By now, most districts and state departments of education have explored the option of response to intervention (RTI). In fact, many have already implemented RTI and are developing steps and procedures to improve implementation at least in reading. Regarding reading and literacy education, many districts have organized screening, progress monitoring, and diagnostic assessments along with a protocol of tiered interventions and expected instructional delivery. This makes sense. The amount of research-supported information available is more than sufficient to develop an RTI program aimed at improving student reading.
However, while there is a great deal of information on reading and RTI, there is a dearth of research on math with RTI. Thus, the development and implementation of reading and RTI has blazed a path to RTMI (Response to Math Intervention). Just like with reading, math education debates continue to erupt over instructional paradigms and theoretical underpinnings. The benefit of an RTI model is that it muffles theoretical debates in exchange for a focus on student learning. Using performance data, schools and school districts make changes in how and what they teach. When data does not support instructional and curricular decisions, revisions must be made, quickly.
Components and aspects of math RTI
In order to get started with a RTMI model it is important to consider three essential components: assessment, curriculum and instructional delivery. Within these three components there are key aspects that must be handled by teachers and administrators. Below is a chart of the three components and some key aspects:
|Screening||Implementing and reviewing screening information||Selecting screening tools and setting time|
|Progress Monitoring||Scheduling time for progress monitoring and making frequent adjustments according to data||Selecting progress monitoring tools and reviewing group data|
|Diagnostic||Implementing diagnostics both informally and formally||Selecting diagnostic tools and reviewing group data|
|Meeting Standards||Document instructional time spent covering each standard or intervention content||Selecting a standards-based core curriculum and calendar to meet standards as well as providing professional development on math content so standards are met accurately|
|Selecting Interventions||Implementing interventions and providing feedback on implementation||Selecting research-supported math interventions matched to students’ assessment data|
|Tier 1 Delivery Methods||Implementing research-supported instructional delivery with fidelity||Providing professional development on research-supported instructional delivery|
|Differentiation at Tier 1||Document use of differentiation before and during student tier 2 intervention||Monitoring differentiation at tier 1|
|Intervention Delivery||Implementing research-supported intervention delivery with fidelity||Providing professional development on research-supported intervention delivery|
|Differentiation at Tier 2||Document use of differentiation before and during more intense intervention||Monitoring differentiation at tier 2|
|Monitoring Delivery Integrity||Responding to integrity data||Collecting data to ensure accurate delivery of instruction and intervention at all levels|
*It is important that administrators choose an expert team to select appropriate assessment tools and systematically review the effectiveness of those tools.
Three assessment essentials exist in RTI models: screening, progress monitoring, and diagnostics. It is important to have a good screening tool in place and use that tool a couple times each academic year. A good screening tool matches the state assessment in that it can reasonably predict student scores on the statewide math test. Using a screening multiple times in an academic year allows for accurate placement and movement among tiers. Using a progress monitoring tool that is aligned with both the statewide math test and the screening tool allows close monitoring of student performance. If a student is progressing in an intervention but not in the core curriculum, then more intervention is necessary. If a student is not progressing in intervention or the core curriculum, then a selected review team must consider whether the student needs additional intervention or more intense interventions at a different tier level. To determine what areas that the student is struggling, a diagnostic tool is useful for pinpointing the content necessary for tiered interventions.
Many state departments of education do not use the term RTI but instead use another title such as Response to Instruction and Intervention. The reason for this name change is to place emphasis on core curriculum (tier 1) before jumping on interventions. For obvious reasons, without an effective tier 1, interventionists at the tier 2 and 3 levels will be overwhelmed and curriculum will often be misguided. Tier 1 curriculum should be based on state standards and delivered accurately in terms of content. There are many guidelines to providing effective tier 1 content as detailed by the National Math Panel (see Additional Help section for NMP link). To help build content knowledge, administrators should consider providing content-focused professional development.
Intervention curriculum is more complex. Intervention curriculum should match students’ needs according to diagnostic assessments. Many options should be considered. My experience is that districts tend to focus on areas such as operational fluency and automaticity, algebra readiness (fractions, decimals, integers, equations, etc.), number sense (whole numbers), and word problem solving strategies. For more intense interventions, it may be determined that an alternate and possibly more functional curriculum is necessary. Once content is selected, an expert team should review the research support for various curricula to determine what best fits their students’ needs. The team should also revisit student performance scores to determine if adequate growth is met and make curricular changes as needed.
