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Masters of Special Education with Academic Instruction Certification

Explicit Practices, Strategic Practices, and the Use of Visual Representation to Teach Arithmetic Combinations to Students with Specific Learning Disorders - Topic 54

What is it?

The current evidence base supports the following instructional practices; explicit practices, strategic practices, and the use of visual representations, to teach arithmetic combinations to students with LD.

Explicit Instructional Practices focus on systemically implemented behavioral practices to teach mathematical concepts.  Current literature supports the use of systematic, explicit instruction for teaching computation to students with mathematical difficulties. This approach is based on the behavioral theory of learning by improving instructional behavior (correct responses per minute) by manipulating consequent events (reinforcement for improved academic or social behavior).  Explicit practices include modeling, high rates of responding and practice, repetition, error correction, review and distributed practice, and frequent monitoring.  An example of this model used alone is the Constant Time Delay procedure.

Strategic Instruction Practices are based on information processing theory, focusing on how students perceive, encode, represent, store, and retrieve information.  By providing specific strategies for students to use, the practice reduces the “cognitive load” for learning higher order math skills, promotes flexibility with numbers, and provides an expanded knowledge base that can facilitate retention and retrieval.  A model that has demonstrated effectiveness is the Count-On strategy, paired with a cross age peer tutoring arrangement.

Use of Visual Representations ,including manipulatives, tallies, pictures, and number lines  to promote understanding of mathematical ideas has been found to have moderate positive effects when paired with other instructional evidence-based practices.  The concrete-representational-abstract (CRA) method used in conjunction with the DRAW strategy is an example of pairing visual representation with strategic instruction practices.

Why is it important?

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The complexities of teaching students who have been identified as having a mathematics LD are often frustrating and confusing for teachers.  It has been suggested that proficiency in solving arithmetic combinations is a critical skill to develop mathematical fluency.  By identifying effective, evidence-based strategies, this review outlines specific approaches for educators to use to help students with LD become more proficient with these foundational skills (Bryant, 2013).


Bryant, D. B. (2013). Instructional Practices for Improving Student Outcomes in Solving Arithmetic

Combinations. In B. &. Cook, Research-Based Practices in Special Education (pp. 61-85).

Boston: Pearson.