What is RTI for mathematics?
Page 1: Overview of RTI
Teachers know that if students are to create a foundation for understanding abstract mathematics concepts, it is important that they begin to develop essential skills and concepts at an early age. However, research conducted since the 1970s has shown that, although U.S. students’ mathematics proficiency has improved somewhat, a large number of students continue to struggle with the subject.
Every year, the National Assessment of Educational Progress (NAEP) administers mathematics achievement tests to 4th-, 8th-, and 12th-grade students in the United States. Student performance indicates the degree to which they have acquired the knowledge and skills expected at their grade level. The results are categorized into one of four levels: Below Basic (little mastery), Basic (partial mastery), Proficient (mastery), and Advanced (beyond mastery). The 2017 results for 4th and 8th grade are illustrated in the table below. The 12th-grade data are from 2015 because the 2017 data are not yet available.
This bar graph illustrates the results of the 2017 National Assessment of Educational Progress (NAEP) mathematics achievement test for 4th and 8th grades and the 2015 data for 12th grade. The table is divided into three columns—one for 4th-grade results, one for 8th-grade results, and the last for 12th-grade results—and each column is divided into two rows. The top row is labeled “Students Proficient & Advanced,” while the lower is labeled “Students Basic & Below Basic.”
The test results are displayed for three categories of test takers: “All Students,” “Students with Disabilities,” and “ELLs.” The “All Students” bars are colored aqua. The “Students with Disabilities” bars are peach. Finally, the “ELLs” bars are yellow.
In the 4th-grade column, “All Students” are 40% in the Proficient & Advanced range and 60% in the Basic & Below Basic range. “Students with Disabilities” are 17% in Proficient & Advanced and 83% in Basic & Below. Likewise, “ELLs” are 15% in Proficient & Advanced and 85% in Basic & Below.
In the 8th-grade column, “All Students” are 34% in the Proficient & Advanced range and 66% in the Basic & Below Basic range. “Students with Disabilities” are 9% in Proficient & Advanced and 91% in Basic & Below. Finally, “ELLs” are 6% in Proficient & Advanced and 94% in Basic & Below.
In the 12th-grade column, “All Students” are 25% in the Proficient & Advanced range and 75% in the Basic & Below Basic range. “Students with Disabilities” are 3% in Proficient & Advanced and 97% in Basic & Below. Finally, “ELLs” are 6% in Proficient & Advanced and 94% in Basic & Below.
For Your Information
Because student behavior strongly impacts academic performance, it is important to have a system of supports in place to address behavior challenges. Positive behavioral intervention and supports (PBIS) is a framework for providing a multi-tiered system of support that can address such challenges.
The response to intervention (RTI) framework has been used to improve students’ mathematics proficiency. RTI is a type of multi-tiered system of support (MTSS) for delivering support through increasingly intensive levels of instruction that are matched to students’ needs and based on data.
multi-tiered system of support (MTSS)
A model or approach to instruction that provides increasingly intensive and individualized levels of support for academics (e.g., response to intervention or RTI) and for behavior (e.g., Positive Behavioral Interventions and Supports or PBIS).
RTI serves two primary purposes:
- To provide early intervening services to students who are struggling. Early intervening is the delivery of services or assistance to struggling students before they fall too far behind their peers. Early intervening services can minimize or prevent the development of substantial academic difficulties by:
- Providing high-quality instruction in the general education classroom
- Implementing evidence-based interventions as soon as students are identified as struggling
- Using classroom data, rather than subjective observations, to make decisions about whether students should be referred for an evaluation for special education services
- Reducing inappropriate referrals and placements in special education
IQ-achievement discrepancy model
The traditional assessment vehicle used to determine whether a student has a learning disability and requires special education services.
Term used to describe a set of procedures designed to assist students experiencing academic or behavior difficulties prior to any consideration of special education services.
