Effective math interventions are essential for helping learners build foundational skills, close gaps, and develop confidence in their mathematical thinking. With so many instructional approaches out there, it’s essential to focus on strategies grounded in research to make the most of valuable time and effort. This article is written for math teachers, interventionists, instructional coaches, and curriculum coordinators dedicated to implementing what works: evidence-based practices proven to support students who struggle.
What is Math Intervention and Why Does it Matter?
Math intervention refers to targeted approaches that help students who are struggling in one or more areas of mathematics reach grade-level proficiency. Intervention can happen at all tier levels and the ideas in this blog are applicable across all tiers.
As educators, one of our fundamental motivations is seeing students achieve. Effective math intervention matters because it provides structured support for students to reach and exceed grade-level expectations. When we successfully equip students to meet these benchmarks, we significantly increase their likelihood of graduation and pursuit of higher education—outcomes we all aspire to see in our students.
Evidence-Based Intervention Practices are Essential
Not all math interventions are created equal! In today's diverse classrooms, math educators face the persistent challenge of helping students build both skills and confidence. With numerous instructional approaches available, focusing on evidence-based practices—approaches proven by research to make a meaningful difference—becomes essential. These methods not only maximize our limited time and resources but ensure every student has a genuine opportunity to succeed in mathematics.
There are so many opinions about everything these days, the question is How do we know what’s effective?. Too often, well-intended classroom activities yield minimal results in terms of actual student achievement. Many educators default to approaches learned from colleagues or simply continue practices that have "always been done." Fortunately, we don’t have to leave things to chance, we have a wealth of research that points us to the most effective strategies. However, research clearly demonstrates that certain classroom practices deliver substantially better outcomes for learners.
As educators committed to student success, we understand the frustration of watching capable students struggle with mathematical concepts. To address this challenge, let’s explore three evidence-based practices that research consistently shows support students who struggle in math:
- Explicit and systematic instruction
- Visual representations and concrete models
- Metacognitive strategies
Explicit, Systematic Instruction
While this approach forms the cornerstone of effective day-to-day classroom practice, it's sometimes undervalued in math intervention and small-group settings.
The Research
- "An influential meta-analysis of mathematics interventions indicated that explicit instruction led to large improvements in student mathematics skills." (Gersten, et al., 2009)
- "The inclusion of explicit instruction in core mathematics instruction for kindergarten students improved their achievement." (Doabler, et al., 2015)
John Hattie's comprehensive meta-analysis—the largest and most thorough examination of effective classroom practices—found this instructional approach has an exceptionally high impact on student achievement. Implementing explicit, systematic instruction with students who need intervention dramatically improves their learning trajectory and mathematical progress.
Best Practices
Explicit, systematic instruction involves teaching concepts with clarity and precision, ensuring students understand exactly what is expected of them. This approach should:
- Follow a carefully planned sequence with progressive complexity
- Present material in a logical, coherent manner
- Connect students' prior knowledge to new learning
- Include teacher modeling through multiple examples
- Incorporate formative assessment to guide instruction
- Balance teacher-guided practice with independent application
Concrete Models and Visual Representation
Mathematics can be highly abstract, involving symbols and concepts that may seem disconnected from students' everyday experiences. Since children are naturally concrete thinkers who learn best through direct, hands-on experiences, the use of visual and concrete representations becomes particularly crucial for students who struggle in math.
The progression from concrete manipulatives to visual representations before abstract symbols bridges a critical gap in mathematical understanding. Research evidence is compelling.
The Research
- The Concrete–Representational–Abstract (CRA) instructional approach has been shown to enhance math achievement and conceptual understanding among elementary students with learning difficulties. By moving from physical manipulatives to visual models and then to abstract symbols, CRA helps learners build deep, transferable understanding. (Agrawal & Morin, 2016)
- Using concrete manipulatives improves student understanding and retention of mathematical concepts, especially for students who struggle or have learning disabilities. Manipulatives support conceptual understanding and promote student engagement. (Carbonneau, Marley, & Selig, 2013)
- "Students who use visual representations to solve word problems are more likely to solve the problems accurately. This was equally true for students with learning disabilities, low-achieving students, and average-achieving students." (Krawec, 2014)
Best Practices
Visual representations that significantly support learners include:
- Number lines and number paths
- Graphic organizers for problem-solving
- Strip diagrams and bar models
- Visual fraction models
- Arrays and area models for multiplication
Students who struggle in math often need more than visual representations and this is where concrete models (manipulatives) come in. The use of manipulatives for these learners, provides tactile learning experiences that research shows improve conceptual understanding. Providing access to concrete materials while students are working independently also serves as a support that will help them complete their meaningful practice tasks where they are required to show their learning or understanding in abstract form.
