Concrete-Representational-Abstract Techniques – a threepart instructional strategy where the teacher uses concrete materials (manipulatives) to model a concept to be learned, then uses representational terms (pictures), and finally uses abstract, symbolic terms (numbers, math symbols).
Explicit and Systematic Instruction – teacher-led demonstrations of various strategies that students, in turn, use to guide their way through the problem-solving process.
Dyscalculia – a form of learning disability that causes an individual to have difficulty in understanding concepts of quantity, time, place, value, and sequencing, and in successfully manipulating numbers or their representations in mathematical operations.
Intervention – specific services, activities, or products developed and implemented to change or improve student knowledge, attitudes, behavior, or awareness.
Mathematical Proficiency – a term developed by the National Research Council that describes five interrelated strands of knowledge, skills, abilities, and beliefs that allow for mathematics manipulation and achievement across all mathematical domains (e.g., conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition) (Kilpatrick et al., 2001).
Operations – mathematical procedures such as addition, subtraction, multiplication, and division.
Peer Tutoring – an instructional arrangement where students work in pairs to help one another learn material or practice an academic task.
Representation Techniques – visually or schematically presenting the ideas or information contained in word problems in language or visual media.
Self-Instruction – an instructional approach that teaches students to use a variety of self-statements or verbal prompts to guide themselves through the problem-solving process.
Strategy Instruction/Strategy Training – an instructional approach that teaches students how to use the same tools and techniques that efficient learners use to understand and learn new material or skills.