The field of education is going through pervasive changes regarding learner outcomes and accountability for all students. As a result, educators are focusing their efforts in a variety of areas. One area receiving enormous attention is response to intervention. Initially, the focus of RTI was directed at improving early literacy programs in an effort to reduce the number of students identified with specific learning disabilities. The RTI movement is now quickly expanding to mathematics.
Many definitions and descriptions of RTI exist, but for the purpose of this discussion, I define RTI as the general process by which educators (often a team) use objective student-performance data to determine when additional instruction and/or interventions are needed prior to any determination of a learning disability. RTI employs a series of instructional tiers with increasing instructional intensity. Within the RTI description, there are several main components, but one especially important component that must be properly addressed is the emphasis on classroom instruction, which includes both content and instructional approach. If instruction for struggling students is not carefully developed and planned, RTI efforts will likely have little positive effect on improving students learning of mathematics.
Refocusing the Debate
Much debate and energy has been spent regarding the “what” and “how” to teach mathematics in this country. Often intense, these debates revolve around content and method of instruction. Unfortunately, the debates among mathematics educators, mathematicians, researchers, and policymakers often have little to do with students. Instead, they are often about posturing to defend or advocate for a certain instructional philosophy. Although debate is healthy in any profession, the debate over what and how to teach mathematics has delayed true educational reform and negatively impacted many students’ math experiences.
The use of an RTI math framework is gradually refocusing this debate back to the content and instructional needs of the students. RTI procedures require that instructional decisions be based on student-learning data, not philosophies or opinions. RTI is helping educators’ efforts in determining what to teach and, more importantly, which instructional approach to follow. As RTI math initiatives continue to expand, however, teachers are often left to their own means to sort through the overwhelming volume of content and instructional recommendations for improving student learning, some of which may seem counterintuitive. Recently, there has been some movement to provide more guidance to educators on the most effective instructional approaches based on high-quality research.
— teacher-directed instruction
— direct instruction
— more models and demonstrations
— explicit problem- solving strategies
— focused instruction on deficit areas
— corrective feedback
— small group (3-10 students)
— one-on-one tutoring
— guided practice
— independent practice
—classwide peer tutoring
— computer-assisted instruction
Source: Response to Intervention Math (Corwin, 2010), by P.J. Riccomini & B.S. Witzel
In 2008, the National Mathematics Advisory Panel released a report to help guide math teachers to improve instruction within an RTI framework. The report addresses the age-old debate around teacher-led vs. student-centered instruction and denies the two are mutually exclusive. In fact, the NMAP report clearly states that research does not support a strict dichotomy. It recommends teachers use a balance of student-centered and teacher-led instruction, particularly in the case of low-achieving students, students at-risk for math failure, and students with disabilities. The NMAP panel recommendations can be used to bolster a RTI math program, particularly for students who are struggling.
Based on the review of more than 16,000 research studies, the NMAP suggests five general recommendations to consider when designing instruction for struggling students within an RTI framework. First, teachers should use explicit methods of instruction on a regular basis. Second, teachers should teach students clear problem-solving methods and strategies. Third, teachers should use carefully sequenced examples to help struggling students facilitate important connections. Fourth, teachers should use concrete representations to promote the understanding of abstract representations in mathematics. Fifth, teachers must provide students with additional opportunities to think aloud. The panel’s recommendations should form the foundation of RTI math instructional decisions.
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As students progress through an RTI system, teachers must carefully consider these five recommendations when developing and implementing instructional interventions. In fact, these recommendations must become more apparent in all instructional tiers, including Tier I, if positive effects are to be achieved. Additionally, it is important for teachers to recognize that students who are not struggling may require less teacher guidance than struggling students. At the same time, teachers must plan to enrich and accelerate more advanced students; their instructional needs must also be considered in the context of RTI.
The Ultimate Goal
Mathematical proficiency is the ultimate goal of mathematics instruction regardless of whether the teacher or the student is driving instruction. Depending on an educator’s point of view, mathematical proficiency may emphasize concepts and problem solving over procedures and computation. However, the NMAP describes effective mathematics programs that promote proficiency in the following areas: conceptual understanding, computational fluency, factual knowledge, and problem solving skills. It is important for teachers to recognize mathematical proficiency requires the seamless blend of each of these five areas outlined by the NMAP. And if students are lacking in any of the five areas, proficiency is not achieved.
With more and more focus placed on improved mathematical proficiency by students, it is imperative that the best available evidence─not educational philosophies─guide the field. Basing instructional decisions on students’ needs and high-quality research is especially important and relevant in the context of RTI. When students struggle in their learning of mathematics, time is at a premium and teachers must rely on effective and efficient instructional techniques.
As a researcher committed to helping improve math instruction, I wholeheartedly support and promote the use of research-validated best practices to the maximum degree possible. As a parent of two children in elementary school, I applaud the teachers who work tirelessly, often thanklessly, to implement evidence-supported mathematics practices every day in their classrooms. Thank you!
A version of this article appeared in the April 12, 2010 edition of Teacher PD Sourcebook as It’s Not Just for Reading