Equity and Excellence Framework for Mathematics Teaching

By Dr. Fawnda Norman, Guest Author

Students learn math best when they identify as a doer of mathematics. Equitable mathematics classrooms should include lessons that address identity, relevance, and agency while teaching math concepts everyday. Many mathematics teachers strive to create classrooms that do that. However, it can be a struggle to put theory into practice. How do teachers attend to identity, relevance, and agency when planning math lessons? That is what I set out to answer when I co-created the Equity and Excellence Framework for Teaching Mathematics. 

There are many important equity theories on how best to create equitable learning environments. Ladson-Billings’ (1995) Culturally Relevant Pedagogy (CRP) states the importance of high levels of student learning and achievement (demand), cultural competence (relevance), and cultural consciousness (agency). Muhammad’s (2020) culturally and historically responsive literacy (CHRL) has five levels to include while teaching: Identity, Skills, Intellect, Criticality and Joy. In mathematics specifically, Guiterrez (2009) has the four dimensions of equity in mathematics: Achievement, Access, Identity and Power. It is these theories that we drew on when creating our Equity and Excellence for Teaching Mathematics framework. The framework sets out to practically address what these equality theories can look like in an everyday mathematics classroom. We used the five levels of Muhammad’s (2020) CHRL, as the elements from the other theories are included in her layers (see Table 1 to show how these theories overlap). In addition to drawing from Muhammad’s (2020) historically responsive literacy framework, the Equity and Excellence Framework encompasses four main components of mathematics lessons: Launch, Explore, Summarize, and Apply. In this article, I will present the five layers of CHRL and how they relate to mathematics teaching and list guiding questions (adapted from Muhammad (2020) to ask while planning math lessons. Then, I will present a lesson planning guide to help incorporate the different levels into mathematics lessons. Finally, I will conclude the article with tips and resources to be successful in using this framework.

 

Equity and Excellence Framework For Teaching Mathematics Layers Identity

 

Identity, the first layer of the framework, is “composed of notions of who we are, who others say we are (in positive and negative ways), and whom we desire to be” (Muhammad, 2020, p. 67). Identity is dynamic and fluid and shaped by our social and cultural environment (Brown & McNamara, 2011). Therefore, opportunities should provide students ways to explore and develop their own identities. Equally important, is learning about others while honoring the differences and how they relate to identities unlike their own (Muhammad, 2020). Students should be learning about themselves and others during mathematics lessons. Guiding questions to ask when planning for identity: How will your lesson help students learn something about themselves or others? How are you ensuring that students see themselves as a mathematician?

Skills

Skills, the next layer in the framework, are defined as the competence, ability, and expertise that students need to be successful in a content area. “Our goal is not to help students become better test-takers or academic achievers, but also for them to gain the confidence to use learning as a personal and sociopolitical tool to thrive in this world” (Muhammad, 2020, p68). The skills that are taught in US classrooms are often the manifestation of learning standards provided by the state and are often the focus of reports on student achievement. Through these reports, we find a gap in achievement between students of color and underrepresented populations compared to their white counterparts. In many cases, mathematics skills can be thought of as procedures. I propose that this layer goes deeper than just procedures and it entails the understanding of mathematical concepts. So, for this layer, we have changed the name to Concepts. Students should learn about and understand mathematics concepts in their math lessons. Guiding questions to ask when planning for skills: What math concepts will you be teaching? What math concepts do your students need to know for this lesson?

Intellect

The third layer, intellect, encompasses understanding, enhancement, and exercising of mental powers and capacities that allow one to better understand and critique the world around them. Here, students learn how to connect mathematical concepts to other subjects and applications in the real world. Intellect is linked to action, which should lead to learning experiences that connect to the human condition. Students should be given the opportunity to make connections during math lessons. Guiding questions to ask when planning for Intellect: What will your students be smarter about? What mathematical practices will students be engaging in? How will your students apply the new math concepts to real-life and problem solving contexts? How does this connect to broader contexts and new situations?

