How often do you ask students to apply the math they know to problems that might arise in life, society, and the workplace? Because we spend so much of our time in math class "drilling and killing," working problem after problem to ensure mastery of fundamental algorithms and formulas, this is often left to the wayside.
However, modeling with mathematics is the fourth standard of practice presented in the Common Core math standards. And it's yet another example of how the Common Core can push us to go deeper with our math teaching—in ways that greatly benefit our students.
Here are three things to consider when thinking about mathematical modeling.
1. Give it context.
When planning to teach math concepts, think about the applications of the work. Yes, students need to develop skills and fluency, but in order for them to deeply understand the mathematics, teachers must find ways to put math into context. Spend less time with repetitive problems and more time on problems with real scenarios.
For example, instead of practicing multiple three-digit addition problems, put the math into a word problem. Knowing how to do 455 + 387 is one thing, but deeper understanding will be reached with this problem: "In April you earn $455 and in May you earn $387. How much did you earn in both months combined?"
2. Go deeper.
Life isn't as simple as the addition problem above may seem, though. Look at ways that you can build longer problems, problems with multiple steps and more than one question.
You might start with the basic April + May earnings problem and create a second question such as: "In June, you earn double what you earned in May. How much have you earned in all three months combined?" And then from there: "In July, you have to spend $250 on supplies, while earning $126 less than you did in June. How much have you earned overall in the four months April through July?"
Notice that these additional questions add depth and rigor because they call upon students to demonstrate understanding of multiple skills. They aren't simply adding two numbers now. They have to understand what "double" means, know that spending money and the phrase "less than" require subtraction, and finally they have to add four numbers.
Here's a fourth grade performance task from the Smarter Balanced Assessment Consortium (one of two consortia charged with developing national CCSS assessments—the other is PARCC). It has four stages and integrates measurement and data, algebraic thinking, and geometry skills. Modeling with mathematics is a critical part of problems such as this one. We can use performance tasks such as this one to help us build problems for our own students.
3. Tap into resources.
Need ideas for how to model mathematical thinking in the problems you share with students? Check out the item and task prototypes from PARCC or the Smarter Balanced sample items. You'll see the type of thinking that the Common Core assessments are going to call for, as well as examples of ways you can model mathematics with students. Another terrific resource has been organized by Ben Rimes, who blogs at The Tech Savvy Educator. He calls them Video Story Problems. These examples bring math to life and present scenarios that will encourage students to make connections between math and the world around them. Teaching Channel also has some amazing videos that will inspire you to incorporate modeling with math into your work with students, such as this real-world geometry lesson.
What are we communicating when we give our students a page of triangle area problems or 40 decimal addition problems? The message: math is dull and mundane. Not only does this approach suck the fun out of math, it fails to help students understand why math is relevant. A page with 40 problems also conveys the message that students' time is not important to us. (And we wonder why so many students are so turned off by math by the time they reach high school…) However, when we present problems with "real world" implications, we demonstrate that what students are learning has value.
How do you teach your students about modeling with mathematics? What resources do you use to help you do this? Please share your ideas by leaving a comment!
Center for Teaching Quality is writing a series of blogs in partnership with Teaching Channel. CTQ is transforming the teaching profession through the bold ideas and expert practices of teacher leaders.
Ben Curran is a K-5 instructional coach at a charter school in Detroit, Michigan. He is also co-founder of Engaging Educators, co-author of Learning in the 21st Century and a member of the Center for Teaching Quality’s Collaboratory. Follow him on Twitter @engaginged.