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With Larry Ferlazzo

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Mathematics Opinion

Teach Math in Ways That Are ‘Proactive’ & Not ‘Reactive’

By Larry Ferlazzo — December 18, 2020 23 min read
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(This is the final post in a two-part series. You can see Part One here.)

The new question-of-the-week is:

What are specific ways educators can make teaching math more culturally responsive?

Part One‘s guest contributors were Chiquita Jenkins, Autumn Kelley, James Ewing, and Cindy Garcia. Chiquita, Autumn, and James were guests on my 10-minute BAM! Radio Show. You can also find a list of, and links to, previous shows here.

Today, Robert Q Berry III, Basil Conway IV, Brian R. Lawler, John W. Staley, Bobson Wong, Larisa Bukalov, Luisa Palacio, Paola Sztajn, Daniel Heck, Kristen Malzahn, and Felicia Darling, Ph.D., share their responses.

Begin “With the Child’s Curiosities”

Robert Q Berry III is a past president of the National Council of Teachers of Mathematics (NCTM) and a current professor of mathematics education at the University of Virginia. He has been a teacher at nearly all levels and collaborates with parents, teachers, and community members across the U.S. to advocate for teachers and students.

Basil Conway IV is a current assistant professor of Mathematics Education at Columbus State University, serves on numerous doctoral committees, and is a previous public middle and high school teacher.

Brian R. Lawler is currently an associate professor for math education and coordinator for secondary mathematics teacher-certification programs at Kennesaw State University. He taught high school math for nine years in a variety of settings.

John W. Staley is the current coordinator of special projects in the Baltimore County public schools, past mathematics teacher, past president for NCSM, and has presented at state, national, and international conferences.

Gloria Ladson-Billings (1994) defined culturally relevant pedagogy (CRP) as one “that empowers students intellectually, socially, emotionally, and politically using cultural referents to impart knowledge, skills, and attitudes” (p. 17–18). In addition to academic achievement, core tenets include cultural competence, referring to ways in which teachers keep the cultures of their children in the forefront of their minds and honor and respect the learners’ home culture within daily interactions and instruction, helping them to navigate dominant cultural capital in order to attain academic achievement while helping learners to simultaneously honor their cultural identity. A final core tenet, sociopolitical consciousness, is developed within historically marginalized youths when teachers help their students to understand the world as it is and equip them to change it for the better (p. 139).

Culturally responsive teaching (CRT), very similar to CRP, validates children’s cultural heritages to “build bridges of meaningfulness between home and school experiences as well as between academic extractions and lived sociocultural realities” (Gay, 2010, p. 31). Both CRP and CRT support teachers with the development of intellectual, social, emotional, and political learning opportunities to teach the whole learner (Gay, 2010; Ladson-Billings, 1994).

CRP and CRT defy traditional educational practices and cultural hegemony and develop social consciousness, intellectual critique, and political and personal efficacy. Teachers honor and respect students’ home culture and incorporate it within their daily instruction. Students believe that achievement is within their reach. Teaching practices that are transformative create structures to help students combat prejudices, racism, and other forms of oppression and exploitation.

  • The first step mathematics teachers can take to be more culturally responsive is to build relationships with students and caregivers.
  • Reach out at the beginning of the school year to introduce yourself to the caregivers.
  • Gather at least one thing the student likes to do or something about their past experiences in mathematics class.
  • Learn how to pronounce your students’ names.
  • Survey your students or have them complete a mathography, sharing some of their interests; things previous teachers have done that they found helpful and those things that made it difficult; extracurricular activities in both school and community; hobbies, sports, favorite book; one thing about their family that is of interest; how they do mathematics outside of school.
  • Create newsletters that can be sent home in which you share topics for the week, possible home connections, and ways the family can engage in some type of activity.

