Real-world math: How to add a sense of wonder
Educators increasingly have been bringing real-world math situations and examples into the classroom to help students contextualize the subject and improve understanding.
Rather than traditional instruction methods—which often involve simply presenting concepts and skills and rote memorization—real-world math educators are adopting new approaches to better connect with students and demonstrate how the subject can be used in their own lives, says Mary Swack, supervisor of secondary mathematics for Carroll County Public Schools in Maryland.
“Application-based mathematics is really the world we live in and it shows stuff that students can relate to,” Swack says.
For example, real-world math curricula in Carroll County feature multistep tasks as unit starters. Students are presented with a relevant problem, such as how coaches may divide players between varsity and junior varsity teams or how wildlife experts might use ratios to protect endangered creatures, and try to solve it as best they can.
More from DA: Why don’t we spend more time teaching math?
Teachers lead students in notice-wonder discussions, asking questions such as “What do you notice about this?” and “What do you wonder about this?”
Students then engage in a “productive struggle” period in which they wrestle with the problem on their own before receiving formal instruction. Finally, they share reflections on their efforts and receive feedback. The student-led, teacher-guided process is repeated until the problem is finally solved.
“When you have an authentic application, it promotes student collaboration and draws upon the student’s backgrounds and experiences,” says Swack.
Educators at other school districts across the country are also increasingly using real-world scenarios and situations to contextualize mathematics.
Real-world math projects inside and outside class
At High Hills Elementary School on Shaw Air Force Base in South Carolina, fifth-grade students recently undertook a project in which they used math (in addition to science, English and social studies) to design food trucks.
Students created math models and built their multiplication skills by figuring out the finances involved with running the business—from buying food supplies to calculating vehicle maintenance and repair costs.
In the Los Angeles High School for the Arts, ninth-grade students address real-world math through studying financial literacy.
Budgeting personal expenses, managing credit cards and paying bills all focus on basic math skills, while exercises such as calculating costs involved with launching a business provide additional learning opportunities.
Some districts have even taken students out of the classroom to provide practical math learning experiences.
More from DA: How to cultivate diversity in STEM education
For example, high school students in Colorado can take “Geometry in Construction,” a class in which they work with Habitat for Humanity of Metro Denver to help construct homes.
In addition to learning how to use power tools, students from 17 schools improve their geometry skills through use in hands-on construction—and in the process, also help those in need.
How to design real-world math curriculum
One of the challenges in a real-world math approach to mathematics is coming up with novel tasks or problems that engage students in the mathematical process and also other content areas, says Robert Berry, president of the National Council of Teachers of Mathematics and a former middle school math teacher.
“A classic example from four or five years ago that we used to use is ‘the cell phone problem,’ in which students had to look at the relationship between minutes and cost,” says Berry, also currently the Samuel Braley Gray Professor of Mathematics Education at the University of Virginia. “Well, that’s not relevant because not too many people purchase minutes any more.”
In finding examples and projects, the mathematics have to be grade-level appropriate, reminds Berry.
“A task might require multiple entry points, so there’s no one right way to enter,” he says. “And that means there may also be multiple solution pathways.”
It’s also important to avoid problem duplication, says Swack. If the same kinds of problems are presented repeatedly, students will try to apply the same strategies to every assignment.
Another challenge is handling the pedagogical shift, says Swack. Many educators learned through the traditional model in which the teacher would present the skill first and then the student would have to apply it to a problem. They are inclined, then, to teach that way themselves.
“The real-world math approach flips that upside down and says, ‘Let’s start with the rich problem, see what we know and what we need to figure out, and then along the way, I’ll introduce skills that will help guide you to a solution,’” says Swack. “It forces students to make connections and think mathematically.”
Ultimately, providing real-world context helps dismiss the stigmas involved with learning math.
“Nobody walks around saying they can’t read, but it’s very typical for students—and parents—to say, ‘Well, I’m not very good at math,’ ” says Swack. “The real-world approach boosts confidence and eliminates that idea that there’s a ceiling in learning math. We can always learn more math.”