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Design Thinking in the Math Classroom

MidSchoolMath National Conference

LANL Foundation STEM Coordinator Dave Forester knows the challenges that students face with mathematics. As a father of two middle school-aged sons, he sees first-hand how his kids have become disinterested and disconnected from the subject. And, as a former high school teacher of an engineering design class, he also observed how limitations in understanding of early math prevented older students from grasping more complex concepts and courses.

“My boys are smart kids, but they think that math holds nothing for them. They don’t see themselves as being good at it and they don’t see math as connected to anything else in their lives,” said Forester.

This is a common challenge for many students. Difficulties with math are less about aptitude or intelligence and have more to do with the way the subject is taught. Poorly constructed textbook curricula, lack of practical application, and problems with online instruction, coupled with ineffective teaching methods compound the issues.

As part of the LANL Foundation’s goal to support teachers and promote interest and opportunities in science, technology, engineering, and mathematics (STEM), Forester and the K–12 Program have sought new methods and curriculum options for teaching and learning math. For one innovative program, they had to look no further than Taos, NM.

While struggling with math lessons, veteran teacher Scott Laidlaw, found that he could “leverage the central role of imagination in how students learn.” He envisioned a new platform for math curriculum at the middle school level, based on conceptual narratives that involve math “games,” and MidSchoolMath evolved.

Founded by Laidlaw and other collaborators, MidSchoolMath offers a different approach to engage kids with math content in a way that makes it more accessible and even fun. Blended digital, video, and print curricula are available for grades 5 through 8, the period when national studies report that students are on a steady decline in math performance and test scores.

Math can be exciting when it involves more than hearing an explanation, taking notes, and working out repetitious problems or homework until students “get it.”  Not giving learners a defined problem and all of the information up front, but instead allowing them to develop their own questions and lead discussions, collaborate, and share ideas can promote greater engagement, retention, and achievement.

MidSchoolMath’s story-based approach transports students to another time or place, where they grapple with complex, conceptual problems and use math as a tool to develop solutions. Some of the background narratives and lessons involve locating an avalanche victim, guarding a castle, evaluating sports statistics, and charting a ship’s course to reach an island.

“These are far from your typical story problems,” said Forester. “Students become immersed in the context of a narrative and seek mathematical solutions to challenging situations.”

Teachers say that the MidSchoolMath curriculum is easy to implement, which means that they are likely to use it regularly and with fidelity. It also allows them to think creatively.

As a promising program, MidSchoolMath received K–12 Program funding for curriculum development. An additional LANL Foundation grant supported El Camino Real Academy in Santa Fe in adoption of the program and its real-world applications to raise student achievement.

Forester attended the March 2019 MidSchoolMath National Learning Conference and led a breakout session. The conference, which drew participants from 49 states and a few other countries, gave teachers the opportunity to step into the learning seat and reexamine their methods of teaching and, at a fundamental level, challenge their beliefs of students’ capacities and how traditional is math defined.

Forester’s session on Design Thinking in the Math Classroom offered a hands-on exploration and problem-solving challenge that involved Doritos snack chips. The design challenge approach was put into practice while also incorporating math standards.

The project began with teachers estimating the number of total chips in each unopened bag of Doritos and the number of whole and broken chips. Small groups collected data then found the average number and percentage of whole chips in one-ounce bags before and after unopened bags were dropped from a height of five feet.

In small groups, teachers were given 20 minutes to design, build, and test a system to keep the Doritos safer than the current packaging. Using 10–13 whole chips and materials provided—card stock, paper plates, cups, straws, tape, foil, zipper bags— the teams discussed and created designs that offered added cushion and damage resistance.

After testing their designs from the same five-foot drop height, they recounted the number of whole chips and recorded the data as a class. The ratios were displayed as the number of whole chips before the drop as the numerator and the number whole chips after the test as the denominator. The resulting statistical data were charted along a histogram, which was also used to measure the success of each design.

The teams were then given the opportunity to modify their packing solution to create an optimal design with a higher level of effective chip protection.

After further testing, the class evaluated the clusters of data that ended up on either end of the histogram. Discussion centered on math standards that were applied throughout the lesson and how the exploration could be extended by adding restrictions to reduce the package size or exclusion of some materials. Time was also given to talking through how standards other than math could be incorporated as well.

In his work leading professional development for teachers, Forester emphasizes the positive side of failure in a way that’s fun and playful that also allows students opportunities to revisit challenges and take the learning further.

“This style of smaller design challenges woven and scaffolded into a larger challenge offers safe scenarios to try things out, make mistakes, and approach the challenge again in a new way due to the iterative nature of the lessons,” he said.

A math consultant in attendance was impressed by the vertical alignment of the lesson. “We were able to go from math to ELA (English language arts) to engineering. The lesson set the stage for a lot more than just math standards. This was all about student freedom. My takeaway is, don’t be afraid to choose tasks that align with other standards, because the students get more bang for their buck from projects like this.”

Another participant in the session said that she teaches math at the middle school level because she believes that it’s “math for life.” The subject provides a learning thread throughout students’ entire lives.

“I loved this activity, it was engaging for me and our group. I can see so many ways that I could development these projects and meet our core in any grade. It’s a challenge to get students to be engaged, so that’s why I think that this design thinking is incredible,” she said.