Mathematics, the Common Core, and RTI: An Integrated Approach to Teaching in Todays Classrooms

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Dolores Burton and Charlotte Rosenzweig. In this chapter you will learn: The importance of teaching students the language of mathematics A definition of mathematical literacy Seven strategies and activities for promoting mathematical literacy Common Core Looks like you do not have access to this content. Click here for free trial login. Loading content A Small. A Normal. Apr 10, AM. Without Warning by Thomas C.

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We take abuse seriously in our discussion boards. Thus, RTI has the potential to influence how and when LD is identified, as well as the nature of early intervention and instruction. IQ-achievement discrepancy, as its name suggests, identifies LD based on severe discrepancy between intelligence and achievement test scores. The approach has been criticized on a number of fronts. Second, the approach has been criticized for its variable implementation Fuchs et al.

Fourth, and conversely, it has been argued that IQ-achievement discrepancy overlooks a population of students with similarly low achievement and processing deficits but no discrepancy Fletcher et al. Collectively, these concerns helped to propel the emergence of RTI. RTI is used to identify students with LD and to determine early intervention. This is accomplished through evaluation of student response to targeted, high-quality instruction that has been demonstrated as effective for most students Batsche et al.

In this sense, RTI emphasizes "student outcomes instead of student deficits" Kavale et al. RTI also prescribes the use of research-validated interventions to help ensure that students have access to appropriate learning experiences. It is focused on providing early and more immediate support for student needs by screening students as early as kindergarten Fletcher et al.

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Steps 2 and 3 are iterative. Initially, students are monitored for their responsiveness to general education instruction, that is, instructional approaches validated as effective for most students and differentiated as needed to meet broad student needs Batsche et al.

Different courses of action can be taken depending on the number of students found not able to perform. If the number is sufficiently large, it is concluded that the instructional program is inadequate and the overall program is modified. If instead only a small percentage of students fail to perform, such students are removed from the general program of instruction to participate in a targeted, empirically validated intervention. Student responsiveness to intervention is used to determine further course of action.

Students who are responsive to the intervention are reintegrated into the traditional program of instruction. Students determined to be unresponsive are promoted to the next "tier" of intervention, different in content or rigor. Their progress is again monitored and the course redetermined. Although some students may respond to an intervention, they still may be referred to special education if it is determined infeasible to maintain the intervention in the regular classroom Batsche et al.

A variety of methods may be used to identify at-risk students. RTI uses empirically-validated interventions that have been demonstrated as effective for most students. The number of levels or "tiers of intervention" ranges from The tiers vary in their intensiveness i. Those who view RTI as primarily a means for identification advocate using fewer tiers, which produces fewer false negatives i.

Those who view RTI more as a means for improving instruction and remediating students advocate using more tiers, which enables more intensive intervention and produces fewer false positives i. Practitioners generally use the problem-solving method, while the standard treatment response method has been used in most research studies.

The distinguishing features of the problem-solving approach are that intervention occurs within the classroom and is individualized to the student. The individualized nature of the approach is based on the belief that success of an intervention cannot be predicted based on student characteristics, and no single intervention will be successful for all students Fuchs et al.

The different versions of problem-solving RTI vary in the number of tiers of intervention. The standard treatment response approach provides the same empirically validated, fixed-duration intervention to all students with similar problems in a domain Fuchs et al.

Unlike the problem-solving approach, the standard treatment response intervention is provided individually or in small groups outside the classroom. Intervention is 2-tiered, and lack of progress in Tier 2 elicits evaluation for possible disability. Because the standard-treatment approach has only 2 tiers, it is thought to be more straightforward to implement, and therefore more practical Fuchs et al. However, it is not known for certain that this approach is implemented more faithfully than the problem-solving approach Fuchs et al.

There is no standardized method for assessing student responsiveness to intervention. Measurement may be based on performance at the end of the intervention, growth over the course of the intervention, or both dual discrepancy [Fuchs, ]. However, RTI has its roots in curriculum-based measurement Batsche et al.


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Use of multiple data sources is also encouraged Fuchs et al. Therefore, progress monitoring is a frequent form of RTI assessment and considered by some a key component of effective RTI Batsche et al. A reference standard for assessing progress must also be chosen: scores may be compared to a normative sample; a limited norm developed using a subset of students who are the focus of the intervention ; or a benchmark Fuchs, Choice of reference method may be constrained by the type of intervention.

With an intensive intervention, it may be necessary to use a limited norm Fuchs, It is unclear how RTI may affect teacher roles. However, it is likely that professionals that formerly spent time administering IQ tests will take on responsibilities focused more on intervention-related assessment Fletcher et al. However, general and special educators are also expected to play a collaborative role, particularly within the problem-solving approach Batsche et al.

Mathematics, The Common Core, and RTI

RTI has the endorsement of many researchers and professional and government organizations Fletcher et al. Controlled, research studies using the standard treatment model have shown a significant impact of RTI on student progress Marston, Evidence addressing the effectiveness of the problem-solving model is less plentiful and has been described as less persuasive Fuchs et al.

The approach is not without potential problems. Presently, RTI may not be feasible for large-scale adoption Fuchs et al. It also has been pointed out there are few criteria for distinguishing between "no response to instruction" and "marginal response to instruction," making it difficult to accomplish consistent implementation Kavale et al. Another criticism is RTI's emphasis on reading disability. Contemporary conceptualizations of LD include deficits in math, writing, and reading comprehension; thus RTI is considered by some an inadequate means to gauge LD Johnson et al.

