Four Ways to Incorporate Tiered Interventions in the Math Classroom
Part 2 of our blog series, Multi-Tiered System of Supports for Math Success
By Bradley Witzel, Ph.D., Winthrop University
Ben Clarke, Ph.D., University of Oregon;
and Paul J. Riccomini, Ph.D., The Pennsylvania State University
In the math classroom, providing each student with the right kind of support requires a strategic approach coupled with a delicate hand. Teachers must be equipped with the tools and skills needed to put the appropriate interventions in place, those that are tiered and intensified based on the individual, and take into consideration the essential elements that will ensure success of all students.
In part one of this series, we took a broad look at Multi-Tiered Systems of Support (MTSS) models and how they can be used in math instruction. In part two, we will explore in detail how mathematics teachers can develop a more complex determination of the intensity of their interventions.
By manipulating aspects like academic learning time, teacher-to-student ratio, content emphasis, and instructional approach, teachers can increase intervention intensity and meet the needs of individual students. Read on to learn how.
Academic Learning Time
Time must be dedicated to mathematics learning every day and for every grade. Mathematics topics can and should be embedded into other class activities and connected across a student’s curriculum (Frye et al, 2013). However, even with good mathematics instruction, many students will still require interventions.To increase the intensity of a math intervention, Vaughn, Wanzek, Murray, and Roberts (2012) suggest increasing the frequency and/or duration of the intervention.
There has been some debate about how much time should be allotted for mathematics instruction. Similar debates occur regarding how much time should be dedicated toward mathematic interventions. Rather than emphasizing only allotted time, it is important to review academic learning time (ALT), or the time that students are actively engaged in the desired content of the lesson. Increasing time for mathematics is necessary but not sufficient for maximizing ALT.
A lesson focused on content with purposeful activities and minimal downtime is essential to improving ALT. Most interventions are structured to include these components:
- Connecting Prior Knowledge/Priming Instruction — 2-5 minutes
- Introduction to the Concept — 3–5 minutes
- Modeling of the Concept — 10–20 minutes
- Guided Practice — 5–10 minutes
- Independent Practice (at least 10 opportunities) — 3–5 minutes
- Procedural Fluency — 3–5 minutes
- Connections to Core Content — 3–5 minutes
- Problem Solving Activity or Application — 5–10 minutes
If students’ attention spans are too low for a 30 or 60-minute intervention, consider breaking the intervention into subsets, such as three sets of 10 or 15-minute interventions. It is important to adjust the instructional focus to the needs of the student to maximize the effectiveness of ALT.
As demonstrated by recent education policies, it is commonly thought that reducing class size has an immediate positive benefit. However, as Whitehurst and Chingos (2011) found in their review of class size, results are rather mixed. They found that reducing large classes by seven to ten students can have a profound, long-term positive impact on student achievement, especially when applied in the early grades, and to students from less positive backgrounds.
The average teacher-to-student ratio has been reduced over the past decades to what is now projected as 14.5/1. Therefore, an appropriate target for Tier 1 additional support or a separate Tier 2 intervention setting for students of the highest need would be a reduction to eight or fewer students. For more intensive tiers of intervention, an additional reduction to as low as one or two students would be most appropriate for increasing the intensity of the intervention. However, reducing the intervention group size will have little benefit if the time spent during intervention is not used properly.
Mathematics is a progression-driven content area: More complex skills typically require a level of mastery of preceding skills. For example, to understand fractions, students must have magnitude and computation fluency. So it becomes even more important to prioritize the skills and content that will be taught during intervention.
- Foundational content: Teachers should give foundational mathematics content such as problem solving, number sense, computational reasoning, accuracy, and speed of recall. Developing reasoning and speed of recall lessens the cognitive load, and helps students better to connect processes from one topic to another. When computational facts became more automatic, the student can concentrate on more complex mathematics reasoning and interpretations.
- Core content: Often, a student that is successful in intervention will continue to struggle in core, therefore, making connections between intervention and core are key to a student’s overall success.
- Upcoming content: Along with re-teaching deficit skills and connecting these skills to current content, consider spending intervention time pre-teaching upcoming skills. When students are prepared for what is to come and understand how the strategies are learned during intervention will help them progress, they are likely to have more confidence in the upcoming lessons (Lalley & Miller, 2006) which will likewise impact their engagement in the lesson.
Student with disabilities and at-risk concerns perform best in mathematics when taught using systematic instruction. This is the explicit and direct instruction that includes a gradual transfer of information from the teacher to the student.
At the base of systematic instruction are stepwise, think-aloud procedures tied to verbal reasoning, a high degree of interactivity, and sufficient guided and independent student practice (Witzel & Clarke, 2015). Archer and Hughes (2011) highlight several components of explicit instruction that should be considered during interventions:
It is unlikely that every component of explicit instruction will be used in each lesson. However, as a student’s needs become more intensive, so too should the components introduced during the intervention.
As students move from one set of intervention supports to the next, review how the intensity is being adjusted to meet the needs of the student. Simply moving the instructional location is insufficient for increasing intensity. No two students are the same, so some students may need more intensity in one aspect over the other.
Adjusting intensity through academic learning time, teacher-to-student ratio, content emphasis, and instructional approach should serve to meet the needs of students who are struggling in mathematics and offer the greatest potential benefit to mathematical performance.
Lalley, J. P., & Miller, R. H. (2006). Effects of pre-teaching and re-teaching on math achievement and academic self-concept of students with low achievement in math. Education, 126(4), 747–755.
Vaughn, S., Wanzek, J., Murray, C. S., Roberts, G. (2012). Intensive interventions for students struggling in reading and mathematics: A practice guide. Portsmouth, NH: RMC Research Corporation, Center on Instruction.
Whitehurst, G. J., Chingos, M. M. (2011). Class size: What research says and what it means for state policy. Brown Center on Education Policy at Brookings. Available at https://www.brookings.edu/ wp-content/uploads/2016/06/0511_class_size_whitehurst_chingos.pdf
Witzel, B., & Clarke, B. (2015). Benefits of using a multi-tiered system of supports to improve inclusive practices. Childhood Education, 91(3), 215–219.
Dr. Bradley Witzel
Dr. Witzel is a Professor and Program Director in the College of Education at Winthrop University. His main areas of research focus on empirically-validated practices with students with disabilities and at-risk concerns, particularly in the areas of mathematics and MTSS. A popular author and professional developer, he has written several books and delivered several hundred workshops, confernces, and video presentations on instructional interventions.
Dr. Ben Clarke
Dr. Clark is an Associate Professor in the School Psychology Program at the University of Oregon. He currently serves or has served as a Principal Investigator on 15 federally-funded research grants (approx. 50 million in funding) in mathematics instruction focused on the development and efficacy-testing of intervention programs spanning the K-6 grade spectrum in both traditional and technology-based formats. Dr. Clark was a practicing school psychologist for three years, during which time he led district efforts to implement mutli-tier instructional models in reading and mathematics.
Dr. Paul J. Riccomini
Dr. Riccomini is currently an Associate Professor of Special Education at the Pennsylvania State University. He began his career as a dual-certified general education mathematics teacher of students with learning disabilities, emotional and behavioral disabilities, and gifted and talented students in Grades 7–12 in his inclusive classrooms. His current research interests focus on the application of evidenced-based instructional practices and interventions in MTSS/RTI framework for students with disabilities and struggling students in mathematics. Additionally, Dr. Riccomini provides high-quality professional development focused on effective mathematics instruction to school districts across the United States.