While overhauls to reading curricula headline the news across the country, its academic counterpart—math—has been somewhat forgotten, despite equally shocking data from the National Assessment of Educational Progress (NAEP) Report. In fact, the most recent data revealed the sharpest decline in math scores since the assessment's inception in 1990.
To counter declining math scores, educators need effective strategies to incorporate into math instruction. When combined with a solid foundation of core instruction, research-based mathematics interventions enable districts to strengthen their tiered systems of support to help all students learn.
Download our toolkit of 12 research-based math interventions.
How Math Interventions Fit Into an MTSS
A core component of an MTSS (multi-tiered system of supports) or RTI (Response to Intervention) framework is interventions: research-based strategies to support students across three levels, called tiers. Math intervention activities teach mathematics topics at a student’s individual level to meet their needs.
- Tier 1 math interventions are included in universal, core instruction provided to all students. These strategies are effective best practices to establish a solid foundation for math success.
- Tier 2 math interventions offer targeted support in small-group instruction for students who need additional resources on top of core instruction.
- Tier 3 math interventions involve intensive, one-on-one instruction and highly individualized support for students who have received both Tier 1 instruction and Tier 2 interventions.
Below are 5 research-based and evidence-based math interventions to share with school teams and add to your district’s intervention menu. These interventions have been selected from Playbook, Panorama’s professional learning library for K-12 educators.
RTI/MTSS Math Interventions:
Concrete Representational Abstract (CRA) Approach
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Key Takeaways:
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Math Songs
Math Songs use rhyme, rhythm, patterns, and repetition to help students remember math concepts, skills, or basic facts. The use of songs helps students retain information in long-term memory.
- Focus Area: Fluency
- Developmental Stage: Lower Elementary, Upper Elementary, Middle School
- MTSS/RTI Tiers: Tier 1
Preparation:
- Consider which topics would benefit from the inclusion of a math song.
- Find math songs about the relevant topic that your students would enjoy. Websites like YouTube, Teachers Pay Teachers, and GoNoodle offer a variety of math songs. Teachers can search for songs on specific topics such as multiplication tables, fractions, or geometry.
- Print out lyrics or display lyrics for students to read along as they sing (as appropriate for the grade level).
Instructions:
- Play or sing math songs at any point during the learning of a math topic, whether as an introduction or throughout the course of study.
- Consider asking students to create their own math song or write their own lyrics to a familiar tune. This will provide an engaging way for students to interact with the topic and take authentic ownership of their understanding.
Math with PALS
Math with PALS (Peer-Assisted Learning Strategy) is an intervention that supports student growth through collaboration, discussion, and practice. Students work in pairs of tutor and tutee to support one another’s understanding of a previously taught math skill.
- Focus Area: Problem-Solving
- Developmental Stage: Lower Elementary, Upper Elementary, Middle School
- MTSS/RTI Tiers: Tier 1, Tier 2
Preparation:
- Choose students who know how to use the skill or strategy in a problem set.
- Pair students ahead of time in heterogeneous pairings. One partner should be stronger in the math skill (tutor), and the other can be a student who needs some support to improve (tutee).
- Create a practice worksheet for students to complete while working in pairs. For younger students, consider adding these coaching questions to the worksheet.
Instructions:
- Pair students and provide worksheets or work materials.
- Allow 20–40 minutes for pairs to work based on grade level and age group.
- The “tutor” partner will support the other partner’s work through questions and modeling. Prompts or questions can be provided for the tutor partner to use.
- If the “tutee” makes a mistake, the tutor should address it and explain their thinking in a respectful way.
- After the pairs complete half of the worksheet, the students switch roles to complete the rest of the worksheet.
- Once the partner work time is complete, students should work individually to complete additional problems, then exchange worksheets and review their partner’s work.
Draw a Picture
This strategy asks students to make a drawing of an applied problem. Drawing a picture can support student understanding of the problem itself as well as how to solve the problem. Additionally, this strategy can pinpoint misconceptions students may have about how to set up or solve the problem.
- Focus Area: Comprehension
- Developmental Stage: Lower Elementary, Upper Elementary, Middle School, High School
- MTSS/RTI Tiers: Tier 1, Tier 2
Preparation:
- Analyze the word problems that students will be asked to solve.
- Choose a word problem to model how to draw a picture to help solve it.
