7 Research-Based Math Interventions for Elementary Students

As elementary teachers, we try to provide our students with a sense of belonging to a classroom community. But for some students, whole-class lessons might go too quickly for them, or after answering a few questions incorrectly, they might refuse to answer any questions at all.

That would be a shame! Not only because children deserve to feel a sense of belonging in a place where they spend nearly a third of their lives, but also because discussing their reasoning and receiving prompt feedback is exactly how they will learn. As teachers, it is our duty to identify students at risk of not meeting grade-level expectations and providing increasing levels of intensity of instruction through intervention. This article walks through a variety of research-based math interventions for elementary students.

What is math intervention?

Math intervention is a type of instruction that uses an evidence-based curriculum with students identified as being behind academically. Students are usually identified for intervention through screening assessments that compare their performance at a certain point in the school year to their expected level of performance at that time. Students who receive math intervention perform one or more grade levels below their expected levels of performance.

Response to intervention, or RTI, is a framework that was created to help identify students at risk of academic failure and give them interventions, monitor progress, and gather data in case special education referrals are needed. RTI math support is, in general, comparable to RTI support in all subjects.

• Tier 1 instruction is whole-class instruction using a core curriculum. Interventions that occur at this level are generally because most of the class needs intervention on a given skill, usually a review of a prerequisite skill or a reteaching at the end of a topic.
• Tier 2 intervention is generally focused on a previously learned skill and taught in a small-group setting.
• Tier 3 instruction is provided beyond Tiers 1 and 2 to increase the intensity of intervention through more instruction time, more frequent intervention, a smaller group setting, or 1-to-1 teacher-led instruction.
• If a student requires more support than what Tier 3 provides, they may be considered for a special education evaluation, with the consent of a family member.

Math skills to target in primary grades intervention

In primary grades, we want to teach young learners to view the world through a mathematical lens. With limited time for intervention in K–2, intervention that exclusively focuses on the properties of whole numbers and operations will build the necessary foundation to develop understanding of more complicated skills and procedures. 

While we are likely teaching skills at a developmental progression, integrating this type of instruction into everyday activities can give your learners additional opportunities to see math as a tool to make sense of the world.

Math skills to target in upper elementary intervention

As students progress in elementary school, analyze screening data alongside state testing results to determine students who are at risk and therefore candidates for intervention in math. 

Start by determining if your intervention students need additional instruction in properties and operations with whole numbers. Once they have a deep enough understanding in whole numbers, intervention for upper elementary students can focus on helping them conceptualize fractions as numbers, fraction equivalents, and operations on fractions. 

Best practices in math intervention

It’s important to recognize that there is consensus on what constitute best practices in intervention for mathematics intervention. The following practices should be implemented school- and district-wide. 

District-wide screening

For educational intervention to work most effectively, it should rely on data to identify student needs. Selecting a screening tool that is valid and reliable (such as NWEA’s MAP Growth universal screener), then using the tool across all schools in a district can provide consistent opportunities to analyze the data and connect it to instruction.

Explicit systematic instruction

There is strong evidence supporting an explicit and systematic approach to mathematical intervention instruction. For the instruction to be systematic, the skills taught should build on each other gradually and logically. For example, teach place value before multi-digit addition.

According to the National Mathematics Advisory Panel, explicit instruction should include the following:

• Teacher modeling of solving several examples of a target problem type, both easy and difficult
• “Extensive” practice of newly acquired skills and strategies
• Opportunities for students to think aloud, often in collaboration or discussion with others
• Many opportunities for feedback

Progress monitoring

Through ongoing progress monitoring, we can determine if we are targeting the correct skills for specific students, regroup students as needed, and evaluate teaching methods. Progress monitoring can be accomplished through observation and checklists, weekly quizzes, and/or exit tickets. Aim to make progress monitoring consistent, using the same amount of problems at consistent intervals. Progress monitoring should occur at least once a month but can be weekly or daily.

Consistency across grade levels

In order to avoid confusion, especially with learners who need additional support with fundamental concepts, consistency of instruction is key. Strive to use the same curriculum across grade levels and teach it to fidelity to ensure consistency of mathematical terminology, instruction, and tools.

Opportunities to respond

In addition to targeting specific skills for specific learners, interventions should be kept small to give students more opportunities to respond, interact with the teacher, and receive corrective feedback. This is especially critical if a student needs a more intensive intervention. Look for ways to give students more opportunities to respond. Generally, it would be by increasing time in intervention or providing intervention in smaller groups or one-to-one.

What the research says: 7 elementary math intervention strategies

The Institute of Education Sciences has for years put out teaching practice guides that are based on a meta-analysis of a swath of recent research. The recommendations in the guide therefore come from multiple studies and are credible findings because they can be replicated across different circumstances. The math intervention strategies suggested in this article are largely based on the recommendations from a recent practice guide of the research supporting elementary school math interventions.

Strategy 1: Review and integrate previous skills

Have you noticed that some students can solve the same type of problem over and over again, but when presented outside of the intervention they are unsure of what strategy to use?

The likely culprit is that students aren’t getting enough practice distinguishing between problem types. By integrating previously-learned content into activities with current skills, learners will practice this distinction. They will become less likely to overgeneralize when to apply certain strategies, deepen their conceptual understanding of the earlier content, and recall procedures.

How to use this strategy:

• Integrate previously-learned content into activities on the current skill. For example: If the current skill is subtraction across zeros, include subtraction problems without zeros.
• Throughout an intervention, ask students to explain previously-learned skills.
• Include a cumulative review of related skills at the end of each lesson.