Next, teachers can make an effort to become more engaged with the lives of their students and their communities outside the school at both a personal and a mathematical level. By spending time with your students and their families, outside the school context and in their communities, mathematics teachers will learn of and value their students’ families and community assets. They can then use these assets to build community networks that promote equity, access, and empowerment of students. The great aspect of teaching in responsive ways to students’ culture is that all students and communities have cultures ready to flourish in the context of mathematics learning. Teachers can get involved/learn about your school’s/students’ community.

  • Attend community events, fairs, or activities where you might be able to see your students.
  • Attend sports or musical activities, greet caregivers, and express an interest in knowing how your student is doing beyond your mathematics class.
  • Reach out to community members to learn more about their roles, such as religious and other organizations that might be connected to or be interested to support the school.
  • Learn about the local, national, and international news events that are significant to your students and their families.

Lastly, teachers can begin by asking their students what they are interested in, what they want to know more about.

  • Your student’s interests identify a potential generative theme (Freire, 2000/1970) that can launch the study of mathematics and allow the teacher to connect the child from their interests to the formal topics of the intended curriculum. By beginning with the child’s curiosities, we are fully engaging all elements of their cultural, familial, social, and academic assets.
  • Ask students what they should do with their new knowledge. By doing this, the teacher once again engages students’ cultural expertise to become both “an actor and author of history” (Garcia, 1974, p. 16). This moves from a pedagogical role of responsiveness (reactive) to one of engagement and enactment (proactive).


Bucci, T. T., & McEwan, L. J. (2015). Weaving math and language arts literacy. Association for Middle Level Education Magazine, 2(5), 10–13.

Davis, F. E., West, M. M., Greeno, J. G., Gresalfi, M., & Martin, H. T. (2006). Transactions of mathematical knowledge in the Algebra Project. In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 69–88). Teachers College Press.

Freire, P. (2000). Pedagogy of the oppressed (M. B. Ramos, Trans.). Continuum. (Original work published 1970)

Garcia, A. A. S. J. (1974). Generative themes: A critical examination of their nature and function in Paulo Freire’s educational model (Master’s thesis, Loyola University Chicago). Retrieved from https://ecommons.luc.edu/luc_theses/2683

Gay, G. (2010). Culturally responsive teaching: Theory, research, and practice. Teachers College Press.

Ladson-Billings, G. (1994). The dreamkeepers: Successful teachers of African American children. Jossey-Bass.


A Culturally Responsive Approach to Students’ Math Anxiety

Bobson Wong and Larisa Bukalov teach math at a large public high school in New York City. They are authors of The Math Teacher’s Toolbox (Jossey-Bass, 2020) and recipients of the Math for America Master Teacher Fellowship:

When people find out that we teach math, they often admit to us that they’re not good at it. They talk openly about their math anxiety—the feelings of fear and tension when doing math that they developed after repeated negative experiences. Math anxiety is not simply a set of emotions but a physiological response that affects heart rate and neural activity. It can be even more problematic when teachers or parents have it since they can pass it on to students, which can negatively affect academic achievement. Students who are angry, depressed, or afraid simply won’t be motivated to learn, rendering even the most engaging and well-planned lesson useless.

To combat math anxiety—which we encounter frequently in our classes—we help them develop the necessary social-emotional-learning skills to manage their emotions and maintain positive relationships with others. In addition, we also use students’ prior experiences to build their learning capacity—what experts call culturally responsive teaching. We find that addressing students’ social-emotional-learning skills and being more culturally responsive in our teaching not only reduces their stress levels but ultimately improves their academic outcomes.

Building Relationships With Students

In order for students to be productive, we try to build a positive relationship with them. Neuroscience research indicates that the brain feels safest and relaxed when people feel a connection to others who are trusted to treat them well. Building trust is critical since it frees up the brain for learning and higher-order thinking. Simple acts that show genuine care for students can create a stronger relationship with them that can serve as a foundation for the ultimate goal, which is to increase their learning capacity. Even gestures that might seem minor to some, such as taking the time to learn how to pronounce students’ names correctly or greeting them by name every day, can show that we respect them. Teachers can learn more about students’ cultures and home lives and use this knowledge to communicate more effectively with them and counter their feelings of alienation toward school.

