From concrete to abstract, manipulatives make math meaningful

Foundation helps fund use of hands-on tools

Rockford — Rockford’s curriculum has long included hands-on tools to drive math concepts home for students, and a recent grant from the Rockford Education Foundation has helped ensure things stay that way.

In 2023, the REF collaborated with Wolverine Worldwide, offering a \$26,000 grant to support the continued use of math manipulatives in classes from developmental kindergarten through fifth grade.

What are manipulatives? Anything students can touch, handle and, well, manipulate, to help illustrate math lessons in the classroom, said Maggie Thelen, director of mathematics, innovation and accountability.

“If students can touch and feel and use objects in learning math, they’ll retain better,” Thelen said. “Students don’t understand … until they can play very intentionally.”

Intentional play was on display during a recent visit to Sharayah Gariepy’s second-grade classroom at Crestwood Elementary. Students excitedly gathered around their teacher near the end of the day, eager to get to work and use some of the new tools.

Learning in Action

Among the manipulatives in Gariepy’s classroom are rekenreks — abacus-like counting frames — as well as magnetized math games, Base Ten Blocks and more. Some have been around for a while, but thanks to the REF, about half of them are new.

The updated equipment is much appreciated by student Lilli Donley, who said math is her favorite subject. Lilli was quick to reason her way through some warm-up challenges, using her rekenrek to answer questions posed by Gariepy.

“Show me 12,” Gariepy told the class, and Lilli got right to work. Within seconds she’d mastered the task, pulling aside two sets of six beads on the rekenrek’s bars and proudly holding up a white board with “6 + 6” inscribed on it.

“I did six plus six for 12, because if I did five plus five, that’s 10, and I’d have two extras. Plus two would be six for each, so I did six plus six equals 12,” she said.

The rekenrek “makes math a lot easier than having to (count) with your hands,” said Lilli.

Elsewhere in the room, Parker Brown and Finley Hartman used counting blocks in a dice-based race to 100.

“You try to roll the dice — like, I got a six,” Parker said, “and you’re trying to get as many as you can to get to 100.”

Dice rolls correspond with multicolored blocks, which students use in a bingo-like fashion to fill up numbered spots on a laminated sheet.

“It’s fun to me,” Parker said, adding as if in passing that “it does kind of teach me math.”

Finley delighted in the game, but the second-grader said he longs for more formidable mathematical tasks.

“Sometimes I don’t really want to play with different math stuff,” he said.

“Are you saying you want something harder?” asked Parker.

“Yeah,” Finley answered. “I like harder sometimes. And more challenging.”

Lucky for Finley, math manipulatives are used at every grade level, so more challenging activities are ahead.

‘If students can touch and feel and use objects in learning math, they’ll retain better. Students don’t understand … until they can play very intentionally.’

— Maggie Thelen, director of mathematics, innovation and accountability

A Natural Progression

While students like Finley might be ready for what’s next, it’s important for young learners to ease into it and learn math in a tangible way before diving into more complex concepts, Gariepy said.

Mathematical understanding starts with the concrete. Then comes representational, followed by abstract, she said, stressing that most of her second-graders are still in the concrete phase.

“Some kids just naturally see it once and can jump to the abstract,” she said. “They wouldn’t necessarily need to build it every single time, but you naturally have to go through that way. Having the concrete phase for all of them helps them move from seeing to representation to the abstracts.”

Having the hands-on learning aids, she said, is a major asset for students.

“I feel like the manipulatives help translate it and make it tangible,” said Gariepy. “It keeps them engaged.”

Thelen sang the REF’s praises for keeping manipulatives in students’ hands.

“REF has been amazing in making sure that they’re supporting the math initiatives that we have in the district,” Thelen said. “They were really instrumental in purchasing manipulatives, especially at the elementary and middle-school level.”

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Riley Kelley
Riley Kelley is a reporter covering Cedar Springs, Grand Rapids, East Grand Rapids and Sparta school districts. An award-winning journalist, Riley spent eight years with the Ludington Daily News, reporting, copy editing, paginating and acting as editor for its weekly entertainment section. He also contributed to LDN’s sister publications, Oceana’s Herald-Journal and the White Lake Beacon. His reporting on issues in education and government has earned accolades from the Michigan Press Association and Michigan Associated Press Media Editors. Riley’s early work in journalism included a stint as an on-air news reporter for WMOM Radio, and work on the editorial staff of various student publications. Riley is a graduate of Grand Valley State University. He originally hails from western Washington.

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