Criticality

Criticality is the fourth layer of the framework. Criticality is defined as “the capacity to read, write, and think of ways of understanding power, privilege, social justice, and oppression, particularly for populations who have been historically marginalized” (Muhammad, 2020, p120). Criticality is learning about empathy, fairness, and helping the community. In mathematics, there are biases as to what is considered the right or best algorithms to solve problems. In many contexts there can be situations that are normalized for the dominant culture, but leaves out other cultures. This can create gaps in understanding for marginalized cultures. Criticality challenges those biases to include many ways to solve problems and to see value in understanding others’ viewpoints. Criticality can help recognize what is being normalized and address it with the class so that all are on the same page. Guiding questions to ask when planning for Criticality: How will you engage your thinking about empathy and fairness? What problem or question in your community will this lesson help solve? What are the perspectives of the situation being presented? What is being normalized in the given situation?

Joy

The fifth layer is joy. Some may judge this layer as trivial and out of place, its significance can assist in the dismantling of the often taught oppression and violence of black and brown people’s stories. “When we frame the stories of people of color as narratives steeped in pain or even smallness, this becomes the dominant or sole representation” (Muhammad, 2020, p. 21). Furthermore, mathematics is often thought of devoid of interesting context or applications, creating a joyless learning experience. This layer of joy is more than just a “happy feeling” it is about feeling content and proud of the work that has been done. Students should leave a math lesson with joy. Guiding questions when planning for Joy: How will your instruction spread and amplify joy? Do you include more than negative contexts for marginalized populations? How are you teaching students about the beauty and truth in humanity?

Equity and Excellence Lesson Planning Guide

Below is the lesson planning guild to help implement the framework into your math lessons.

How to use the Equity and Excellence Framework Guide

This framework provides a lens to examine current mathematics lessons and a guide for creating new ones. As you look at existing lessons, you can ask yourself the guiding questions for each layer to see if it is present. If that layer is missing, you can use the guide to find which of the lesson’s components (Launch, Explore, Summarize, or Apply) fit to add the layer into the lesson. You can also use it to create new lessons. As you are reviewing the math concept you are going to teach, you can ask yourself the guiding questions and use the guide to help decide which components of the lesson each layer will fit. 

Layers can be presented through any of the components of the lesson. For example, you may have identity represented in the launch, skills in the explore/explain section, intellect in the summarization, criticality and joy in the apply section. Another lesson may have identity represented in the apply section, skills and intellect in the explore/explain, and criticality and joy in the launch. The combinations of where each layer is represented may change, and oftentimes more than one layer will be present in a component of the lesson, but it is important to include all five layers somewhere in the lesson.

Tips to implement the Layers of the Equity and Excellence Framework

Creating an equitable learning environment is a skill that we should all be continually working on. With any new skill it is best to start small and build up as you go. Trying to implement all the layers in every lesson is overwhelming and likely to lead to burnout. I suggest starting small. Choose one layer to work on and add to your lessons. When you feel successful with that layer, add on another layer. Another option is to choose 1 or 2 lessons to revamp with all the layers and then add more lessons each year. 

Find someone to work with and set some goals together. Having someone to bounce ideas off is beneficial when learning a new skill. Find another mathematics teacher that has equity goals and schedule a time to meet and discuss your lessons. Having a colleague to work with can also help with accountability and motivation to finish before the next meeting. 

Finally, do not expect to get it right the first time. As we learn new things, sometimes we fail. That does not mean we give up. You and your students will be learning new ways to learn mathematics together. It might be a little bumpy along the way. Maybe your students did not relate to your identity layer task, or they were not engaged in the intellect layer activity. It is ok! Learn from your mistakes and try again! This is where having a colleague is also helpful to talk things over and be encouraged to keep going.

Resources

In this section I will showcase some resources that you can use to help implement the different layers of the framework. I have found that most mathematics curriculums do a good job of including the skills layer so I will include resources that are helpful in the identity, intellect, criticality and joy layers.

