As students move up through the grades in elementary and middle school, math marches relentlessly forward—whether they’re ready or not.
Math is a hierarchical field, building sequentially on prior concepts. Likewise, math standards in each grade presume that students have mastered the skills that came before in previous grades, and often require that kids apply that knowledge to tackle what they’re learning now.
But many older students have significant holes in their foundational math knowledge, presenting teachers with a complex challenge: How can they help students learn new material and shore up gaps at the same time?
A new special report from Education Week explores this problem and its possible solutions.
Most elementary schools have dedicated time in the day for math intervention and staff trained to support students who struggle. But middle and high schools often don’t have those same resources or scheduling frameworks, experts said.
Education Week spoke with principals, teachers, and instructional leaders in one state who are trying to solve this puzzle—carving out time in the school day to reteach foundational math skills, and making sure that what students are learning in this extra help period lines up with grade-level content in their main math classes.
Read on for two different models of what math support can look like in upper grades.
Tutoring to address gaps—and move forward
Math class can move fast. But taking a second, slower pass at the day’s lesson can often pinpoint the root of students’ misunderstandings, said Jamie Rhinesmith, the math learning design team leader with TutorND, an Indiana tutoring partnership run out of the University of Notre Dame.
Through the program, Notre Dame students work one-on-one with elementary and middle schoolers in the South Bend district and other schools and community organizations in the area.
Tutors meet with students during time set aside in the school day for independent practice. Sessions focus on grade-level content that students are learning in their math classrooms, but intentionally work in time for practice with related foundational skills, Rhinesmith said. It’s important to strike the right balance, she added.
“If we just address the gaps, then these students are going to fall even farther behind, and it’s going to be harder for them to catch up,” she said.
Recently in a 7th grade classroom, students were working on finding the slope of a line. Some students struggled working with negatives in those equations, so tutors revisited multiplying and dividing negative numbers.
“It was a quick, ‘Let’s just readdress this, and remind ourselves what it means,’” Rhinesmith said.
Tutoring is most effective when it’s connected to classroom instruction in this way, researchers say.
“It’s OK that this gap is not mastered in this one lesson,” Rhinesmith continued. “We’re going to keep touching on it, and that repetition, that spiraling is going to keep building it.”
A math ‘lab’ class focuses on foundational skills
At Adams High School in South Bend, incoming 9th graders who are struggling with math take two classes: Algebra 1, and a support class called algebra lab.
This approach, referred to as “double-dose” algebra, has been shown to increase student test scores and lead to long-term gains in high school graduation rates and college enrollment. But it comes with tradeoffs, too, reducing time in students’ schedules for other classes like electives.
For James Seitz, Adams High School’s principal, requiring the class for students with the greatest math needs felt necessary. “We’ve had to break down going back to adding and subtracting integers, fractions,” he said. “If you don’t understand how to solve [equations with] integers, it’s really hard to understand anything in math.”
The lab classes focus on basic skills, like working with negative numbers, solving equations with decimals and fractions, and reading graphs, said Joe Hardman, one of the algebra lab class teachers at Adams.
“I always try to talk about money to the kids, because they understand money,” Hardman said. Teaching about ratios and percentages through dollars and cents helps make the abstract concepts feel more real, he said.
Hardman knows that many students won’t have mastered 9th grade Algebra 1 by the end of the year. Some students enter the lab classes four or more grade levels behind, he said.
“When we build our students up one to two grade levels, we don’t consider ourselves a failure,” he said.
Most of Hardman’s students start the year not liking math. “The biggest thing I battle is their confidence level,” he said.
One of his main goals is to get students feeling comfortable and successful in class—a shift in attitude that encourages better academic habits, like completing homework or studying for tests, he said.
“As soon as they can build a little confidence in themselves,” said Hardman, “then all of the sudden it can jump really big and really quick.”