- Choose one or two to use as guided practice. Students can then work independently using a drawing.
Instructions:
Explicit Instruction:
- Choose a word problem to display and ensure students have a copy.
- Model reading the problem aloud carefully.
- Talk through the thought process for how to draw a picture to represent the problem. This may include what you notice, what values you are starting with, and what you will do.
- Draw the picture as you explain, and ask students to do it along with you.
Guided Practice:
- Provide students with a selected word problem.
- Ask students what information is provided in the problem.
- Guide students to draw a picture to represent the problem. Facilitate student thinking with your own thinking aloud and with guiding questions.
Explore Before Explain
Explore Before Explain is a learning environment where students explore real-life situations as they relate to a concept before an explanation of the concept occurs. Activities to practice a concept are not introduced until students have had time to gain meaning through exploration.
Explore Before Explain helps avoid the question “When will I ever have to use this?” Making connections between math concepts and the real world will help students be more engaged and remember what they’ve learned
- Focus Area: Comprehension
- Developmental Stage: Lower Elementary, Upper Elementary, Middle School, High School
- MTSS/RTI Tiers: Tier 1, Tier 2, Tier 3
Preparation:
- Think about student experiences that can relate to the math concept in consideration. Consider how students could explore an experience to discover useful information about the concept. This might include a demonstration, using the classroom environment describing a relatable scenario, or watching a video
- In elementary school, this might be a great time to bring in a guest expert—a parent or other relative of one of the students who uses this concept in their work or daily lives.
Instructions:
- Engage students in the context. Provide expectations of the task at hand. Do not formally introduce the math concept at this stage.
- Allow students to explore a common experience related to the concept.
- Explain how the exploration connects to the formal concept.
- Have students elaborate on the concept by applying the concept to a new scenario or using follow-up practice questions.
- Evaluate student understanding of the formal math concept.
Concrete Representational Abstract (CRA) Approach
Students begin the CRA process by using concrete models to represent math concepts. Next, students transition to the use of drawings to represent the same concepts. Finally, students translate model representations to abstract representations using numbers and symbols.
- Focus Area: Computation
- Developmental Stage: Lower Elementary, Upper Elementary, Middle School, High School
- MTSS/RTI Tiers: Tier 1, Tier 2, Tier 3
Preparation:
- Gather concrete manipulatives (counters, blocks, cups, algebra tiles, etc.) that can be used to model the math concept being discussed.
- Choose problems that avoid complicated calculations.
- Download the CRA worksheet.
Instructions:
Concrete: Students work with actual objects to solve the math problem.
- Hand out the manipulatives to each student or pair. Give the students a few minutes to explore the manipulatives.
- Demonstrate how the concrete materials connect to the problem. Allow students to see you “think through” some sample problems.
- Using a whole-class approach, work through a few more problems together. Check for understanding. If needed, work through additional examples.
- Finally, give students a few problems to work through individually or in pairs.
Representational: Students draw or sketch representations of the objects to model problems.
- Using the same math problems from the concrete examples, transition students to pictorial models.
- Ask for suggestions from students of different ways they can represent the concept on paper instead of with objects.
- Have students practice using pictorial models individually or in pairs.
Abstract: Students write symbolic representations using numbers and symbols.
- Continue with the same math problems. Review previous methods using concrete objects and pictorial representations. Transition students from representational models to abstract displays using math notations.
- Have students practice solving problems using only symbolic notations. Provide additional support, if needed.
Identify Students & Administer Math Interventions With Panorama
District and school users can identify students who score below benchmark on math assessments—such as iReady, FastBridge, STAR, and NWEA MAP—and create support plans in Panorama Student Success. With all student data in one platform, educators can easily take action with intervention planning workflows, collaboration tools, and evidence-based strategies.
Conclusion
These interventions not only enhance comprehension and problem-solving skills, but they also foster a deeper understanding of mathematical concepts across all tiers of support.
By incorporating research-based and evidence-based math interventions into an MTSS or RTI framework, school and district leaders ensure all students receive the support they need.
Download these and other research-based strategies in our Math Interventions Toolkit.
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Frequently Asked Questions How can school leaders support teachers in implementing these strategies? How can educators determine the effectiveness of an intervention? What strategies can be used if a class has a wide range of math skill levels? What are some ways to increase student engagement and motivation while using these interventions? |
