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Response to Intervention in the Mathematics Classroom
Awsten Olyano
Seattle Pacific University
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Response to Intervention in the Mathematics Classroom
When we first talked about response to intervention (RtI) this quarter I liked the idea of using a
preventative framework with a tiered system to identify and assist students having difficulty in the
classroom with general instruction. My first thought was how could RtI be used within a mathematics
curriculum to better serve all students and inform my practice as a reflective educator. The special
education law IDEA introduced RtI in 2004 as a paradigm shift in thinking about special education. RtI
is an accepted and increasingly popular alternative to the discrepancy model of identification for
struggling students. Instead of using the discrepancy model to identify struggling students RtI seeks to
screen students and measure their growth to research based interventions in order to choose the most
effective strategies for instruction. If the student fails to respond to the intervention then special
education services may need implementing. Within the RtI framework the responsibility for teaching
students relies on teachers being data driven research based decision-makers (Lembke, Hampton &
Beyers, 2012), which is something that rings true to my own educational philosophy on the profession of
teaching. In summary "RtI is a set of scientifically research-validated practices that are deployed in
schools using the scientific method as a decision-making framework" (Tilly, 2006 as cited in Moors,
Weisenburgh-Snyder, & Robbins, J. (2010, p.227).
The RtI approach has frequently been used and researched in reading interventions but less often
with in mathematics instruction. Response to Intervention in Mathematics: Critical Elements by Lembke,
et al. (2012) seeks to provide a description of the elements necessary for RtI implementation to be
effective within mathematics. The necessary elements of RtI in mathematics are screening, progress
monitoring, data based decision-making, diagnostic assessment, and a tiered intervention framework used
to guide intervention and assess effectiveness. These elements form a basis for implementing RtI within
the mathematics curriculum and are predicated on using high-quality research-based practices for core
instruction also well as during interventions (Lembke, et al.).
In order for RtI to be implemented effectively professional educators first need access to high
quality data about student performance, which is the purpose of screening. Screening should be used
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three times throughout the school year for example fall, winter and spring (Lembke et al., 2012).
Screening must be reliable and valid in order to provide needed high quality data to inform on
effectiveness of a given instructional strategy. In addition screening involves all children so those who
could have learning difficulties can be identified, further assessed and assisted as needed. Lembke, et al.
cites several resources for choosing screening tools that have been evaluated for validity and cites one
commonly used measurement for screening called Curriculum-Based Measurement CBM. This screening
process provides information about student performances several times a year and is used to identify
students who may be at risk of learning difficulty or who are already below benchmark standards.
In addition screening can also provide progress monitoring to inform a data-driven decision about
instructional practices and intervention. Progress monitoring of students academic growth aligns with the
opinion of the NCTM who recommend teachers gather data and alter instruction based on interpretations
of the data. This can include changing the “instruction, content, pacing, review, and enrichment or
remediation for students who may be struggling” (Lembke et al., 2012, p. 259). Student growth is
attained through screening while the use of progress monitoring is the key tool used to inform data-based
decision-making. Progress monitoring allows teachers to determine the effectiveness of a given
instructional program among individual students. For example after monitoring the progress of a student
to a given intervention then the educator can make projections about whether or not a change in
intervention strategies is needed.
If the student has not shown expected growth additional analysis can be used in the form of
diagnostic assessments to provide educators with a more complete picture of students understanding of
concepts and procedures. Several tools are mentioned by Lembke et al. (2012) include ConcreteRepresentational-Abstract (CRA) assessment, error analysis and teacher interviews. CRA measures a
students understanding at all three levels as opposed to most mathematical assessments, which
concentrate on the abstract level of symbolic manipulation to solve problems. Error analysis can be used
to classify the types of mistakes made by the student as well as documenting the frequency with which
different types of errors occur. Error analysis allows teachers to target specific types of misconceptions
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by the learner. A third approach mentioned is teacher interviews with individual students while solving
mathematical problems this diagnostic method allows teachers to take notes on the students thinking
about the problem and identify misconception in procedure and concept. The use of screening, progress
monitoring and diagnostic data is to provide professionals with the information in order to make datadriven decisions about the extent and types of intervention necessitated by the information attained.
Within the RtI model screening, progress monitoring, diagnostic assessments and data-driven
decisions all inform which tier of intervention is suitable for the student. The RtI model uses a threetiered system. Tier one or primary intervention is done school wide with research-based core curriculum.
High frequency of implementation of research-based core curriculum allows educators to determine if
additional support is need at the next level of intervention. The second level or tier-2 is for students who
may fall just below their average achieving peers to students just above tier 3 students on assessments.
Tier 2 interventions provide additional support for small groups of students multiple times a week for
between 10 to 15 weeks (Lembke, et al., 2012). With tier-2 students it is especially important to monitor
progress to assess whether or not the intervention is successful or needs further modification. Lembke, et
al. also suggests tier-2 instruction should be explicit, systematic and supplemental to the core-instruction.
Further instruction at the second tier should involve modeling, guided practice and corrective feedback
while learning the targeted skill. If a student does not respond to primary or secondary tier intervention
strategies or students are far below average peers on benchmark assessment they may necessitate the most
intensive intervention in the form of one-on-one tutoring. As with tier-2 students Lembke, et al. suggest
using explicit instruction, opportunities to verbalize thought processes, using concrete examples, frequent
feedback and weekly progress monitoring.
While RtI is a multi-tiered framework that requires research-based practices be implemented at
every level of instruction, many benefits can be seen from implementing such a system within a
mathematics curriculum. Lembke, et al. (2012) describes both what is needed to implement RtI
successfully within the mathematics classroom and some of the key features of the element involved. RtI
in mathematics is a viable option for increasing students success within a subject traditionally viewed as
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difficult to master. I agree with Lembke, et al. that RtI starts in the general education classroom with
research-based instructional strategies where students are assessed and identified for interventions that are
more intensive. I like the framework of RtI for many reasons, first RtI is research based and data-driven
allowing educators to feel confident they are doing the most possible to ensure student success. Secondly,
I like that RtI focuses on student growth as a measure of success. Third I like the idea of a preventative
strategy which identifies struggling students before they become so far behind that catching up with their
average achieving peers is not plausible. Finally, mathematics is a subject, which builds upon previous
knowledge and seems like the perfect setting to implement a preventative strategy for struggling students.
Thus, more research into the specifics of which research-based instructional strategies work well along
with other factors that might determine successful implementation of RtI would be desirable. In addition,
procedures for assisting teachers in implementing RtI need investigation so RtI can be used without
substantially increasing the time demands on educators who already have significant time demands.
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References
Lembke, E. S., Hampton, D., & Beyers, S. J. (2012). Response to Intervention in Mathematics:
Critical Elements. Psychology In The Schools, 49(3), 257-272.
Moors, A., Weisenburgh-Snyder, A., & Robbins, J. (2010). Integrating Frequency-Based
Mathematics Instruction with a Multi-Level Assessment System to Enhance Response to
Intervention Frameworks. Behavior Analyst Today, 11(4), 226-244.