To help identify students with learning disabilities (LD). The RTI approach is an alternative to the traditional IQ-achievement discrepancy model used during the pre-referral process to help identify students with learning disabilities. Students who do not respond adequately to high-quality instruction provided in the general education classroom or to increasingly intensive levels of intervention might be eligible for special education services. By using RTI to help identify students who might have learning disabilities, school personnel can more quickly provide those students with individualized services and help them to avoid years of frustration and failure.
Did You Know?5%–10% of all students have mathematics learning disabilities. These students have a number of common characteristics.
Common Characteristics of Students with MLD
Although every learner is unique, students with a mathematics learning disability (MLD) tend to display any of a number of characteristics that affect their mathematics performance, including:
mathematics learning disability (MLD)
Condition characterized by significant difficulty in mathematics calculation and/or problem solving; a specific learning disability (SLD) in the area of mathematics, sometimes referred to as dyscalculia.
- Difficulty processing information
- Difficulty identifying relevant information in mathematics problems, especially in word problems
- Problem maintaining attention
- Difficulty selecting an effective problem-solving strategy
- Poor reasoning and problem-solving skills
- Memory and vocabulary difficulties
- Weak visual/spatial representational skills
- Learned helplessness—that is, having low motivation, being a passive learner, and attributing both successes and failures to external, uncontrollable factors (e.g., luck)
- Mathematics anxiety
- Deficits in the areas of mathematics facts and computational skills
- Difficulty translating information into a mathematical expression or equation
- Difficulty reading about mathematics
- Difficulty understanding the language, or vocabulary, of mathematics
- Difficulty understanding mathematics concepts and how concepts relate to procedures
- Difficulty solving multi-step problems
- Working through a problem without making sure all steps are completed or that the answer makes sense
In the video below, Tessie Rose Bailey, a technical assistance provider for the National Center on Response to Intervention, discusses the differences between pre-referral and RTI (time: 5:15).
Source: National Center on Response to Intervention (rti4success.org)
Transcript: Differences between prereferral and RTI
Question: How does RTI differ from previous approaches to providing interventions?
Tessie Rose Bailey: So when the terminology of RTI came out in the new reauthorization of IDEA, I think what a lot of schools, districts may have done is just taken what they were originally doing for what we would consider pre-referral or a process of providing interventions prior to students going into special ed and renamed it RTI. And when you really look at what RTI is, it’s more of a preventative framework as opposed to a pre-referral, and that really is the big difference. In a pre-referral strategy, what we see is we wait till a student fails in some way, is recognized as failing, is referred to a team, folks try to come up with an intervention that will, in a sense, remediate that deficit before we make a referral to special ed. And in RTI, we’re really looking at a preventative framework, and we use what we refer to as screening tools to predict who may be at risk for failure, as opposed to waiting until a kid fails before they are referred. And in a preventative model, those students who are screened and who might be at risk for poor learning outcomes then receive interventions to prevent them from having struggles in the future, and those students who then don’t respond to highly qualified or highly effective interventions may be referred to special ed.
I often get questions about, well, is RTI really just an intervention framework? And when we talk about RTI at the RTI Center, we’re looking at it as a school-wide prevention framework. So core instruction is really part of that prevention, and all students should have access to that. And those students who are struggling or who may be at risk of struggling are identified through those screening tools that are reliable and valid. In an effective preventative RTI framework, what you would end up seeing is that students who are struggling may start moving through the tiers in an upward fashion, but the majority of those students, if their intervention at secondary and tertiary are effective, would then move to less-intensive tiers. And this is very different from a pre-referral model in which students tend to take a one-way street up. So they are no longer performing at a rate that we would expect them, so then we intervene and then they may be referred. But very few of those in a pre-referral model actually move back down to less-intensive tiers, and that to me is what really separate RTI as a prevention framework versus our past traditional pre-referral model.