Instructional delivery or pedagogy receives much of the debate in mathematics education. While the paradigmatic debate helps drive research strands, it is not as useful to educators who must deliver the instruction. Supported by the NMP and IES Practice Guide panelists (Gersten et al., 2009), an explicit and systematic form of instructional delivery is most effective for students with mathematics difficulties. Thus, even in tier 1, if a large number of students struggle learning mathematics, it is important to use an explicit instructional delivery. Explicit instruction includes but is not limited to clear models of problem solving with teacher think alouds, scaffolded instruction with plenty of independent practice. With the increased instructional time during interventions, interventionists should consider adding student think alouds, direct instruction, and increased use of a graduated sequence of instructional prompts before working with abstract numbers, such as the concrete to representational to abstract sequence of instruction (CRA). Learning mathematics typically has less to do with what one is learning and more to do with how they are taught. Many teachers and interventionists benefit from sustained professional development to learn research-supported instructional delivery.
Who does a math RTI model help?
The immediate goal of RTI is to improve student performance scores as a whole. To improve scores, it is important to have an efficient model in place so that students who are struggling receive support for their learning as soon as difficulty is identified. Appropriate support comes in all tiers, from the standards-based curriculum to research-supported instruction and intervention delivery to individual and small group differentiation. This approach does not diminish special education but rather provides an alternate route to identification of learning disabilities in that it should reduce misdiagnosis that may have been a result of poor instruction and/or curriculum.
RTI has received some critique in that is focuses instruction on students who are struggling and not necessarily on those who are higher achieving. While this may be the case in many RTI models, possibilities of differentiation and tiered enrichment for high achieving and gifted students is possible. For that reason, Figure 1 does not present RTI as a bottom-up pyramid but rather a chart. Until more research reveals how to use RTI with higher achieving students, RTI models will focus on helping students who score below expectations.
Math achievement and tiered movement
Tier 1 involves the instruction of a core curriculum that meets state standards and helps a large majority of students succeed. Within tier 1, teachers must use instructional delivery approaches that best help students achieve. The term differentiated instruction is commonly considered a tier 1 idea. However, meeting the unique needs of learners is important in all tiers. Every student who is potentially going to achieve a standard diploma must be in tier 1.
If a student is not succeeding in tier 1, as determined by screening tests, the student should be considered for tier 2 intervention. Tier 2 intervention does not replace grade level standard-based instruction but rather fills gaps of learning for students who are struggling. In other words, a high school student may be in tier 2 for fractions computation but they are still in tier 1 so that they can potentially achieve state standards. Tier 2 is typically with small groups of students for approximately 30 minutes.
Students who are struggling in tier 2 and tier 1 must be considered for tier 3 intervention. This intervention is considered more intense because it lasts longer every day and groups students in smaller and more homogenous groups. A fourth grade student struggling in tier 1 may be in tier 3 for computation of whole numbers but remain in tier 1 so that he can keep up with standards. Tier 3 is typically a tutorial environment lasting approximately 50 minutes.
I have the fortunate position of working with several schools, districts, and state departments in their development and implementation of RTI. There are many variations of RTI implementation working from a multitude of policies and procedures. During early stages of implementation, expect there to be growing pains as research tries to catch up with ongoing needs. As a teacher and a parent I applaud the determination of educators to apply research-supported instruction and curriculum in their classrooms and schools. As a professional, I appreciate the extra work on everyone’s part as we develop better RTI practices to better the math achievement of all of our students.
For more information on RTI practices, visit the National Center on Response to Intervention
For more information on assessments used with RTI, visit the National Center on Student Progress Monitoring .
For recent information on mathematics education, see the work of the National Math Advisory Panel .
For more information on RTI and math instruction and intervention, read the Institute of Educational Sciences practice guide Assisting Students Struggling with Mathematics: Response to Intervention (RTI) for Elementary and Middle Schools .
For additional information on Math and RTI, see the work of Riccomini and Witzel (2010)