What is mathematical modeling?

Mathematical modeling is the process of creating a mathematical representation of a real-world problem in order to understand it. To learn more about mathematical modeling check out our page on What is Mathematical Modeling?

What does mathematical modeling look like in a classroom?

Students work together (in pairs or small groups) to solve authentic, real-world problems with multiple assumptions and multiple solutions. You can start with MEAs (Model Eliciting Activities) which help students to develop a modeling mindset. These short parts of a task can help students to become familiar with the process of making assumptions and working with others to develop solutions. Once they become comfortable with the MEAs, then move to full modeling tasks which may take several class periods. Students should solve the problem, discuss with their group, and then time should be allocated for each group to present to the class and receive feedback. Students should be encouraged to change their model as they find new assumptions that they had not previously considered. 

Why should students engage in mathematical modeling?

Students gain experience solving problems that have applications to their life. The problems capture their interest because they are relatable, as opposed to contrived textbook problems that often do not resemble their lived experiences. In addition, the open-ended nature of the problems allows students to think creatively and to understand that often there are multiple solutions to a problem. It also reminds students that their assumptions are important, something they are rarely asked to consider in standard textbook problems. 

What are the benefits of mathematical modeling for students?

There are a number of benefits of mathematical modeling for students that include helping students see the importance of math, deepening students' understanding of mathematical concepts, and promoting problem solving skills.

To learn more about the benefits of mathematical modeling check out our page on What is Mathematical Modeling?

How can in-service teachers or pre-service teachers learn about mathematical modeling?

There are many resources for current and future teachers related to modeling. You can view our page of Modeling Tasks. If you are a mathematics teacher educator you might want to check out our research on Pre-Service Teacher Modeling. If you conduct professional development with current teachers you may want to check out our research on In-Service Teacher Professional Development.

How can mathematical modeling be integrated in to your school's curriculum?

It is helpful to create a library of possible tasks that align with your school's curriculum. Having multiple teachers contribute activities to a bank of modeling tasks can offer teachers options that suit their classrooms' needs. Seeing how modeling activities align to the content being taught in class can help teachers to feel more comfortable enacting those activities. Allowing time for teachers to try the tasks together before implementing the tasks allows teachers to share ideas and to become comfortable with the activity before using it in class. 

What resources are needed to implement mathematical modeling?

In an optimal situation, common planning and PD time is allocated for teachers of the same course to meet regularly to both select tasks and to try them so teachers can offer feedback to each other. Shared drives on the school's network can allow teachers to build and organize a library of modeling problems. Technology is helpful for many of the problems, and that can take many forms from graphing calculators to laptops. Many good tasks are available online at no cost which eliminates the need for additional textbooks or online programs. Finally, there are tasks which require no more than a pencil, paper and scientific calculator. If technology is not available, that does not preclude teachers from conducting modeling activities. See our Modeling Resources page for some ideas. 

What should I expect when facilitating my first modeling task in my class?

Hopefully your students will be interested, will be engaged and will notice that this doesn't look like the problems they may be used to seeing. They could be excited to work with peers and to work on a problem that has more than one correct solution. 

The first time does have its challenges. Students may be unnerved that there is more than one possible answer. They may ask you if they got the "right" answer. They may also forget that their assumptions are important and can have a big impact on the answer. As a teacher, they may have a lot of questions, not all of which you have the answer to. Some students who are not used to working in groups may find it challenging to make sure all voices are included. As you encounter these challenges, consider how you might set expectations differently for the next task. As students and teachers become more familiar with the process, there tends to be fewer of those issues and more working together toward solutions. Additional ideas can be found on our In-Service Teacher PD page.