Making Math Meaningful for All Learners: A Math Modeling Approach

Math modeling, also known as mathematical modeling, is the process of using mathematical concepts, equations, and data to create representations of real-world situations. Math modeling helps students make connections between math and the real world by encouraging them to apply mathematical concepts to everyday situations. (See our math solutions)

It fosters flexibility in using math, allowing students to approach problems from different angles and develop both conceptual understanding and procedural skills. Through math modeling, students learn to solve real-world problems, interpret the results of their work, and make informed predictions about future outcomes. Additionally, it helps students visualize data, making abstract concepts more accessible and meaningful in practical contexts.

For many students, mathematics can feel disconnected from their lived experiences, making engagement and comprehension more challenging. Traditional instruction often presents math as a series of abstract concepts rather than as a tool for understanding and solving real-world problems.

However, by leveraging mathematical modeling, educators can create meaningful, accessible, and applicable learning experiences for all students. The Wisconsin Vision for Mathematics emphasizes "Making Math Meaningful for All Learners" by fostering critical thinking, problem-solving, and real-world connections.  

Below are four strategies that align with this vision and enhance mathematical learning through modeling.

1. Generate Problems with Student-Centered Contexts

Math modeling is included in the math practice standards because it teaches students how to apply mathematical concepts to real-world situations, making math relevant to their lives and fostering critical thinking skills by requiring them to analyze problems, make assumptions, and interpret results within a practical context, preparing them for decision-making beyond the classroom.

Teachers can integrate mathematical modeling to which students in their classrooms can connect by doing the following:

• Framing Modeling Tasks within Stories: Presenting real-world problems from students’ lived experiences within historical, cultural, or personal narratives to deepen engagement.
• Encouraging Student-Created Math Problems: Having students create mathematical scenarios based on their own experiences and communities.
• Ensuring Representation in Word Problems: Ensure students can see their lives in the names, scenarios, and contexts presented in problem sets.

Authentic relationship-building with students is key to being able to select relevant modeling tasks that reflect their cultural backgrounds and lived experiences.

2. Highlight Mathematical Contributions

A math curriculum should reflect the global history of mathematics and the contributions and models from a variety of cultures. 

3. Encourage Collaborative and Discussion-Based Modeling

Mathematical modeling thrives in collaborative learning environments where students analyze, justify, and refine their models through discussion. Educators can foster engagement by:

• Group-Based Mathematical Investigations: Students work together to solve complex, open-ended problems relevant to their lives and communities.
• Inquiry-Based Discussions: Encouraging multiple solution paths and diverse perspectives in problem-solving.
• Student-Led Modeling: Empowering students to identify real-world challenges, gather data, and construct mathematical models to propose solutions.

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4. Expand Methods for Demonstrating Mathematical Understanding

Students process and express mathematical understanding in multiple ways. To support all learners, educators can:

• Utilize Hands-On and Visual Modeling Tools: Employing manipulatives, graphing software, and interactive simulations to visualize complex concepts.
• Offer Multiple Forms of Assessment: Allowing students to demonstrate understanding through verbal presentations, written reflections, or coding mathematical models.
• Encourage Flexible Problem-Solving Methods: Valuing different computational strategies.
• Use Math Tools as Needed: Students have the ability to choose and use the math tools they need to model their thinking.

Bringing It All Together

By incorporating these high-yield teaching practices into your math classroom, it allows access points for all students. Using these techniques allows educators to transform math instruction into an engaging, and empowering experience. When students see mathematics as a tool for understanding their world and addressing real issues, they develop confidence, agency, and a lasting interest in the subject.

How have you integrated mathematical modeling in your classroom? Let’s continue the conversation!

(Kim Walters, Director, contributed to this article.)