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School of Education
Training & Technical Assistance Center

A Six-Step Approach to Teaching Mathematics To Students With Disabilities Elaborated

By Mary Murray Stowe, M.Ed.
 
February/March 2014

 

Emerging research suggests that students with moderate and severe disabilities can learn content maligned with grade-level standards while continuing to work on basic numeracy (Saunders, Bethune, Spooner, & Browder, 2013).  Use of evidence-based instructional strategies and practices is critical to ensure students learn necessary content. Based on the findings from several studies, Saunders, Bethune, Spooner, and Browder (2013) developed a six-step approach to teaching mathematics that can be used in all math classrooms—both general and special education. The following example is from a seventh-grade class.

Step One requires selecting the topic and creating objectives.  Mathematics classrooms across Virginia use the Virginia Mathematics Standards of Learning (VAMSOL) to guide the selection of topics and creation of objectives.  For the purposes of this example, SOL 7.16 was selected and an Enhanced Scope and Sequence lesson was used as the abstract (within the Concrete-Representational-Abstract approach) or final lesson, Properties (7.16).  Of further assistance would be an examination of the standards from grade levels that precede the seventh grade SOL.  Those leading into work at this grade level include 3.20, 4.16, 5.19, and 6.19.

Step Two involves identifying real-life or real-world situations for application of content.  This step makes the learning “real” for the students and provides motivation to engage in the learning.  Teaching core content in a meaningful way leads to better maintenance and generalization of the targeted skill (Collins, Hager, & Galloway, 2011).  This notion is evident within the Virginia Math SOL, including wording such as real world or practical problems.  For the SOL selected (MA 7.16), we must discover real-world application.  Several sources were located through an Internet search.

Which of the operations below are commutative (changing the order of addition/multiplication does not change the meaning) and which are not?  Explain your answers.

  1. To put on your coat and to pick up your boots.
  2. To wash your clothes and to dry them.
  3. To put on your left shoe and to put on your right shoe.
  4. To hang up the phone and to say goodbye.

If three envelopes can be mailed using three 24c stamps and three 17c stamps, one of each on each envelope, what would you need if you used one stamp on each envelope instead of two?

3(24 + 17) = 3(41)

Step Three ensures the incorporation of evidence-based instructional practices to provide effective instruction.  Effective instruction for students struggling with mathematical concepts must include explicit, systematic instruction with appropriate, corrective feedback.  For purposes of this concept, properties, the concrete-representational (pictorial)-abstract (CRA) approach was selected.  Several sources exist to support the CRA approach.

  • Beller, L. (2010). Creating meaning in mathematics for ALL learners. Norfolk, VA:  TTAC Network News. http://ttac.odu.edu/wp-content/uploads/pdfs/Feb_March_2010.pdf, p. 4.  This article describes the process of creating a CRA lesson.
  • CRA Mathematics Planning Tool, accessed by clicking on the word Tool.
  • Resources From the TTAC William and Mary Library:       
    • Hands-on standards, deluxe edition: The first source for introducing math manipulatives (Call Number CMT 134).  Lessons covering the concept of properties for addition and multiplication are included in both editions listed here:  Grades 5-6 Edition and Grades 7-8 Edition.
    • Teaching inclusive mathematics to special learners, K- 6 by Julie A. Sliva (Call Number CMT 97).  The text offers excellent information, including a chart of strategies and supports (pp. 51-53).
    • Teaching mathematics meaningfully: Solutions for reaching struggling learners by David Allsopp (CMT 86) with his colleagues, Maggie Kyger, and Louan Lovin (2007).  This source provides a guide for creating CRA lessons.
    • Response to intervention in math by Paul J. Riccomini and Bradley S. Witzel (2010). (Call number currently being assigned.)
  • Dr. Bradley Witzel explaining the CRA instructional sequence  
  • The Math Vids website includes a page on the instructional sequence using the CRA approach

Teachers should also consider additional avenues to intensify instruction.  These considerations may be found within the chart linked here. Finally, teachers must identify Mathematical Process Skills to be present within effective lessons.  Click here to access the document outlining these skills and their evidence within a well-constructed lesson.

Step Four includes consideration of instructional supports.  Instructional supports include graphic organizers to aid with problem solving.  Teaching Inclusive Mathematics to Special Learners, K- 6 by Julie A. Sliva (Call Number CMT 97) mentioned above provides a chart of strategies and supports (pp. 51-53).  If the teacher has not selected the CRA approach as the evidence-based instructional strategy, manipulatives would be considered a support.  Other supports might include extended time on tasks or exams, increased white space on paper, preferred seating, structured notes for differentiation, reduction of the number of written problems, and so on.

Step Five points to the importance of progress monitoring both during and after instruction.  The type of progress monitoring selected depends on the concept being taught and the instructional delivery method used.  If the CRA approach is used, a CRA assessment may be used to determine where along the continuum understanding has been mastered, and then approach instruction at the level of student understanding.  Allsopp and colleagues (2007) discussed this approach to beginning instruction.  Progress is subsequently monitored as the student moves through the levels of understanding.

Step Six involves planning for generalization. The instructional process must incorporate a plan for addressing generalization and mastery of the skill being taught.  Struggling students will need sufficient practice of the skill (to include additional numbers and contexts) and inclusion of real-world situations emulating Step Two to increase the likelihood of generalization taking place.

Use of this six-step process increases mastery for struggling students as the necessary components are built into the plan to ensure understanding. 

 References

Allsopp, D., Kyger, M., & Lovin, L. (2007). Teaching mathematics meaningfully: Solutions for reaching struggling learners. Baltimore, MD:  Brookes Publishing.

Beller, L. (2010). Creating meaning in mathematics for ALL learners. Norfolk, VA:  TTAC Network News.  http://ttac.odu.edu/wp-content/uploads/pdfs/Feb_March_2010.pdf, p. 4.

Collins, B. C., Hager, K. L., & Galloway, C.C. (2011).  Addition of functional content during core content instruction with students with moderate disabilities.  Education and Training in Autism and Developmental Disabilities, 46, 22-39.

Saunders, A. F., Bethune, K. S., Spooner, F., & Browder, D. (2013). Solving the common core equation: Teaching mathematics CCSS to students with moderate and severe disabilities. Teaching Exceptional Children, 45(3), 24-33.                                                                         

Resources

IES Practice Guide on Mathematics and RtI:  Intentional Teaching: http://educationnorthwest.org/webfm_send/718/

Virginia Department of Educational Mathematics Instructional Resources: http://www.doe.virginia.gov/instruction/mathematics/index.shtml