In my K–12 experience, I can’t remember why mathematics was important to my life. I do remember, however, a heavy emphasis on procedures with little application. I had great teachers back then, and at the same time, connecting student experiences to problem-solving was not as much of a focus in math education years ago as it is now. But if you asked me how and why I could apply adding fractions with unlike denominators to my specific context, I would’ve been perplexed. When students are able to see their lives through a mathematical problem, they build stronger connections and remember content better, compared with students under traditional pedagogical strategies.
Mathematics isn’t detached from reality. It’s a vibrant, flexible, and engaging subject that’s worth teaching to its fullest potential. After years of trial and error, research, and practice, I’ve found three effective strategies to connect student experiences to problem-solving in mathematics.
1. Know the Community
Familiarity with the community allows you to understand students on their own turf in order to center their experiences in the learning process. The following examples are a good start:
- Research the landmarks, restaurants, and history in the neighborhood.
- Tour the community and visit local establishments.
There’s a local ice cream shop called La Michoacana in my Memphis, Tennessee, school community that I often visit and where I see many of my students. When I give my students mathematical problems that center around familiar landmarks such as this, I witness more engagement and more buy-in to persevere through problem-solving. Familiarity builds confidence in my students to tackle real-life math scenarios, and they’re able to see math as a useful tool to understand their communities. Planning accordingly with this in mind will allow you to reframe superficial word problems from a curriculum to relatable and realistic applications.
2. Know Your Students
At the beginning of the year, it’s crucial to know your students’ names and how to pronounce them, and to discover their interests. Some practical ways to do this include the following:
Create interest surveys to gather personal student data: At the beginning of the year, allow students to express themselves where survey questions can center around their favorite hobbies, favorite types of music, favorite food items, and much more.
Interview students about their interests throughout the year: These interviews should be informal, and I typically interview students during small-group instruction, a planning period, or a separate intervention bloc where there is sufficient time to understand their personal experiences and assess their mathematical understanding of a particular topic.
Collect verbal and nonverbal feedback from students: My students are my most important teacher evaluators. In my class, I use weekly data trackers to collect verbal feedback from partner discussions when engaged in a real-world math task. Use the data trackers that you’re already using, and leave space for teacher notes when intensely monitoring.
I listen to the types of questions that students ask each other, the feedback they give each other, and how the task is meeting their needs to deepen their understanding and engagement in mathematics. As I assess their understanding, I am beginning to hear more of “Oh, I think I get it now,” “Hey, I know what this is!” or “Did you do it a different way?” If I see that students are confused about the context of the problem and have disinterested faces, I know I may have taken a wrong turn somewhere in crafting the task.
Coordinate student focus groups throughout the year: Christopher Emdin named these cogenerative dialogues. Using data from formative and summative assessments, surveys, and observations, these groups consist of different social, ethnic, high-achieving, low-achieving, engaged, and shy students as much as possible.
Students are incentivized through class prizes for their participation (stickers, free lunch or snacks, extra computer time, etc.), and this typically happens at the beginning of a quarter or semester during a planning period or any moments in the schedule when I can gather them without interruption. This provides a comprehensive diagnosis of my instruction: how well I’m reaching every student in the class with the problems that I give them.
3. Start Small
Don’t overwhelm yourself, but simply start small by first knowing and internalizing the mathematical content. This is crucial before attempting to make problem-solving more relevant and connected to student experiences. Understand your required curriculum, the grade-level standards, and the mathematical practices (MPs) before trying to adjust your problems. Without synthesis of those components, problems could be relevant without any connection to what is expected of every math learner in terms of the standards and MPs.
Engaging in Culturally Relevant Math Tasks: Fostering Hope in the Elementary Classroom discusses the concept of establishing demand and access through one problem at a time. After establishing demand and access, I’m prepared to center cultural and community inquiry into the problem-solving that the book describes to get my students knowledgeable about their communities and themselves. For example, the book poses a “naked fraction problem” (fraction problem without context) that states, “Add the fractions and show your work: 5/8 + 1 2/3 = ______.” This type of problem could also be similarly presented in my school’s math curriculum program inside the problem set or application problem without much cultural and personal connection.
Remember, we as teachers create the magic to bring these problems alive. The authors transform the problem as, “Yuki is making a traditional Japanese kimono for her daughter to wear for a special cultural ceremony. Her daughter’s costume needs 5/8 yard of fabric and Yuki’s costume needs 1 2/3 yards of fabric. How much fabric will Yuki need? What might Yuki’s dream design look like?”
Depending on your school community context, these names and situations can be adjusted based on data derived from student interest surveys, feedback, and focus groups. When starting small, practice with one lesson or one problem within a lesson per week. Then, as you gain confidence, scaffold in additional problems or lessons. Creating culturally relevant problems is becoming easier for me, but I’m still growing. Be patient with yourself, and expect growth and mistakes along the way.
I recall facilitating a lesson on division with three-digit dividends and one-digit divisors. Instead of just dividing numbers without context, I knew my students were curious about extreme weather due to their ongoing questions around the overwhelming news coverage on hurricane season. I decided to center the lesson around Hurricane Harvey, where students learned how to divide canned goods on their tables from a Memphis supplier for hurricane victims. The conceptual understanding and motivation to make sense of problems and persevere in solving them while critiquing the reasoning of others were evident.
Connecting mathematical problem-solving to student experiences is a pursuit of preparing our students to be critical thinkers and problem solvers in their community and workplace. Our students will be able to have sustained academic success, develop critical consciousness to challenge the status quo of their current situations, and maintain cultural competence in an increasingly diverse world.