trucks and things that go. These applications may be very appropriate for students with these interests or interests in certain types of engineering. However, exposing students exclusively to such applications signals to students who do not have such interests that mathematics is not relevant for them. Consider diversifying such tasks and (depending on the interests of your students) include applications to medicine, biology, conservation, music, baking, etc. Here are a few suggestions I have used with my own students.

*Chris and Jake are ***cooking*** pancakes. Jake ladles the pancake batter into the fry pan. While the pancake cooks, the radius of the circular pancake formed increases at a rate of 1 cm per minute. How fast is the circumference changing when the radius is 7 cm?*

*At a ***conservation*** site in the Amazon rainforest, a hyacinth macaw ***parrot*** is spotted flying horizontally 37 feet above a research site. The parrot is flying at 20 ft/sec. How fast is the distance from the parrot to the research site changing when the bird is 35 feet away?*

*The ***velocity of blood*** in a human’s blood vessels is related to the radius R of the blood vessel and the radius r of the layer of blood in the blood vessel. This relationship known as Poiseuille’s law and is given by** *\(v=375(R^2-r^2)\)*. Assume the radius of the layer of blood r is constant but cold weather causes the radius of the blood vessel R to contract at a rate of 0.01mm per minute. What is the velocity of blood flow when the radius R of the blood vessel has contracted to 0.03mm?*

**2. Expose students to a diverse group of mathematicians.**

Who are the mathematicians you tell your students about? Are they white, male, and introverted? These common stereotypes make students who do not identify with such qualities feel they do not belong in mathematics (Carlone & Johnson, 2007; Cheryan & Plaut, 2010; Good, Aronson, & Harder, 2008; Thoman, Arizaga, Smith, Story, & Soncuya, 2014). Diversify your students’ image of mathematicians by highlighting mathematicians who do not fit the typical stereotype. Describe mathematicians as multidimensional individuals with struggles, hobbies, and families. Communicating short biographies to students and showing students pictures of mathematicians from underrepresented groups are great ways to do this. If students are able to see mathematicians as genuine individuals, they are more able to identify with them and see themselves in mathematics. For resources to increase your own exposure to individuals in the mathematics community, consider perusing books and websites that highlight important contributions from women or individuals from underrepresented ethnicities in the field. For example, check out the Mathematically Gifted and Black website, recent articles such as Lathisms: Latin@s and Hispanics in Mathematical Sciences and The Black Female Mathematicians Who Sent Astronauts to Space, or books such as Kenschaft, 2005 and Murray, 2000.

Communicate stories of mathematicians to students while engaging in mathematical contributions the individuals have made. For example, in a calculus course, consider discussing with students the mathematics related to the curve known as the “Witch of Agnesi” (a mistranslation from *averisera* meaning “turned sine curve”) given in Figure 1 from Weiqing Gu’s website. This curve was studied in the calculus textbook *Analytical Institutions* written by the Italian mathematician Maria Gaetana Agnesi (1718-1799). Agnesi published this text at the age of thirty; she began writing the book at age twenty, originally writing the text as a resource for her brothers (Osen, 1975). The curve can be constructed by tracing the points P obtained from the \(x\) (horizontal) and \(y\) (vertical) coordinate of the points \(A\) and \(Q\) (respectively) in Figure 1 below. The curve can be given parametrically as \(x(t)=2a \cot(t)\) and \(y(t)=a[1-\cos(2t)]\) (for \(0 \leq t \leq \pi\) and a suitable positive constant \(a\)). Activities for students related to this curve could have students construct the parametric equation (from a more suitable description of the curve) or deriving an equation of the tangent line at any point P on the curve (see MathForum for a construction of the curve).

**3. Design assessments and assignments with a variety of response types. **

We as mathematics instructors have been successful mathematics students. Thus, many of us have likely found success with traditional mathematics assessments in traditional settings. However, not all students succeed in such environments. Create and structure assignments to include a variety of types of problems as well as settings. For example, consider including problems that ask students to write long responses to explain their thinking or draw a visual to demonstrate an argument. Vary the test environment by allowing students to work in groups or give a take-home assessment in order to give students flexibility in the amount of time for completion. Consider allowing students to retest. This strategy has been shown to provide students who experience math anxiety with a mental “safety net” that can help alleviate some of the pressures involved in testing and improve their test performance (Juhler, Rech, From, & Brogan, 1998). If you are not able to vary the assessments in your course (possibly due to departmental or other constraints), consider using these suggestions in class assignments or quizzes.