Strategy 2: Use accessible numbers 

In order to gradually develop a new mathematical concept, use numbers that are familiar and accessible to learners when introducing the new idea. This strategy ensures that students are focusing more on the new concept than on time-consuming or confusing procedures. For example, when introducing single-digit division, you might start by dividing by 2 and 5 since students are more likely to have those multiplication facts memorized. Once students have demonstrated understanding of the concept of division, then move on to numbers they might be less likely to have memorized like 6, 7, and 8.

Strategy 3: Use worked-out examples to highlight subtasks

Presenting fully or partially worked-out examples can provide students with experiences that will get them more comfortable with prerequisite material before tackling a more complex task. In systematic instruction, we gradually make our way to complex mathematical ideas by focusing on smaller tasks and building up to more complicated problems or concepts.

To apply this strategy:

1. Select a problem that your students are building toward solving.
2. Present a similar worked-out example problem with familiar numbers.
3. Explain the reasoning for each step of the solution. The reasoning should be within reach, using skills students already have.
4. Present a new problem and ask guiding questions to have the students explain each step to the solution.
5. Have students solve similar problems with a partner, listen to conversations, and provide corrective feedback as needed.
6. Integrate more difficult problems into later lessons to allow students to hone this skill and solve more complex problems.

Strategy 4: Provide immediate, supportive feedback

When elementary students receive intervention support, it is to understand the skills required to meet the major standards at their grade level. It is essential that students work closely with a teacher who can provide supportive feedback, identify and address misconceptions, and ask and answer questions along the way.

One recommendation for elementary students is to use visual and verbal supports. These could take the form of guiding questions, verbal prompts, gestures, or visual representations (which are especially impactful as Tier 2 support), either as hints or to connect the abstract to the concrete. For example, you might point to a visual representation on an anchor chart or illustrate a problem using a drawing or diagram.

Educational technology can do a good job with providing interventions tailored to individual students’ needs and providing immediate corrective feedback. The most helpful math intervention programs include both visual and verbal support, although teachers should always monitor student progress to ensure they are making expected progress.

Strategy 5: Model using precise mathematical language

Sometimes, coming up with fun, colloquial names for math ideas can cause confusion in the long run. Consistency matters. Just think about the different names students might hear for regrouping, such as “carrying” or “borrowing.” When a student comes across regrouping in a later grade, many will be able to make the connection, but some—especially those needing the most support—may not.

To put this strategy into practice:

• Always model using precise and accurate mathematical terminology. It could take multiple lessons before students begin to use the language correctly.
• If you realize you’ve used a more informal word, just throw in the correct math term right after.
• As a school or district, work across grade levels to set math vocabulary norms. You can start with the glossary of your current math curriculum.
• Make sure to use student-friendly definitions with previously-learned math terms. The definition of “equal” might look different in second grade than it looks in fifth grade.
• Offer sentence starters, stems, and frames to provide structure for student explanations.

When students consistently hear math terms used repeatedly by their teachers and peers, they will begin to use these terms as they discuss and write about their own ideas and reasoning. 

Strategy 6: Use timed activities to build fluency

It is important to note that timed tests do not assess fluency and can even be harmful for many students’ math development. However, the evidence consistently shows that short timed activities with low stakes can build fluency, especially in the elementary grades. See, for example, studies involving students in kindergarten, second grade, and sixth grade. While repeatedly using the strategy of “drill-and-kill” is rightfully maligned, the full story is more complex. In order to build fluency, students need to regularly practice quick fact retrieval.

In my first year teaching, I followed my math curriculum to a T. We focused on using properties to figure out the products of one-digit numbers. My students could choose the strategies that made the most sense to them and were never pressured to retrieve facts quickly. Even if there was a test, they essentially had unlimited time to figure out the answers.

Cut to the next year: I’m moved to 4th grade and teaching double-digit multiplication to many of the same students, who were still working through models to figure out basic multiplication facts. Since they kept being pulled away from the main problem they were trying to solve, their lack of fact fluency was increasing their cognitive load.

At that point I decided we were going back to basics, and so I included timed fluency activities to the beginning of each lesson. I didn’t want it to be strict drill-and kill, so we made flash card games and used technology. This is another area where technology can be helpful. Students can practice basic arithmetic facts using online games with immediate feedback, and teachers can receive data on what skills students most need help with. Students are also motivated by seeing their own progress with facts—but be careful not to make it a competition between students!

In general, the goal of timed fact retrieval activities should be to accurately solve as many problems as possible in the allotted time. Remind students that accuracy is more important than completing all the problems. 

Strategy 7: Number lines

For students having trouble with math, come back repeatedly to the representation of a number line. Of all models, the number line is unique in how flexibly it represents different types of numbers in the number system. Whole numbers, fractions (an especially important topic to cover with intervention students), decimals, and negative numbers can all be placed together in a single representation. Number lines also help students conceptualize the relative sizes of numbers, model operations, and prepare for more advanced work in the coordinate plane, which is essentially just two number lines placed orthogonal to one another.

Students can be introduced to number lines with concrete representations like number paths, where whole numbers are laid out one by one along a line. You can also teach students how to build their own number lines using manipulatives. Then as they get more adept at concrete representations of the number line, move them to more abstract visual representations where only certain numbers need to be called out on the line and distances do not have to always be to scale. Using number lines consistently throughout interventions can lead to an internalized model that will help them solve a huge range of math problems. 

What will intervention look like in your classroom?

So, what will intervention look like with your current group of students? Start with the data and figure out which skills to target with your students. You will probably want to focus on whole numbers and concrete representations in primary grades and move up to the more advanced fractions when considering math intervention strategies for elementary students in upper grades. Make sure to repeatedly use number lines to introduce and reinforce concepts across all grades. Remember that, in addition to your intervention time, these activities can be woven into the day to help students see that math can do more than help them solve specific problems, it can help them understand the world.

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Looking to unlock mathematical learning in the students who need it most? Explore our math intervention programs for students in Grades 3–12.