This article is the second part of a two-part series on teaching math to students with disabilities. This issue focuses on the types of materials and knowledge teachers need for teaching math to students with disabilities, particularly mathematical disabilities. The focus of Part 1 was on the needs of students learning math and how teachers can provide instruction to meet those needs. Part 1 can be found in the Fall 2018 CORE Academic Quarterly.
Students with Disabilities Learning Math – Part 2
Recap from Part 1
In Endrew F. vs Douglas County School District RE-I (2017) the United States Supreme Court ruled that for any student the “educational program must be appropriately ambitious in light of his[/her] circumstances” and “every child should have the chance to meet challenging objectives” (p. 14). This means students with disabilities, like all students in math, need to develop mathematical proficiency along all five strands described by the National Research Council in Adding It Up (Kilpatrick, Swafford, & Bradford, 2001).
- Productive disposition
- Conceptual Understanding
- Adaptive Reasoning
- Strategic Competence
- Procedural Fluency
Students with disabilities often struggle with learning math, but research verifies these students are capable of high-level learning. Two major challenges are finding the appropriate level of rigor for students and having resources that best enable teachers to provide effective instruction. There are three types of resources teachers need: materials to teach with, math content and pedagogical content knowledge (pedagogy on techniques for teaching specific content), and information or data on student math needs and progress (McLeskey et al 2017). This article is focused on understanding the importance of these three types of teacher resources.
Good instructional materials provide lessons that are focused to maximize learning time, provide prompts and directions to actively engage students, and address content systematically across all tiers of instruction. According to McLeskey et al. (2017),
Instruction, when delivered with fidelity, is designed to maximize academic learning time, actively engage learners in meaningful activities, and emphasize proactive and positive approaches across tiers of instructional intensity. (p. 69)
Many special education teachers are only provided math materials from the general education core curriculum. Core math programs do not meet the needs of students with significant learning challenges or large gaps in knowledge. Core programs have specific grade-by-grade development of key ideas designed for students on pace at grade level for tier 1 instruction. Special education teachers need materials targeting more intensive needs. These are materials designed to address the foundational math for which their students need the most help, using instructional methods that are proven effective for students struggling with math.
Teachers must resort to developing or piecing together their own curriculum materials when they are not provided appropriate materials. However, some special education teachers do not have deep math content and pedagogical content knowledge. This lack of knowledge severely limits the quality and cohesiveness of the curricula they may create on their own. Additionally, they do not have time to write and create a curriculum. Most of their students require lessons that are more explicit and focused on key foundations through systematically designed instruction (Archer & Hughes, 2011; Gersten et al., 2009; Fuchs et al., 2015). Math intervention curricula are specifically designed for students struggling with math. When they are not provided appropriate materials, teachers are placed in a situation that does not allow them to provide an effective math education. Thus, special education teachers need a math intervention program with which to teach.
Math Content and Pedagogical Content Knowledge
Special education teachers usually have good general math knowledge but may lack specialized training in math. However, they are tasked with teaching math to students who often have the greatest difficulties learning math. Strong content knowledge and pedagogical knowledge are necessary for effective special education (McLeskey et al., 2017). Special education teachers deserve to receive quality professional development centered on math instruction. All teachers teaching math need to understand the concepts being taught. They must understand the connections between and across grade level work, foundations necessary for success, and the most effective teaching and learning techniques for these concepts. This knowledge includes the connections between concepts and facts and procedural fluency, techniques for developing fluency, and techniques to teach students how to apply concepts and skills to solve a variety of problems. Special education teachers need more than general math knowledge to teach math effectively. Professional learning opportunities should both build teachers’ knowledge and equip them to implement evidence-based practices with students.
Data on Student Needs and Progress
Teachers need information on what their students need to learn, and on the progress their students are making toward student learning goals. Diagnostic assessments identify specific learning needs. For instance, a student may be strong with multidigit addition, but may need more work with multidigit subtraction. A teacher with the right content and pedagogical knowledge, will work with this student to zero in on whether the need is primarily one of skill proficiency or requires conceptual work that addresses understanding the process and purpose of regrouping and making connections to place value. Throughout instruction ongoing formative assessment is important using a variety of data resources. “Teachers should collect, aggregate, and interpret data from multiple sources (e.g., informal and formal observations, work samples, curriculum-based measures . . .)” (McLeskey et al., 2017). After instruction on specific concepts and skills, it is vital to know if the learning has taken place. This requires progress monitoring on a regular basis. Therefore, assessment data is a vital resource for teachers. “Assessment, then, in the context of effective mathematics instruction, is a process whose primary purpose is to gather data that supports the teaching and learning of mathematics” (NCTM, 2014, p. 89). Data informs teachers about the needs and progress of students and when and where instruction needs to be adjusted to better meet the learning needs of students.
Teachers of students with special needs must have resources that allow them to provide the best education possible for their students. The key resources necessary are materials designed to meet the needs of students struggling with learning math, content and pedagogical content knowledge for teachers on what and how best to teach math, and information or data on what their students need to learn and on the progress students are making during and after instruction. With the right materials, knowledge, and information special education teachers will have the resources they need to provide their students with an appropriately challenging math education.
Archer, A. L., & Hughes, C. A. (2011) Explicit Instruction: Effective and efficient teaching. New York, NY: Guilford.
Endrew F. v. Douglas County School District, RE-1, 580 U.S. (2017).
Fuchs, L. S., Fuchs, D., Compton, D. L., Wehby, J., Schumacher, R. F., Gersten, R., & Jordan, N. C. (2015) Inclusion versus specialized intervention for very low-performing students: What does access mean in an era of academic challenge? Exceptional Children,81, 134-157.
Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools (NCEE 2009-4060 ed.). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/PracticeGuide/2
Kilpatrick, J., Swafford, J., and Bradford Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Research Council, National Academy Press
McLeskey, J., Barringer, M-D., Billingsley, B., Brownell, M., Jackson, D., Kennedy, M., Lewis, T., Maheady, L., Rodriguez, J., Scheeler, M. C., Winn, J., & Ziegler, D. (2017, January), High-leverage practices in special education, Arlington, VA: Council for Exceptional Children & CEEDAR Center.
National Council of Teachers of Mathematics. (2014). Principles to Actions Ensuring Mathematical Success for All. Reston, VA: Author.