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How to Develop an Effective Math Intervention Program

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How to Develop an Effective Math Intervention Program

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Engaging students in thought-provoking activities encourages them to grow in their mathematical understanding and identity.

Achieving equitable mathematics education has been long debated, even more so after recent learning disruptions, with many sites and districts having much-needed conversations about mathematics intervention to address learning disparities. However, it's important to keep in mind what we know about the benefits of detracking, which has been at the forefront of many of these equity conversations. The National Council of Teachers of Mathematics suggests that moving forward, it's important to identify students for additional intervention that doesn't replace their core math class, sometimes referred to as math support classes or double dose math classes.

I believe that these classes can be an effective solution if they're designed effectively and supported adequately. Over the last several years, I've seen 88 percent of students in my math support classes pass and excel in their core math class, which ensures that they stay on track to graduate high school or move on to higher education.

The key to an effective math intervention class is to customize the curriculum to help students succeed in their core math class and grow their mathematical understanding and identity. With many sites considering this model, I have some suggestions to help ensure its success.

Preteach Big Ideas and Priority Content

One of the most impactful components of math intervention curriculum is preteaching priority content and big ideas before the core math class introduces the concept. It's important to focus on priority content to allow time for students to explore, use manipulatives, build upon prior knowledge, make connections, fill in gaps if needed, gain conceptual understanding, work toward procedural fluency, and gain a deep understanding of these concepts.

I work closely with the core math class teachers to coordinate calendars and plan my math support class curriculum so that big ideas are taught two to three weeks before they're taught in the core math class. Preteaching provides a boost in student confidence as well as engagement, because students are seen as the experts in their core math class and can even be called upon to help other students. Another benefit is that preteaching promotes retention. Students learn a concept on a deep level, then relearn and review it several weeks later. My students often say that this is their favorite aspect of math support because it makes them feel more confident in math.

Provide Just-in-Time Intervention to Fill in Gaps

Rather than focusing an intervention class solely on remediation, it's important to provide targeted intervention ifit is needed and when it is needed. Teachers may find that students have gaps in prior knowledge that prevent them from accessing the big ideas of the grade-level content, sometimes referred to as load-bearing walls. They can and should be addressed through thoughtfully built-in interventions that build into the grade-level content, because it's effective to teach math as a series of connections that activate and strengthen prior knowledge.

For example, two to three weeks before I teach a concept, I will start giving preview warm-ups exposing students to the concept of a load-bearing prerequisite skill. It could be an open-ended kind of question just to see how much students know, how much vocabulary they use, etc. From these formative preassessments, I can usually gather information about what students know and are able to do and where they might have gaps.

While planning these interventions, it's important for teachers to understand and identify the load-bearing walls of big ideas, anticipate student knowledge, and formatively assess students to gather information about their gaps as well as strengths. This information can help teachers design the appropriate intervention that will build on student strength and address the knowledge and skills they need to access content.

One of my favorite strategies is using my two daily warm-up problems, the " Review and Preview," which can serve as formative assessments, activation of prior knowledge, or mini-lessons, depending on the day and need. Just-in-time interventions allow teachers to address gaps and also propel students forward in their understanding of grade-level content.

Embed Accessible, Open-Ended Activities

Students who have historically struggled in math often struggle with number sense; a low self-esteem in math; and not much mathematical identity, or belief in themselves as successful math learners, which is why it is important to incorporate accessible activities in math intervention classes.

Some examples of these activities include Which One Doesn't Belong, Notice and Wonder, Number Talks, and Dot Talks. These kinds of activities promote engagement and send the message that everyone's ideas are important. They also put an emphasis on strategy and explanation, which helps students develop important skills of forming arguments and critiquing the reasoning of others.

These activities can blend easily into daily routines and can take as little as 3 minutes. In some cases, they can also be used as formative assessments to provide teachers with valuable information about what students know about a concept.

Promote Learning Goals and Self-Advocacy

In a math intervention class, it is important to structure learning around goals while also building in routines for self-assessment and self-advocacy. Routines, structure, and organization provide predictability that lowers student anxiety and increases comfort and engagement by freeing up students' minds to do the heavy lifting of mathematical thinking. Learning goals can be communicated to students regularly, and teachers can consistently ask students to reflect on their understanding, which helps them to identify areas where they can ask for help.

Other tools, such as daily exit tickets and a set weekly schedule focused around specific learning targets, can provide even more clarity. I do this by providing students with a detailed graphic organizer that states learning goals, asks reflection questions, and requires students to advocate for themselves. My students and I meet regularly so that they can self-assess and communicate their personal goals about grades, and I also coach them to advocate for themselves with their core math teacher. Providing students with this structure helps them develop these skills that they can use long after they leave the class.

