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December 2023 – Link Lines

Educator’s Article:

Addressing Specially Designed Instruction in the Co-Taught Math Classroom
by Jason Betzner, M.Ed.


Administrator’s Corner
Facilitating Inclusive Specially Designed Instruction in Mathematics
by Cathy Buyrn, M.Ed.

School leaders have been struggling with the post-pandemic challenges of addressing learning loss for all students in K-12 schools. All content areas have been impacted by specific skill gaps, but these gaps have been especially troubling in the areas of literacy and mathematics. The need for skill-gap closing targeted instruction in literacy and mathematics has never been more critical than it is now. Targeted instruction is necessary for all students with learning loss related to the pandemic, but it is critical for students with disabilities who have layers of skill gaps related to their specific disabilities that have been exacerbated by pandemic related learning loss. This edition of Link Lines will address skill-gap closing specially designed instruction (SDI) in mathematics. Look for strategies for facilitating skill-gap closing SDI focused on literacy in the next edition of Link Lines.

Prior to the pandemic, during the 2016-2017, 2017-2018, and 2018-2019 school years, the Virginia Mathematics Standards of Learning (SOL) assessment results indicated that pass rates for students without disabilities were consistently above 80% (i.e., 84%, 82%, 86%) (Virginia Department of Education [VDOE], 2023). During those same years, the pass rates for students with disabilities were consistently below 60% (i.e., 48%, 48%, 55%) (VDOE, 2023). The achievement gap between students without and students with disabilities was significant prior to the pandemic (VDOE, 2020a). That means the challenge of meeting the needs of students with disabilities in the mathematics classroom was already an area that needed to be addressed with improved efforts to develop more effective SDI. The pre- and post-pandemic pass rates for these same student groups on the Virginia Mathematics SOL assessments indicate that the achievement gap between students without and students with disabilities remains significant (See Table 1).

Table 1 

Pre- and Post- Pandemic Virginia Mathematics Pass Rates for Students without Disabilities & Students with Disabilities

Note: There were no SOL Assessment results during the 2019-2020 academic year because of COVID-19 related school closures. (VDOE 2023)

These data indicate that SDI focused on closing specific skill gaps in mathematics should be a priority for inclusive school leaders. Students with disabilities will never have full access to the general education curriculum or make progress in that curriculum (see our Summer Edition) if changes aren’t made to mathematics SDI. Inclusive school leaders need to help teachers determine how to balance participation in the general education classroom during mathematics instruction, SDI focused on students’ mathematics Individualized Education Program (IEP) goals, and the critical links between the two. It is not the job of the special education teacher to just help students with disabilities fill in the blanks of all general education assignments in the mathematics classroom. Closing specific skill gaps to build prerequisite skills should be a priority. 

A common strategy for giving students access to grade level mathematics is the provision of accommodations. Mathematics accommodations are meant to allow students to develop grade level concepts without the barriers created by prerequisite skill deficits. A common accommodation is allowing the use of a calculator when calculators are not allowed for students without disabilities. Inclusive school leaders should provide guidance to special education teachers about the appropriate use of mathematics accommodations including calculator use. It is important to make sure that calculator use is not used as a replacement for SDI focused on developing critical prerequisite skills and concepts.

A calculator accommodation may be necessary for some students with disabilities to participate in grade level mathematics activities, however as noted, it is not a replacement for developing mathematical conceptual understanding or fluency. If students have a calculator accommodation, teachers should provide SDI focused on the appropriate and proper use of that calculator. A first step in calculator SDI should be to help students determine whether the calculator is an appropriate tool for a specific problem. After students have become proficient with determining the appropriate use of the calculator for specific mathematics problems, they should receive explicit instruction in the proper use of the calculator for each type of problem. For some students it might be more appropriate to provide SDI on the use of a completed hundreds chart or multiplication table instead of providing a calculator (VDOE, 2020b). More information about math aids allowable on the Virginia SOL mathematics assessments can be found in the Explanation of Testing Accommodations for Students with Disabilities:  Math Aids resource (VDOE, 2020a). 

While guidance regarding the use of allowable mathematics testing accommodations is helpful for special education teachers making decisions about their students, school leaders should make sure that teachers do not substitute accommodations for SDI focused on building conceptual understanding, fluency, and progress in the general education curriculum. Additionally, it is important that special education teachers understand the difference between allowable testing accommodations and accommodations appropriate for developing concepts and fluency during instruction. Students should have access to all accommodations necessary to develop skills, regardless of their appropriateness during standardized testing.