Many parents and guardians also experience math anxiety. We find that acknowledging parents’ discomfort toward math and giving them concrete ways to address it can help both parents and students. Research shows that children learn less when parents who have negative feelings about math help their children with their homework. To address parents’ math anxiety, we provide reassurance that they shouldn’t feel pressured to help their children with their homework. When we communicate with parents, we talk about our experiences of difficulty with math and what we did (or wish we had done) to improve our understanding. Parents can also foster a growth mindset in their children by pointing out that their mathematical intelligence is not fixed or inborn but can increase with more effort and studying.

Promoting Mathematical Communication

Research indicates that students who improve their mathematical communication skills are more likely to experience less “math anxiety” and to develop a more positive mathematical identity. We encourage discourse in several ways.

First, we show students that we value understanding more than simply getting the correct answer. One of the most effective ways that we do this is to use open-ended questions, which have unlimited answers. Incorporating questions like “What should we do next?” or “What made you think of that?” allows students with different levels of understanding to engage in the mathematics.

We also create a classroom environment in which students feel safe to take risks. When students are not sure of an answer, we allow them to express their opinion without fear of being embarrassed (“Let’s try something and see where it takes us”). When we make a mistake, we allow students to point out our error to us and say to them that we are human. Teaching students to use sentence starters (“I disagree with this answer because…”) helps students structure their thinking. These small but simple steps also help reinforce the idea that students can develop the skills necessary to improve their mathematical reasoning.

In addition, many students feel anxious about math because they struggle to articulate mathematical ideas precisely. In our experience, math is a language and should be taught like one. Thus, we use language- acquisition strategies often used for English-language learners. When introducing a new symbol or term, we take extra time to pronounce it and ask students to repeat it. Since our students usually write math by hand, we spend a great deal of time showing students how mathematical symbols are written, often giving tips to help students write them clearly. We ask students to try other methods or use alternate representations to find a more efficient solution. Our students create vocabulary charts, short writing exercises, and other visual and verbal aids that help them become more familiar with mathematical language.

Making Mathematical Connections

We believe that math should be taught in a way that makes sense to students. In our opinion, part of the reason why math anxiety is so prevalent is that many see it as a collection of disconnected and confusing “tricks.” By the time students graduate, they should have the confidence and ability to apply mathematical and critical-thinking skills to real-world situations.

Whenever possible, we relate the math that we teach to other mathematical concepts. When students see math as a logical and consistent system of ideas, they become better at solving problems since they can use multiple viewpoints. In addition, when they relate new material to previously learned ideas, they can see the “big picture” and may gain a greater appreciation of math. We use an area model to teach multiplying polynomials and whole numbers so students can see their connection. We use proportional reasoning to connect the similar figures and trigonometry that we discuss in high school with the ratios and proportions that students learn in elementary and middle school.

Connecting to Students’ Prior Experiences

When possible, we like to incorporate aspects of our students’ culture into our work with occasional classroom activities, homework assignments, or group projects. When discussing place value and its relationship to like terms in algebra, students can research the origins of the Arabic numeral system and compare it with other systems, such as Chinese or Roman numerals. Students can also use math to analyze and propose solutions to problems that exist in their communities. For example, they can compare the density of schools or supermarkets in their neighborhood with those in other areas.

Many students that come from different cultures have literacy and math skills in other languages that can be applied to developing similar skills in English. For example, after many of our Latin American students showed us a more systematic way to factor numbers into primes, we incorporated elements of this method into our teaching.

In our experience, trying to incorporate history or culture into every lesson or even every unit is difficult. Including cultural references in lessons will not magically motivate students who feel marginalized or abandoned. We recommend using historical or cultural references as part of a larger process of creating more genuine relationships with students so they will improve academically.