In my experience, implementing these suggested structures and strategies, along with resources that I've developed, has helped make the math intervention programs effective in boosting student achievement. Try them out in your school to help promote more equitable mathematics teaching for our students.

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How to Develop an Effective Math Intervention Program

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Engaging students in thought-provoking activities encourages them to grow in their mathematical understanding and identity.

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with Mathematics: Intervention

in the Elementary Grades

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Schools Prioritize Reading Intervention. But What About Math?

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Schools Prioritize Reading Intervention. But What About Math?

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Throughout Tiffany Trevenen's more than 30-year career in Moffat County schools in Craig, Colo., she has seen students experience the same math struggles again and again.

"It was very apparent in upper elementary to me that kids did not have number sense," said Trevenen, now a learning coordinator at Sandrock Elementary School in the district, referencing the basic understanding of quantity, magnitude, and arithmetic that lay a foundation for higher order math skills.

"They didn't have a relationship with numbers. I didn't know how to fill those gaps," she said.

Moffat schools have long used screening assessments in reading to catch students who need extra help early on in their elementary years. But they didn't have anything similar for math. "We didn't have the resources, nor the time slots, to do math intervention," Trevenen said.

This year, though, that changed. Administrators purchased intervention materials and put dedicated blocks in the schedule. Now, Trevenen and her colleagues are puzzling over how best to use the time to support students-whether they should work with them in small groups, for example, or when to use tech programs to practice newly learned skills. "We're at the front end of figuring it out," she said.

Math has 'lagged' behind reading in education policy

The tendency for math to take a backseat to reading shows up both in policy and, historically, in public perception.

"Math, on both the assessment side and the intervention side, has always lagged behind reading," said Ben Clarke, a professor of school psychology at the University of Oregon, who studies math assessment and instruction.

"The joke was [President George W.] Bush had his Reading First initiative-and it was reading first, and math at some point in the future," Clarke said, referencing the federal grant program of the early 2000s aimed at raising reading scores. "Ask 100 people on the street what's the most critical skill kids learn in elementary school, 98 of them are going to say reading."

Data confirm that schools are more likely to offer targeted instructional support and intervention in early reading than in math. A 2015 study of 13 states found that while 71 percent of schools had implemented Response to Intervention practices in 1st grade reading, only 35 percent had done so in 1st grade math. (RTI is a tiered system for intervening, giving progressively more intense support to students who struggle with whole-class lessons. Many schools now use multi-tiered systems of supports, or MTSS, which combines academic interventions with social-emotional support.)

But intervening earlier in math isn't just possible, it can also have big effects for students down the line, said Nancy Jordan, a professor of learning sciences at the University of Delaware.

"We do know that these early number abilities are malleable. If children get these interventions, they can improve their number knowledge," she said. "If you don't learn the early number skills, and you're not facile with those, you're going to have trouble learning the higher order skills, because they're so intertwined."

What early math screeners evaluate

To identify which students need more help, schools might use a math screener-a short assessment to determine whether a student is performing at grade level. Most math screeners that students take in kindergarten or 1st grade aim to get a snapshot of students' number sense, said Jordan.

Number sense is a nebulous term, referring at the same time to kids' ability to understand quantity, relate numbers to each other, and perform simple operations like addition and subtraction. Separate tasks can assess these different abilities, researchers say.

For example, a student might be asked to count a set of objects, with their teacher monitoring for certain skills, Jordan said: Can they count in a stable order? Do they count each number once and only once? Do they know that the final number in the set represents the total number of objects? Students might also have to identify a missing number in a sequence, said Clarke.

To test their understanding of magnitude, students would be asked which number is bigger-4 or 6, for instance. Kids might also be asked to compose and decompose numbers, said Clarke, testing their understanding that 5, for example, is made up of 2 and 3. Older students in 1st and 2nd grades would be screened on their fluency with these kinds of addition and subtraction operations, Jordan and Clarke said.

"Young children who have this good number sense and can think about number operations and can add and subtract small quantities ... they tend to do much better in math when they reach 1st grade and beyond, because they have built these fundamental understandings," said Jordan.

Still, screening students for difficulties with these skills is just the starting point, said Clarke. "You have to have that link to intervention, otherwise you're just admiring the problem."

And the tools can be crude: Many label a student with a number, or a color designation-green for on track, yellow for borderline, and red for below grade level. "That's only vaguely helpful," said Mary Pittman, the director of mathematics for TNTP, an organization that consults with schools on teacher training and instructional strategy. "It tells you that you need to figure out what you need to do for that child."