Use Graphs to Start Conversations

Analyzing graphs can open up pathways to including identity, intellect, criticality and joy layers. In this data driven world, students are encountering graphic representations from multimedia sources. It is important to help our students learn how to read and analyze these graphs. 

Choosing graphs from current events is a way to make your lesson relevant. Chartr.co and Statista.com are excellent places to select interesting graphs for your students to investigate. In my lessons, I will show my students a graph and ask them what they notice or wonder about the graph. Notice and wonder is a great way to get all students involved in the conversation and engage in critical thinking. Oftentimes, from notice and wondering, we can get to issues like: Who is collecting the data? Where is the data taken from? What information is being left out? - leading to criticality. Then, from the notice and wondering, we can select a topic to explore mathematically, leading to joy because the students are part of the process of problem solving. 

Slow reveal graphs are another excellent way to engage students in the identity, intellect and criticality layers. Slowrevealgraphs.com has several graphs that only show a small part of the graph at a time and ask students what they think the data is about. It starts with just the bars or lines of the graph with no labels or numbers. Each step is another part of the graph (adding the numbers on the axis) and students are asked to make predictions along the way. Finally, all the labels are shown and students are asked more questions about the graph. This process of slowly revealing a graph creates space for students to make predictions in a safe environment. The first couple of steps of the graph, no one knows what it is about, so it is ok to get wrong answers. Then, as more is revealed, students learn to use the information given to add on to what they already guessed. This is another way to show that students can use graphs to learn about others (identity), think critically about what is being presented and what data is being left out (criticality), as well as help choose math topics to explore (joy). 

Three-Act-Math

Three-act-math activities are another great way to include the intellect, criticality and joy layers. Three-act-math activities present problems in three parts. Act one is introducing a situation (usually as a video or a picture), asking students to notice and wonder. This act also has students ask math questions about the situation. Act Two is choosing one of the math questions to answer and gathering the data needed to solve it. Act three is revealing the answer (finishing the video) and having a class discussion. This three-act process helps students see the relevance of math because they are part of the problem solving process from the creation of the question, gathering the data needed to solve the problem, predicting the answers and getting to see the answer revealed. Dan Meyer has great three-act-math tasks for secondary mathematics and Graham Fletcher has great three-act math-tasks for elementary mathematics. 

Connecting Books to Mathematics

Integrating literature into mathematics is a great way to include the identity, criticality and joy layers into lessons. Seeing and hearing math as a story is a way to engage students in math content in a different way. Students can learn about other cultures, have empathy for people in tough situations, and engage in social action about how math can be helpful in their community. Social Justice Books has a great list of multicultural math story books. Kids Math Talk has a list of 15 math books to build identity. Math Start also has great math themed story books. 

Conclusion

It is my hope that this article is helpful to math educators who are on a journey to equity and excellence in their math classrooms. Taking equity theory and putting it into practice is difficult and I hope that the equity and excellence framework guide can be a resource for mathematics teachers to use as they create lessons that give access to all students to identify as mathematicians.

 

 

 

Dr. Fawnda Norman, Guest Author

Fawnda Norman, Ph.D. is an Assistant Professor of mathematics education at the University of Wisconsin-Oshkosh. Her research focuses on mathematics identity, mathematics teacher identity, and equitable teaching practices in STEM classrooms. Contact her at normanf@uwosh.edu

References

Brown, T., & McNamara, O. (2011). Implications for Practice. In Becoming a Mathematics Teacher: Identity and Identifications (pp. 139–167). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-007-0554-8_7

Gutiérrez, R. (2009). Framing equity: Helping students “play the game” and “change the game.” Teaching for Excellence and Equity in Mathematics, 1(1), 5-7.

Ladson-Billings, G. (1995). But that's just good teaching! The case for culturally relevant pedagogy. Theory into Practice, 34(3), 159-165.

Muhammad, G. (2020). Cultivating genius: An equity framework for culturally and historically responsive literacy. Scholastic.
 

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01/06/2025