Effective manipulatives that allow students to physically interact with mathematical relationships include:
- Base-ten blocks
- Fraction tiles
- Algebra tiles
- Geometric models
Metacognitive Strategies
In simple terms, metacognition is thinking about and becoming aware of your thoughts and thought processes. This is particularly important for math students with limited problem-solving approaches. Evidence of strong metacognitive skills includes the ability to plan appropriate solution pathways, self-monitor progress during problem-solving, and even the willingness and confidence to adjust strategies where necessary but being able to do all these things requires significant support and training.
As an educator you may have experienced that students who struggle in mathematics, often have very limited strategies to solve problems and they often attempt to apply these same limited set of strategies to all problems they encounter. Teaching students to develop their metacognitive abilities, equips them with a variety of tools (strategies or approaches) as well as the decision-making skills to choose the most appropriate methods for the variety of problems they may need to solve in math.
Developing strong metacognition involves two key components:
- Providing students with specific cognitive strategies (the "what" of problem-solving)
- Supporting students to develop metacognitive awareness (the "when" and "why" of strategy selection)
Combining these two components on a consistent basis will serve as an effective way to improve students' mathematical thinking and their ability to approach tasks in an appropriate way.
Cognitive Strategies
Effective cognitive strategies for math learners include:
- Self-questioning techniques ("What is this problem asking me to find?")
- Problem-solving frameworks (Read, Plan, Solve, Check)
- Visual organization methods for multi-step problems
- Self-monitoring checklists for procedural accuracy
- Error analysis protocols that encourage reflection
Metacognitive Awareness
One component of helping students to develop their metacognition is teaching them how to use self-talk. They learn to coach themselves through tasks by asking questions of themselves. Once students have the cognitive skills necessary, teaching metacognition is easily implemented by teachers as this can be woven into the explicit instruction they provide. Simply by modeling these types of questions and seeing this modeled repeatedly, students can learn to develop their metacognition.
Effective strategies to build metacognitive awareness include prompts such as:
- What is this asking me to do?
- Are there any parts of the task I don’t fully understand yet?
- What is the important information?
- Where would be a good place to start?
- Can I represent this problem using manipulatives or visually?
Bringing It Together: A Unified Approach
As mathematics educators committed to helping all students, including those who struggle, we owe it to our learners to implement approaches with proven track records of success. The research is clear: evidence-based practices like explicit instruction, visual and concrete representations, and metacognitive strategies yield significantly better results than intuition-based or trend-driven approaches.
The beauty of these research-validated methods is that they complement and reinforce one another. When thoughtfully integrated into a cohesive intervention plan, they address multiple learning pathways simultaneously, building procedural fluency alongside conceptual understanding while developing students' mathematical confidence.
As you plan your next math intervention lesson or small group session, think about how you could deliberately incorporate these strategies into your approach. By consistently applying these evidence-based practices, you'll create learning experiences that not only remediate current gaps but build enduring mathematical understanding.
It’s so important that students who struggle get to experience feeling successful in math, and so using math intervention approaches that are proven to work will position students for success. When we ground our practice in research evidence rather than trends or assumptions, we maximize our impact and truly fulfill our mission of helping every student experience mathematical success.
Citations
Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084
Doabler, C. T., Baker, S. K., Kosty, D., Smolkowski, K., Clarke, B., Miller, S. J., & Fien, H. (2015). Examining the association between explicit mathematics instruction and student mathematics achievement. The Elementary School Journal, 115(3), 303–333. https://doi.org/10.1086/679969
Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202–1242. https://doi.org/10.3102/0034654309334431
Krawec, J. L. (2014). Problem representation and mathematical problem solving of students of varying math ability. Journal of Learning Disabilities, 47(2), 103–115. https://doi.org/10.1177/0022219412436976