The goal of screening should be to connect kids with these supports, rather than to label them as permanently "behind," said Bailey Cato Czupryk, the senior vice president for research and impact at TNTP. Often, state policy is written to encourage flexible grouping and ensure that students who need additional help aren't missing out on grade-level instruction, "but we don't provide teachers support on how to do it," she said.

How schools are responding to state mandates

"That law puts math on equal footing with reading, where it's saying both are legislatively required, and you have to figure out a way to fit it into your schedule," said Elizabeth Abel, a district elementary math coach in Florida's Hernando County schools and the president of the Florida Council of Teachers of Mathematics.

Before the law passed, Hernando County was already screening students for math difficulties, and relied on several different resources for interventions, Abel said.

Guaranteeing consistent time to provide this additional instruction has been a challenge for some schools, especially if students need support in multiple subjects, Abel said. Some schools in the district are trying to schedule intervention blocks before or after school as a solution.

Abel hopes that a sharper statewide focus on intervention leads to more attention on everyday, whole class math instruction, too. Throughout math classes, teachers should be using the same strategies that research shows support struggling students, she said.

It's a view that Clarke, the University of Oregon professor, holds too.

"The real power of these screening systems ... is they often change core instruction," he said. "Educators start to realize, if 60 percent of our kids are off-track, 70 percent of our kids are off-track-and that's common-we cannot small-group our way out of this issue."

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Schools Prioritize Reading Intervention. But What About Math?

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Early intervention can have large positive effects for students down the line, researchers say.

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Creating Student-Centered Classrooms Using Math Workshop Lempp Tyler

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Dyscalculia and Dyslexia: Reading Disabilities Offer Insights for Math Support

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Dyscalculia and Dyslexia: Reading Disabilities Offer Insights for Math Support

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Dyscalculia and Dyslexia_ Reading Disab...fer Insights for Math Support. - EBSCO

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Curricula are usually structured to deliver content to students in sequential blocks-one concept follows another, and often, previously learned material doesn't resurface until larger assessments at the conclusion of a term.

While this approach might be successful for an immediate understanding of content, research suggests that when students don't intentionally practice recalling and building on recently-learned material over a longer period of time, they often lose that information just as quickly as they learn it.

"Students might learn these skills in the short term, but they often don't transfer this knowledge to their long-term memory," Sara Delano Moore, a former middle school teacher and education consultant, writes in SmartBrief. "Our brains need time to practice the information and to consolidate learning."

To stimulate long-term retention of knowledge, an authoritative review of research spanning hundreds of studies points to the effectiveness of spaced learning, teaching new material in small chunks spread out over time, and frequently revisiting the material after it's taught.

A 2021 study, for example, found significantly improved retention in seventh-grade students who solved 12 math problems spread out across three weeks, when compared with students who solved the same number of problems in a single day. When both groups took the same test one month later, the students who used spaced practice scored 21 percentage points higher.

How frequently should recently-learned material be revisited-and how should teachers do it?

In SmartBrief, Delano Moore says that simple moves, like including several problems from one day's lesson, a few problems from the prior week's work, and two to three problems from topics introduced a month ago, can make a difference. Meanwhile, cognitive psychology researcher Shana Carpenter argues there's no universal schedule. She suggests planning gaps that span days, weeks and months-with more time between sessions when material is already familiar to students, and less time when students are first learning new information.

If you want to use spaced practice in your classroom, here are some strategies to try.

A Holistic Approach

Bill Hinkley, a high school math teacher in Maine, recommends thinking holistically about your curriculum at the start of the year so you can determine how a spaced learning approach can be integrated.

The first step, he writes for Ed Surge, is to identify the foundational material in your curriculum, and instead of teaching it during specific blocks, break it up into smaller chunks that can be taught-and resurfaced-on a spaced out timeline.
Bill Hinkley/EdSurge, Chart: Edutopia
To do this, Hinkley created a chart to visually illustrate his approach to spaced practice for one unit of material in his AP Calculus class. After kicking off with a lecture on the material right before winter break, Hinkley assigned in-class practice, homework, quizzes, and a team project, two weeks later, after break. A unit test followed a week later, and he also included more practice with the material in a mid-year exam.

It's also important to have students engage with material in a variety of learning modalities, according to Hinkley. For instance, he assigned a hands-on project to encourage both in-class and independent work, and replaced his usual mid-unit quiz with a group review exercise designed to be more memorable for students.

When planning out your curriculum, Hinkley recommends trying to answer key questions like:

Which skills from previous units can I integrate into my next unit?

How can I space out the learning in this unit to combat the compartmentalization often inherent to curriculums?

How can I create opportunities for students to think about previously learned topics outside of the classroom and during homework time?

