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Teaching the hardest-to-learn math concepts

What are the concepts within core math topics that students struggle to understand in particular?

Under the direction of Melendy Lovett, president of education technology for Texas Instruments, that was the question TI recently set out to answer.

The company partnered with Gail Burrill, an instructor in the department of teacher education at Michigan State University, and Thomas Dick, a professor of mathematics and coordinator of collegiate mathematics education at Oregon State University, to find out which math topics students traditionally struggle with more than others.

Burrill and her team of researchers at Michigan State, and Dick and his team of researchers at Oregon State, examined all of the high-stakes assessments they could find in all 50 states and looked at how well students performed on each individual item.

“We tried to categorize items in terms of whether students were succeeding, and we looked to see, across the space, if there were clusters [of difficulty] around the same mathematical topic,” Burrill said.

Algebra is one common area of difficulty, and Burrill said it was clear that students struggled with the notion of equivalents, equivalent expressions, and other algebraic concepts.

The researchers weren’t able to do a full item analysis for every state, but for those states that made performance data available for each individual test item, Burrill and Dick said they saw a common pattern of math struggles emerge.

“The research we did really was around trying to get a better handle on what were those problem topics that kids were having difficulty with,” said Dick. He noted that the research “set the stage for us to think [of] ways that we could use [the TI-Nspire] to target these topics.”

Based on what they learned, Burrill and Dick—who both are project researchers and academic advisors for TI’s Math Nspired initiative—brainstormed ways of using the TI technology to help students master these hard-to-teach concepts.

The researchers brought their ideas back to Lovett at TI. The company gathered a group of educators to evaluate these prototypes, and the educators, researchers, and TI team members shared their thoughts on addressing tough-to-teach areas using the TI-Nspire system and the prototypes.

“One of the things we’ve been thinking about is that technology serves two roles. It serves as a mechanism for doing the operations, performing the calculations, and freeing up kids to think about what is actually happening mathematically,” Burrill said. “Its other role is to develop understanding. We really focused more on developing understanding—not ignoring its ability to do things, but we were really trying to help address the [mental hurdles to understanding] that surfaced in the tough-to-teach, tough-to-learn areas.”

Dick said that because the TI-Nspire lets students play with equations and see corresponding changes immediately, it opens up a chance for teachers to ask students not just what happens, but why—and students can explore the math however they please.
“To us, that’s what was so exciting,” he said. “It really opened up a lot more opportunities. You could still use it as your workhorse, but it also revealed a chance to design some action-consequence environments: Students can take a purposeful action and immediately see the consequence. There are lots more chances to ask ‘why’ questions.”

Burrill added: “The really important thing is that every student is engaged in thinking about those ‘why’ questions. They’re not observing someone else do it, they’re not listening to someone tell them what is happening, they’re actually engaged in it, in an interactive math classroom having conversations with each other and with the teacher about what might be causing the consequences and how they might think harder about the mathematics.”

The researchers’ work is reflected in many of the resources contained in TI’s Math Nspired (, an online collection of classroom-ready lessons that address these tough-to-teach concepts using the TI-Nspire system.

Burrill said interactivity in math classrooms makes children more visible to teachers—they can’t hide their written work under their hands and can’t avoid eye contact if a teacher has a classroom system that displays every child’s screen and work on a master computer or unit. And because teachers have that access, they can help students who might not grasp a specific topic in a more sensitive way.

“I think, with teachers in general, the approach has resonated,” said Dick. “Teachers are always looking for an alternative way to get through to kids. One approach might work for the vast majority of the class, but you want to reach everyone in the class—so having some alternatives is what’s neat about having these explorations.”


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