# Visualization + Discussion = Effective Team-Based Math Modeling

When it comes to team-based math modeling—especially tackling complex, real-world problems and coming up with creative solutions—there's a lot more involved than just crunching numbers. Two key elements that make the whole process smoother and more effective are visualization and discussion. These processes help teams work better together, ensuring everyone is on the same page and communicating clearly throughout the math modeling process.

**The Role of Visualization in Team-Based Math Modeling**

Visualization is a game-changer when it comes to making tricky math problems easier to understand, especially when you’re working in a team. It lets everyone break down and simplify the issues at hand. By using things like graphs, charts, or specialized software, teams can create visual representations of data and models that everyone can follow and contribute to, making sure the whole team is on board and working together smoothly.

Think of it this way: visualization takes abstract math concepts and turns them into something you can actually see. This makes it way easier for teams to get a handle on the relationships between different variables and assumptions in their models. Whether it’s drawing diagrams, using graphing tools, or diving into more advanced software, being able to "see" the problem is key to making teamwork in math modeling more effective.

**The Importance of Discussion in Team-Based Math Modeling**

Now, let’s talk about discussion. This is just as important as visualization in team-based math modeling. Open and ongoing conversations allow teams to refine their ideas, challenge each other's assumptions, and make sure their solutions hold up under scrutiny. Discussion isn’t just about talking; it’s about critical thinking, building consensus, and making sure that everyone is contributing to a strong and well-supported final model.

When students engage in discussions, they’re encouraged to talk through their thought processes, question the methods they’re using, and explore alternative solutions. This back-and-forth helps deepen their understanding of the problem and can uncover mistakes or missed opportunities. Good communication within the team is essential for coming up with a well-rounded and accurate mathematical model.

**Incorporating Visualization and Discussion into the Classroom **

So, how can you bring these powerful tools into the classroom? Here are some practical tips for educators to help students get the most out of visualization and discussion.

**Structured Group Activities:**Break students into small groups and give them a math modeling problem to solve together. Encourage them to use visual tools like whiteboards, graphing software, or even physical models to share their ideas. Guide them on how to use these tools effectively to make their thinking visible.**Interactive Software:**Introduce students to interactive visualization tools like GeoGebra, Desmos, or even simple graphing calculators. These tools help students create visual representations of their models, making abstract concepts more concrete. Make these tools a regular part of assignments and projects to build their skills.**Facilitated Discussions:**After students have developed their models, hold class-wide discussions where groups present their solutions and the visual aids they used. Encourage other students to ask questions and give feedback. This not only helps refine their models but also fosters a culture of collaborative learning and critical thinking.**Cross-Disciplinary Projects:**Create projects that require students to apply math modeling in real-world scenarios, like environmental studies, economics, or social sciences. These projects show students the practical applications of math modeling and the importance of teamwork, visualization, and discussion in solving complex problems.**Reflective Journals:**Have students keep a journal where they reflect on their group discussions and the visual tools they used. This practice helps them internalize what they’ve learned and appreciate the value of collaboration and visualization in the math modeling process.

Visualization and discussion aren’t just add-ons in team-based math modeling—they’re essential for deeper understanding, effective communication, and successful collaboration. By fostering these skills in the classroom, educators can better prepare students for the real-world challenges of mathematical modeling.

Are you ready to see team-based math modeling in action? Our international math modeling contests at the middle school, high school, and undergraduate levels challenge students to form, organize, and manage a team to model and solve a real-world application problem and present a solution report. Learn more and register today.

# Written by

### COMAP

The Consortium for Mathematics and Its Applications is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world.