Enabling All Students to Succeed

The strategies that we describe here help all students—not simply students of color or students who struggle with content—develop the necessary skills to succeed. This requires developing the right mindset, in which we see all students as individuals who can learn and look at all aspects of their identity to enable them to grow. We recommend that in order to make these techniques truly successful, teachers should constantly reflect on their beliefs and practices to find ways that students’ culture, like other aspects of personality, can be used to strengthen learning.


Connecting With Parents

Luisa Palacio is an ESL and Spanish teacher from Colombia with 19 years of teaching experience. Luisa holds a bachelor’s degree in modern languages: English and French, and an M.A. in TESOL from Greensboro College. Currently, she teaches K-12 at Northampton County schools and Spanish with South Carolina Virtual Education:

At the elementary level, I believe teachers could get parents more involved. There is a misbelief that math is a universal language. Some teachers say numbers are numbers. However, different countries use different math methods, and that is why I believe it is important to make parents aware of that. Many times students go home and when their parents try to help them out, students say: ”That is not how my teacher did it,” which causes feelings of frustration for both parents and students. Teachers could offer some workshops for parents where we not only inform them the methods are different, but we can also teach them strategies to help their childrenat home.

Teachers also need to have some information about the students’ backgrounds, so that they can include some cultural points on the examples they provide within their lessons allowing students to make connections to understand concepts. When I say examples, I am not referring to names in a different language. I mean teachers, for example, need to know Latin American countries use the metric system. So they should be able to talk to students in terms of the metric system and teach them how to make conversions to the imperial system.


“Attending to Language”

Paola Sztajn is a professor of mathematics education at North Carolina State University, is a principal investigator in Project AIM (All Included in Mathematics), and has written over 90 papers focused on elementary school mathematics teachers and teaching.

Daniel Heck is the vice president of Horizon Research Inc. and is also a principal investigator for Project AIM. His research and development work spans many areas of mathematics education: classroom learning environments and discourse; teacher professional-development design, enactment, and impacts; curriculum design and enactment; and student problem-solving.

Kristen Malzahn is a senior researcher at Horizon Research Inc. in Chapel Hill, N.C., and a co-principal investigator in Project AIM. She began her career as an elementary school teacher, has an M. Ed. in curriculum and instruction, and over the past two decades, she has worked on several mathematics education research and evaluation projects and published a number of journal articles and book chapters.

Their most recent book is Activating Math Talk:

One component of culturally responsive math teaching is attending to language, a key part of culture. Language shapes students’ identities and can foster or hinder students’ participation in opportunities to learn math. Research continues to highlight the importance of high-quality, purposeful math discourse to foster learning for each and every student. Thus in our work, we focus on how to engage all learners, including emergent multilinguals, in math discourse that offers opportunities to develop students’ conceptual understanding of mathematics.

When teaching diverse students to activate math talk in the elementary classroom, it is important to consider that all students in the elementary grades are emergent math communicators; that is, they are all learning how to use academic language to communicate their mathematical ideas. In diverse classrooms, that include emergent multilingual learners, this means the teacher needs to spend time learning more about each student as an individual, identifying their history, assets, and prior math learning experiences. Getting to know students and focusing on the cultural, linguistic, and mathematical assets they bring to the classroom allows teachers to respect students’ unique backgrounds and strengths, focus on a growth mindset instead of ideas that assign fixed math capacity of potential to their students, and avoid deficit perspectives or language.