However, from an instructional standpoint, RTI can be used with any academic subject for which frequent data-sensitive measurements are available Batsche et al. Although these are generally less well developed outside of reading, they are potentially feasible. Potential change to how students with LD are identified and early intervention is designed is of great potential significance, and RTI is currently being investigated by the National Research Center on Learning Disabilities and the Office of Special Education Programs.

Many experts believe that more needs to be understood before RTI can be accepted as a valid method for LD identification Fuchs et al. Indeed, today's classrooms are incredibly diverse, housing students from different cultures, socioeconomic backgrounds, and disability groups. By contrast, traditional curricula are "one-size-fits-all," designed to meet the needs of the "typical" student. UDL was inspired by universal design in architecture, a movement to design structures with all potential users in mind and incorporate at the outset access features such as ramps and elevators Connell et al. By working at the design level, accessibility features could be incorporated more elegantly and inexpensively.

UDL applies this same strategy to curricula, considering the needs of all students at the design stage and building in features that support full accessibility. Technology plays an important role in UDL, its flexibility enabling practical and elegant solutions. Another source of guidance and inspiration for UDL is neuroscience.

Neuroscience research suggests the existence of three broad neural networks in the brain that oversee three fundamental facets of learning e. What is distinctive about the UDL perspective is that this triad of abilities is understood to differ from student to student. The three UDL principles guide the design of flexible curricula by calling for the embedding of options that support differences in recognition, strategic, and affective networks:. Using these three principles, all aspects of the curriculum — goals, methods, materials, and assessments — are made flexible.

These teaching methods reflect neuroscience-based insights into how each learning network functions, combined with an understanding of how digital media can support flexibility. For example, the third teaching method to support recognition learning is to provide multiple media and formats.

This teaching method leverages the fact that recognition networks can extract meaning using different sensory modalities and acknowledges that the optimal presentation modality may differ from student to student. Although presentation of multiple media and formats might be challenging in a classroom limited to printed text and hardcopy images, it is realizable using digital materials.

This is one example of how digital materials and UDL teaching methods can facilitate the successful implementation of UDL. Figure 1. CAST has developed three sets of UDL teaching methods to help teachers support learners' diverse recognition, strategic, and affective networks. For example, CAST has developed digital, supported reading environments that integrate research-supported approaches to reading comprehension instruction with UDL features.

CAST is conducting this work with diverse students including students with learning disabilities, students who are deaf or hard of hearing, students with cognitive disabilities, and English language learners. RTI and UDL differ from one another in that RTI is a process for making educational decisions based on an at-risk student's success or failure during specialized intervention, while UDL is a process for making curriculum design decisions to maximize success in the general curriculum.

However, RTI and UDL share the objective of improving educational outcomes for students with disabilities and are similar in several important ways. First, both RTI and UDL recognize that poor achievement does not necessarily reflect disability, but rather may also reflect poor instruction. That is, in some cases the curriculum, not the student, may be deficient. RTI puts this belief into practice by prescribing that general education curricula incorporate research-validated instruction and intervention by making LD identification contingent on the program of instruction and by acknowledging that there are cases where changes should be made to general classroom instruction in place of student intervention Batsche et al.

UDL also encourages the use of research-validated instruction and intervention Dalton et al. Second, RTI and UDL both reflect the understanding that a curriculum that is effective for one student may not be effective for another student. With RTI, this is most readily apparent with the individualized approach to intervention that is part of the problem-solving method. With UDL, the curriculum is designed to incorporate a wide variety of options in its goals, materials, methods, and assessment so that the curriculum in its entirety is flexible and accommodating of individual student needs.

Third, RTI and UDL treat assessment as something that should inform instruction and intervention and consider once-a-year test scores insufficient to determine student ability. In RTI, students' responsiveness is commonly monitored over time and with respect to multiple interventions; while in UDL, multiple, ongoing assessments are administered. The use of curriculum-based measurement as a means to inform teachers about the effectiveness of instruction and guide decision-making regarding appropriate instruction and intervention is a key point of convergence of RTI and UDL.

With effective implementation of curriculum-based measurement, interventions can be determined while instruction is still ongoing and before a student fails. Thus, professional development and ongoing support within the schools is important. In addition, technology may be an important tool. Thus, technology can be used to reduce some of the difficulties of implementation.

Its inherent flexibility helps make the design of an adaptable curriculum much more feasible. Indeed, RTI has been criticized as lacking a systematic decision-making process i. Moreover, individualization, a central component of the problem-solving approach, is of great difficulty for teachers Batsche et al. The UDL framework offers a potential means to guide such decisions.

Mathematics, the Common Core & RTI: An Integrated Approach to Teaching in Today's Classroom

For example, differences in recognition, strategic, and affective learning parameters offer a means for selecting effective interventions. The problem-solving approach to RTI is already an individualized approach that considers students in a case-by-case fashion. The UDL framework could help to guide analysis and decision-making for each student as part of RTI by focusing attention on individual learner's recognition, strategic, and affective strengths and challenges. By designing interventions with flexible supports for recognition, strategy, and affect it may be possible to reduce the number of RTI tiers that are necessary and increase the number of students who respond.