In my own courses, I encourage students to express and develop their thinking outside of class through something I call “Try it” opportunities. Try it opportunities have included responding to open-ended questions I post on our course discussion board, posting practice test solutions, or responding to fellow students’ practice test solutions. I also encourage students to tweet class summaries to my professional Twitter account, bring to class a picture or news article of a math concept we have discussed in class that they see in their own lives, or take a photo of their math study group. The following is an example of an open-ended question I asked students in a recent geometry for teachers course on our course discussion board as part of a try it opportunity.

*Discuss the following two statements: “two triangles put together always make a square” and “a square cut in half always forms two triangles.” Are these statements true? Why might a student think this? What would you tell this student?*

The question provided students an opportunity to think about their own conceptions of triangles and shapes before we formally discussed the topic in course. The setting of the discussion board environment allowed students the flexibility in their timing of response and opportunity to reflect on other students’ thinking.

**4. Use systematic grading and participation methods.**

Who are the students that you expect to succeed in your course? Who are the students whose contributions you encourage in class? Teachers often have expectations and judgments of different groups of students based on student identity (Anderson-Clark, Green, & Henley, 2008; Riegle-Crumb & Humphries, 2012; Van den Bergh, Denessen, Hornstra, Voeten, & Holland, 2010). It has also been reported that teachers provide a “warmer” academic climate to students for whom they hold higher expectations, in the form of in-class interactions and assignment feedback (Rosenthal, 2002). Such treatment has positive effects on student performance.

Attempt to hold all of your students to the same high standard. Consider implementing systematic ways of getting student participation and methods of grading. Keep a record of which students participate in your class and make an effort to elicit contributions from all students. While grading, create a rubric to evaluate student work. After grading, look over the comments and feedback you give your students. Do all students have similar depth and specificity of feedback? Consider having a colleague who is unfamiliar with the identities of your students look over a sample of the work you have graded and provide *you* feedback on the types of responses you give to your students.

**5. Consider your course logistics.**

*Office Hours. *What time do you host office hours? Are they immediately after class when a student might have to rush off to work in the campus cafeteria? Or early in the morning when a student might be commuting into campus? Another useful item for a pre-semester survey is a question about the best times for office hours.

*Deadlines. *When are your assignments due? What obligations do your students have outside of your course? Requiring students to turn in a homework set to your office door by 5PM might not be doable for a student who has to work until 6PM. Having an online homework set due on Sunday evening might not be feasible for a student without access to a computer on the weekends.

*Technology. *What technologies do your assignments require? If your department requires online quizzes or homework, is there technology on campus that students can use to complete these assignments? Know when such resources are available to students and be sure your students know as well.

**6. Encourage students to embrace a growth mindset.**

Carol Dweck’s popular work shows that individuals’ mind-sets regarding intelligence can influence their academic motivation and performance (Dweck, 2008). Dweck describes students with a fixed mindset as having a static view of intelligence and students with a growth mindset believing intelligence can be developed, the latter mindset being able to persist in the face of challenges and setbacks and grow in the process.

Remind students that mistakes are an essential part of learning and a vehicle for growth. Provide feedback on students’ strategies and reasoning, rather than just their answers. Celebrate students’ effort and persistence and avoid praising a student for getting an answer quickly. Treat exams as an opportunity for students to demonstrate their effort and understanding rather than their intelligence and ability. Allow students to engage in productive failure by providing limited scaffolding and challenging students to collaborate with each other (Kapur & Bielaczyc, 2012).

In my own classes, I begin the semester by assigning my students the task to watch and give a short reflection on the TED talk by Eduardo Briceno on “Mindsets and Success.” My students’ responses reflect encouragement from the talk; many express a shift from believing they are “not good at mathematics” to believing they are “not good at mathematics *yet*.” I then usually emphasize to students that they *are* already mathematical thinkers but with persistence and effort they can feel success in our mathematics course.

I hope these strategies invite you to reflect on your teaching practices and consider the influence we can have in creating inclusive classrooms that support diversity. As a final recommendation, I hope this post can start or continue conversations with colleagues on the topic of diversity and inclusion in mathematics. Having a community to discuss and develop the ways we teach and interact with students is essential for making such efforts lasting and productive.