To build on emergent multilingual students’ assets, Driscoll, Heck, and Malzhan suggest in their book chapter (2012) that teachers can incorporate established guiding principles into their daily math instruction. These principles suggest that teachers (1) engage all students with challenging tasks that support equitable access to opportunities to learn, (2) use multiple modes of communication (e.g., gestures, diagrams, multiple languages) that draw on students’ assets to help them think through math problems and more readily express their thinking and reasoning, and (3) purposefully teach academic language in ways that build from students’ language assets, including first language. Other specific actions teachers can implement to support emergent multilingual students include:

  • Explicitly consider emergent multilinguals when planning for lessons and think about expectations for their full participation. Consider the assets they bring to the lesson and how to build from those.
  • Make sure the language and context of problems do not create barriers for students’ engagement with the math. When understanding that the context requires specific knowledge, provide background information and visual examples.
  • Model discourse practices to encourage students and show them how they are expected to participate.
  • Use small-group structures as a “safe space” where emergent multilinguals can practice how to communicate their mathematical ideas and, over time, develop their math communication precision. Purposefully group students using different grouping strategies.
  • Provide ample time for the rehearsal of explanations before whole-group presentations. Notify students ahead of time that they may be asked to share so they can practice what they are going to say or show while still in a small-group or private setting.

Don’t Make Assumptions

Felicia Darling, Ph.D., is an instructor, author, researcher, and teacher educator. She wrote the book, Teachin’ It! Breakout Moves that Break Down Barriers for Community College Students and research articles including, Incorporating Cultural Assets in Yucatec Maya Classrooms: Opportunities missed? Currently, Felicia teaches math at Santa Rosa Junior College in California:

Culturally responsive math instruction is not culturally-assuming math instruction. There are many great ideas available for making math culturally responsive. However, there are exceptional challenges for math educators trying to deliver culturally responsive instruction in classrooms where students come from a wide variety of cultural backgrounds.

If teachers have a majority of students in their classroom from Latin America, they can teach base-20 math—which is credited to the Mayans. To include women and students of color, teachers can explicitly teach moments in math history that include the contributions by mathematicians of color or mathematicians who are women. While these are strong culturally responsive practices, they may not resonate with the cultures of every single student in the classroom. What if some students are from Thailand and the teacher does not cover math contributions from Thailand? What if a student identifies as transgender? How will teachers include culturally responsive instruction for those in the LGBTQ+ community? As educators, we do not have intimate knowledge of the identities and cultural backgrounds of all of our students.

Today’s classrooms are diverse, and this presents challenges for teaching culturally responsive math. A powerful solution is to solicit information about students’ core values and cultures by asking them to create word problems or data sets that are meaningful to them. In this way, students can choose what they want to share about their core values and cultural identities. Teachers can find out who students are. This creates an inviting space for students to embrace their cultural and core values during math instruction.

I asked students to create a real-life word problem that was meaningful to them, that included adding and subtracting positive and negative numbers, and that included a visual model. Some of these problems were included on a unit test and some students did presentations on their word problems. Rayan, who was born in Jordan, created a word problem that resonated with his cultural values. He smiled proudly, when he asked the class to solve his problem, “How far would you travel if you walked from the bottom of the Dead Sea to the top of Mount Nebo?

In another example of a culturally responsive math assignment, students were asked to create a real-life data set that was skewed to the left or right. They were required to create a data set that was meaningful to them and to modify it to ensure it was skewed. Anahi created a data set using data from her family tree, because it made her feel closer to her family members who lived in México. It contained the ages of 45 living family members. In order to modify the data set to make it skewed to the right, she added the ages of her grandparents who had already passed.

Culturally responsive instruction does not mean culturally-assuming instruction. We cannot assume we know students’ cultures. We must lean in and listen to our students’ voices to deliver culturally responsive instruction. We do not always know the cultures of all of our students. However, we can still deliver math instruction that is responsive to the cultural identities, values, and backgrounds of our students. Asking students to create real-life math problems and data sets not only promotes Bloom’s higher-order thinking of math concepts, but it also invites all students’ cultural perspectives into our classrooms.


Thanks to Robert, Basil, Brian, John, Bobson, Larisa, Luisa, Paola, Daniel, Kristen, and Felicia for their contributions!

Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.

Consider contributing a question to be answered in a future post. You can send one to me at lferlazzo@epe.org. When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo.

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