Students at The Miquon School recently participated in The Barnes Foundation Art of Math Challenge, a weeks-long project comprising the union of fine art and mathematics, as well as an extensive study involving literature, art history, strategic thinking, and collaboration, and they won awards for their work.

Using polymer clay, paint, cardboard, wood, and more, students were tasked with designing and building a three-dimensional scale model based on one of three well-known paintings: “The Raft,” by William James Glackens (1915, Oil on canvas); “Bathtub and Cat” by Angelo Pinto (c. 1944, Reverse painting on glass); and “Interior Scene” by an unidentified artist (Late 18th or 19th century, Chinese black ink and heavily applied pigments on silk).

Through this process, students in first and second grade were able to experience and develop a deep understanding of two-dimensional (rhombus, triangle, circle, trapezoid, etc.) and three-dimensional (cube, pyramid, sphere, cylinder, etc.) shapes. They were exposed to works of fine art and their history. They honed their skills making observations, learning about perspective, and grappling with concepts like number, vertical/horizontal positioning, negative space, and size. They learned how to measure and produce accurate three-dimensional scale models based on a 1:1 ratio of two-dimensional work–specifically, measuring a projection of the painting that was the same size and dimensions of the physical base of the model.

Much of this work entailed the constructivist approach to learning, or the idea that children learn best when they are given opportunities to formulate their own understanding of a concept or topic. Often this means giving students the time and the space to explore their passions while meeting curricular goals. In other instances, this means allowing children to share what they observe, notice, and wonder as a guide to the classroom work–even as much as that which is provided by the teachers.

Throughout the Art of Math project, children were not told how to make their scale models in a step-by-step guide provided by the teachers. Instead, the students were given just enough information to think through the measurement and building process and arrive at their own conclusions.

For example, Evan Mohr, of Mt. Airy, a first-grader, shared what he knew with the class.

“The painting is 32 inches,” he said.

Next, he explained how he used that information to make a hypothesis about how large to build the painting’s bathtub in their scale model.

“I measured with my eyes and the bathtub is half as wide as the painting.”

From there, other students had the opportunity to build on Mohr’s suggestion and move the project forward.

Second-grade student Declan Aptowicz, of Mt. Airy measured to check Mohr’s thinking. She found that in the painting, the bathtub was 16 inches.

“That’s half of 32,” said Mohr, and the class moved on.

In another group, the students observed that the color copy of the painting, Interior Room, was a perfect square. Following this, they were able to articulate a specific plan to create an accurate scale model using their math skills. Discovering that their model base measured 20” x 30,” and knowing that 30 minus 10 equals 20 inches, they trimmed the base to make it into a square like the original, measuring 20” x 20.”

To take their measurements, the students used rulers as well as other units of measure, such as Unifix cubes.

“We measured a lot, because we didn’t want stuff to be the wrong size,” said Miles Kane, of Mt. Airy, a first-grader.

In addition to acquiring extensive experiential knowledge in measurement, shape, and scale, the students were able to work together on a project that required them to collaborate, chart out plans, practice decision making, listen to partners, speak up with their own ideas, and other 21st-century skills, or those that will be required for the jobs these children will take on when they enter the workforce.

“[We had to] write all of our materials and write our next steps. We talked about what we wanted to do in pairs. We talked about size and materials and background. We counted and measured and then we started building,” said second-grader Maxine Dezort Reynolds, of Germantown.

All seven of Miquon’s entries were presented along with submissions from other area schools at The Barnes Foundation on March 3. One first and second grade Miquon group, that created The Raft scale model, was selected as the winner for Mathematical Reasoning out of the first-fourth grade entrants. Another Miquon first- and second-graders’ model of Bathtub and Cat won the popular award for first-fourth grade models.

One of the judges, Annie Fetter, founding staff member of the Math Forum and Math Education Specialist at the 21st Century Partnership for STEM Education remarked, “[It was] the perfect sort of project for Miquon. Not only do they already approach learning as a community activity and try to integrate subjects whenever possible, but they also have the flexibility to allow students to really dig into something.

“It [was] so fun to meet so many of the students and hear more about their thinking, both mathematical and artistic, as well as their experiences working in a group,” said Fetter.

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