One of the things that often makes it clear if people are using a pre-referral versus a prevention framework is that they’ll use things like, “Oh, I RTIed this kid,” or “That’s an RTI student.” But if you think about RTI as a prevention framework in which core is part of that prevention framework then in a sense all students are RTI kids. And if you are just looking at RTI as an intervention only, then it may really be that you’re addressing deficits as opposed to intervening early to prevent those poor learning outcomes. And if you think about special ed, a lot of people mistake RTI as preventing special ed, and in reality special ed is part of this larger prevention model, and so those students who were…I mean, really, the purpose of school is to prepare students for post-secondary outcomes. In kindergarten, we’re preparing them for elementary, in elementary for middle school, and we want to adequately prepare them not only for state tests but this bigger success in school.
And so part of what special ed’s role is is to prevent those students from experiencing struggles that they may have had, had they not had special ed. So I think really that the idea that RTI is not really just another name for a pre-referral model and instead is this larger school-wide prevention model is really the key to making sure that students, all students, are successful.
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Many schools implement a RTI framework with three tiers (or levels) of instructional support: core instruction, supplemental intervention, and intensive intervention. Other schools implement more tiers of support to meet the needs of their students. Below is a representation of a RTI framework with three tiers, accompanied by a brief description of each. The percentages of students associated with each tier of support noted in the illustration are typical for most schools. However, some schools—for example, Title I schools—might see higher percentages of students in need of support.
Tiers of Support
Tier 3 (also referred to as tertiary intervention or intensive, individualized intervention) is intensive intervention that is individualized based on data; it is provided with more frequency and in smaller group settings than the Tier 2 intervention.
Tier 2 (also referred to as targeted or secondary intervention) offers supplemental intervention using a standard validated approach or program to students in a small-group setting; it is provided in addition to and aligned with core instruction.
Tier 1 (sometimes referred to as primary instruction) is high-quality core instruction provided in the general education classroom.
The movie below illustrates the number of students in the average classroom who might struggle with mathematics and who might benefit from more instructional support (time: 0:35).
In an average class of 25 students, approximately six will struggle with mathematics. Of those six, about five will need additional or more intensive instruction to remediate their skills. Approximately two of those five students will require even more intensive, individualized mathematics instruction. Implementing RTI is one way to provide additional instructional support to students struggling with math and to identify students who may have learning disabilities.
A typical MTSS framework includes supports that address both academic and behavioral challenges. However, this module focuses on the academic portion of this framework and discusses the provision of increasingly intensive levels of instructional support. The terms associated with this framework differ among experts and practitioners. First, some refer to this process as RTI and others as MTSS. Even federal laws that govern the education of students use different terminology: The Every Student Succeeds Act (ESSA) requires schools and districts to develop a multi-tiered system of supports to respond to students’ academic and behavioral needs, whereas the Individuals with Disabilities Education Act (IDEA) allows schools to use “a process based on a child’s response to scientific, research-based intervention” as part of the procedure to determine whether a student has a specific learning disability. Second, some experts and practitioners refer to levels of support and others to tiers of support. Additionally, implementation of the framework varies across states and districts. Some schools implement three levels of support (with special education being the third level) while others implement four or more levels (with special education being the most intensive level).
Every Student Succeeds Act (ESSA)
Federal school reform legislation originally enacted in 1965 that aimed to increase school accountability for student learning, offer more choices for parents and students, create greater flexibility for schools in the use of funds, and emphasize early-reading intervention. This act now mandates the use of academic and behavioral evidence-based practices. When this act was reauthorized in 2001, it was referred to as the No Child Left Behind Act (NCLB). The Every Student Succeeds Act (ESSA) reauthorized the Elementary and Secondary Education Act in 2015 and went into effect in fall 2017.
Individuals with Disabilities Education Act (IDEA)
Name given in 1990 to the Education for All Handicapped Children Act (EHA) and used for all reauthorizations of the law that guarantees students with disabilities the right to a free appropriate education in the least restrictive environment. The most recent version was reauthorized in 2004.
In this module, we will:
- Define the process of providing more intensive levels of academic instruction as RTI
- Use a framework that consists of three tiers of support
- Refer to the third, most-intensive tier of support as “special education services”