Inclusive school leaders should work with teachers to ensure that students with disabilities receive SDI focused on their mathematics deficits designed to reduce reliance on accommodations and make progress in the general education curriculum. Students should simultaneously receive accommodation supported grade level concept development and skill-gap closing SDI. Evidence-based SDI in mathematics includes explicit instruction, formal mathematical language, concrete-representational-abstract (C-R-A) connections, fact and computational fluency, and problem-solving strategies (VDOE, 2020a). The key points of these five evidence-based SDI mathematics strategies are detailed in Table 2.

Table 2 

Evidence-Based Specially Designed Mathematics Instructional Strategies

Strategy Key Points
Explicit Instruction Effective explicit instruction involves the teacher providing the following:

  • Modeling steps using concise language.
  • Providing guided practice opportunities.
  • Providing independent practice opportunities.
  • Using supports during modeling and practice.
    • Asking the right questions.
    • Eliciting frequent responses.
    • Providing feedback.
    • Being planned and organized.
Formal Mathematics Language Teachers should promote students’ understanding of formal mathematics vocabulary by:

  • Using formal mathematics vocabulary terms.
  • Using similar or related terms correctly and precisely.
  • Planning for language use prior to instruction.
  • Including explicit vocabulary activities in instruction.
  • Holding students accountable.
Concrete, Representational, and Abstract (C-R-A) Connections The Concrete-Representational-Abstract (C-R-A) framework includes three forms of mathematics: concrete, representational (pictorial), and abstract.

  • Concrete: three-dimensional, hands-on materials and objects
  • Representational (Pictorial): two-dimensional pictures, images, or virtual manipulatives
  • Abstract: numbers, symbols, and words

The use of C-R-A supports students in developing a deeper conceptual understanding of mathematics beyond superficial procedural knowledge.

Fact and Computational Fluency
  • Students exhibit computational fluency when they demonstrate strategic thinking and flexibility in the computational methods they choose and are able to explain and produce accurate answers efficiently.
  • Teachers should use activities and games to promote fact fluency.
  • Beyond mathematics facts, students should develop fluency with computation (i.e., multi-digit addition, subtraction, multiplication, or division).
  • Fluency practice should be brief and occur daily.
Word Problem Solving
  • The majority of routine word problems that students solve in elementary and middle school fall into one of the six different schemas:
    • Total
    • Difference
    • Change
    • Equal Groups
    • Comparison
    • Ratios or Proportions
  • Teachers should provide students with verbal and gestural cues to review and recall the six schemas.
  •  When teaching problem solving strategies, DO NOT tie key words to operations.
  • When teaching problem solving strategies, DO NOT define word problems by the operation.
  •  When teaching problem solving strategies, DO teach students an attack strategy to help guide the process of problem solving.
  • When teaching problem solving strategies, DO teach word-problem schemas.

Note. Retrieved from Students with disabilities in mathematics:  Frequently asked questions, VDOE, 2020, pp. 10-11.

It is important that school leaders provide guidance and support for special education teachers about the effective use of accommodations and SDI in mathematics. It may be necessary to make sure both general and special education teachers understand that there are some common practices that need to be discontinued for all students in order to develop skills and concepts at all levels (VDOE, 2020c). As noted in Table 2, the use of key words and operation specific definitions of word problems are ineffective strategies for all students. It is not helpful for special education teachers to replace these strategies with more effective schematic strategies if the general education teachers are still using ineffective approaches. 

Inclusive school leaders can point teachers to the Educators’ Lesson in this edition of Link Lines for  more information about developing effective SDI in mathematics. In addition to the strategies detailed in this edition of Link Lines, school leaders should provide a comprehensive professional development plan designed to improve mathematics instructional practices for both general and special education teachers. Outdated and ineffective practices only create confusion for students and limit outcomes. In our post-pandemic classrooms, students have no time to waste if we are ever going to address learning loss and persistent achievement gaps between students without and with disabilities.

Additional Resources

Virginia Department of Education Evidence-Based Specially Designed Instruction in Mathematics Webinar

Virginia Department of Education Mathematics Professional Learning

IRIS Center at Vanderbilt University High-Quality Mathematics Instruction:  What Teachers Should Know

IRIS Center at Vanderbilt University Progress Monitoring Mathematics

National Center on Intensive Intervention at The American Institutes for Research Mathematics Sample Lessons for Intensifying Intervention

National Center on Intensive Intervention at The American Institutes for Research Intensive Intervention in Mathematics


VDOE, (2023). Test results build-a-table [Database].

VDOE, (2020a). Evidence-based specially designed instruction in mathematics resource guide.

VDOE, (2020b). Explanation of testing accommodations for students with disabilities: Math aids.

VDOE, (2020c). Students with disabilities in mathematics:  Frequently asked questions.


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