Spaced Quizzes

Quizzes, especially low-stakes ones, are not just a tool for quick assessment-they can also be a powerful way to implement spaced learning, write psychology researchers and co-founders of the Learning Scientists project Yana Weinstein and Megan A. Smith. "[T]aking a quiz (or doing any activity that forces you to bring information to mind from memory) actually causes learning," the authors note.

The "power of low-stakes practice tests" is further confirmed in 2022 by researchers John Dunlosky and Shana Carpenter, who found that asking students to review previously learned material through activities like quizzes can "generate memory improvements that persist for 9 months," while the positive effects of retrieval "over multiple sessions can last for at least 8 years."

Testing can take the form of ungraded multiple choice, free-recall, or short-answer quizzes-the idea is to create easy, low-stakes ways to prompt students to recall and apply concepts they've already learned.

Former middle school history teacher Patrice Bain writes that mini-quizzes that included a mix of new and old material helped increase her students' retention so much that she replaced homework assignments with them. The key, she said, was to keep them truly low-stakes-she rarely graded the quizzes, and if she did they were worth very few points. "I put them on two-inch by three-inch pieces of paper. They're very non-threatening. Five quick questions," told the Cult of Pedagogy podcast.

If you do plan to grade quizzes, Weinstein and Smith suggest having students take them on free self-scoring apps, like Socrative, Memrise, or Google Forms that can provide you with an immediate snapshot of where your students stand.

Spaced In-Class Review

In-class review works hand-in-hand with low-stakes quizzing to prompt students to recall and apply older material over time. For example, Bain often incorporated "blasts from the past" into her new lectures, in addition to her daily mini-quizzes. "When I was talking about, for example, Ancient Egypt, I could say, 'Oh, remember when we talked about Mesopotamia? What, what was important about that river?'" she told Cult of Pedagogy.

Having students explain material to themselves or peers also can be an effective form of review. Weinstein and Smith suggest having students write a summary of the key points from last week's class as a quick in-class activity. To build in more complexity, students can check their notes and revise their key points. It's important that students eventually write these summaries in their own words-from memory, if possible-which increases retrieval and results in stronger retention.

Similarly, you can try starting your class by pairing students for 90 seconds of rapid review: Have them summarize what they learned in the prior class, then present to the larger group-or use think-pair-share activities to get students processing key facts and ideas from a topic previously covered in class, then pair up to compare notes and look for gaps in their learning.

Cognitive scientist Pooja Agarwal, who joined Bain on The Cult of Pedagogy to discuss the book they co-authored, warns teachers to be prepared for discomfort when students struggle to remember material and feel frustrated during this process. That's a sign your spaced approach is working: "Students are going to forget," she says. "But it's important for students to forget. Because with spacing, they bring it back up, and that then solidifies that learning moving forward."

A Spaced Approach to Studying

Teaching students how to incorporate spaced learning into their study routines at home can help them take advantage of its benefits themselves.

Chicago-based educator and neuroscientist Edward Kang suggests introducing students to a specific approach to working with flashcards that uses spacing to structure retrieval practice. "The cards they're able to answer immediately should be placed in a pile to review three days later; those answered with some difficulty should be reviewed two days later; and those that they answered incorrectly should be reviewed the next day," he writes.

To help students integrate spaced learning into their study habits, AP psychology teacher Blake Harvard uses a class activity to show its effectiveness. First he creates a content-specific chart to help students organize information about a concept, for example, Piaget's Theory of Cognitive Development.

Students fill in the chart using what they remember from prior class work-without using their notes-and highlight those answers in yellow. Next, they use their notes to correct the chart, highlighting those additions in orange. Finally, they ask peers and skim textbooks to fill in any remaining blanks, highlighting that in blue.

A few days later, Harvard distributes new, blank charts, and the students follow the same process. A week later, he repeats the activity again and has students review all their charts and pull out insights. "Most will see an increase in yellow highlighting, indicating they've remembered more information from day to day, or from retrieval to retrieval," he writes.

To emphasize the usefulness of this strategy-and motivate students to make use of it on their own-Harvard asks students to discuss questions like: "Did this take more time than cramming?" and "Was it more effective at showing you what you know and don't know?"

Responses are generated by artificial intelligence. AI can make mistakes.

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How to Incorporate 'Spaced Learning' Into Your Lesson Plans

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This powerful, evidence-based strategy works across subjects and grade levels-but you have to plan for it.

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Math Interventions Across Educational Settings: ECE to HS

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The 5 Strands of Mathematical Proficiency

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What is Mathematical Proficiency? How do you define mathematical proficiency? Had I been asked this question early in my teaching career, I might have