**Acknowledgements:** I would like to express my gratitude to Laura Provolt, Debbie R. Hale, and Dr. Kecia M. Thomas for their helpful feedback and many insightful discussions.

References

Anderson-Clark, T. N., Green, R. J., & Henley, T. B. (2008). The relationship between first names and teacher expectations for achievement motivation. *Journal of Language and Social Psychology, 27*(1), 94-99.

Carlone, H. B., & Johnson, A. (2007). Understanding the science experiences of successful women of color: Science identity as an analytic lens. *Journal of research in science teaching, 44*(8), 1187-1218.

Cheryan, S., & Plaut, V. C. (2010). Explaining underrepresentation: A theory of precluded interest. *Sex roles, 63*(7-8), 475-488.

Dweck, C. S. (2008). *Mindset: The new psychology of success*: Random House Digital, Inc.

Good, C., Aronson, J., & Harder, J. A. (2008). Problems in the pipeline: Stereotype threat and women’s achievement in high-level math courses. *Journal of Applied Developmental Psychology, 29*(1), 17-28.

Jones, M. G., Howe, A., & Rua, M. J. (2000). Gender differences in students’ experiences, interests, and attitudes toward science and scientists. *Science education, 84*(2), 180-192.

Juhler, S. M., Rech, J. F., From, S. G., & Brogan, M. M. (1998). The effect of optional retesting on college students’ achievement in an individualized algebra course. *The Journal of experimental education, 66*(2), 125-137.

Kapur, M., & Bielaczyc, K. (2012). Designing for Productive Failure. *Journal of the Learning Sciences, *21(1), 45-83.

Kenschaft, P. C. (2005). *Change is possible: Stories of women and minorities in mathematics*: American Mathematical Soc.

Lopez, A. D., Sosa, G., Langarica, A. P., & Harris, P. E. (2016). Lathisms: Latin@ s and Hispanics in the Mathematical Sciences. *Notices of the American Mathematical Society, 63*(9), 1019-1022.

Murray, M. A. M. (2000). *Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America*: MIT Press Cambridge MA.

Osen, L. M. (1975). *Women in mathematics*: Mit Press.

Riegle-Crumb, C., & Humphries, M. (2012). Exploring bias in math teachers’ perceptions of students’ ability by gender and race/ethnicity. *Gender & Society, 26*(2), 290-322.

Rosenthal, R. (2002). Covert communication in classrooms, clinics, courtrooms, and cubicles. *American Psychologist, 57*(11), 839.

Thoman, D. B., Arizaga, J. A., Smith, J. L., Story, T. S., & Soncuya, G. (2014). The Grass Is Greener in Non-Science, Technology, Engineering, and Math Classes Examining the Role of Competing Belonging to Undergraduate Women’s Vulnerability to Being Pulled Away From Science. *Psychology of Women Quarterly, 38*(2), 246-258.

Van den Bergh, L., Denessen, E., Hornstra, L., Voeten, M., & Holland, R. W. (2010). The implicit prejudiced attitudes of teachers: Relations to teacher expectations and the ethnic achievement gap. *American Educational Research Journal, 47*(2), 497-527.

Whitney, A. K. (2015). The Black Female Mathematicians Who Sent Astronauts to Space. 2017, from __http://mentalfloss.com/article/71576/black-female-mathematicians-who-sent-astronauts-space__

thanks you! It’s great having such concrete suggestions!

I completely agree with your ideas. The problem with teaching mathematics is that the students who take the courses are split into two groups. The ones that enjoy mathematics and take the courses because of their interest and the students that are forced into taking mathematics course to fulfill their major requirements or have to take the courses to graduate like in high school. The problem with this is that you have to find a balance between helping the students that want to continue with mathematics and push them forward in the field, and reaching the students who are only there because they have to be there. The trick is assisting both groups of students within the necessary time limit i.e. the semester or during class itself. With this in mind I really like your idea of varying mathematical assignments to reach the students who don’t necessarily want to be there. I agree completely that the best way to reach the kids who don’t want to be in the class is by varying the problems to reach their interests. It’s absolutely necessary to promote the mathematics process because whether or not the students want to admit it or see it, mathematics models into almost every aspect of life or higher education.