What must students possess to be successful in mathematics? Conceptual Understanding Concepts, operations, relations Procedural Fluency Carrying out procedures flexibly, accurately, efficiently and appropriately Strategic Competence Ability to formulate, represent, and solve mathematical problems

Success Continued Adaptive Reasoning Logical thought, reflection, explanation, and justification Productive Disposition Seeing mathematics as sensible, useful, worthwhile, along with a belief in diligence. Kilpatrick, Swafford, & Findell, 2001

Effective Mathematics Instruction: What Works! Systematic and explicit instruction Self-instruction Peer-tutoring Visual Representation

Explicit Instruction Instruct- ional Delivery Compo- nents Provide Feedback Frequent Student Responses Appropriate Pacing Adequate Processing Time Monitor Responses

More information about explicit instruction……. licitInstruction_Mathematics.asp licitInstruction_Mathematics.asp bin/cgiwrap/specconn/main.phy?cat=instruction&sec tion=main&subsection=di/math bin/cgiwrap/specconn/main.phy?cat=instruction&sec tion=main&subsection=di/math strategies/sp strategies/sp

Self-Instruction Setting goals Keeping on task Checking your work as you go Remembering to use a specific strategy Monitoring your own progress Being alert to confusion or distraction and taking corrective action Checking your answer to make sure it makes sense and that the calculations are correct

More information on self- instruction… htm htm x/abstract x/abstract lSlving_upperelem.asp lSlving_upperelem.asp

Peer-Tutoring The teacher trains students to act as both tutors and tutees. Peer-tutoring programs benefit from using highly structured activities. Materials used for the lesson should be provided to the students. Continual monitoring and feedback from the teacher helps students stay focused on the lesson and improving their tutoring and learning skills. A student with LD should be paired with one more proficient.

More information on peer- tutoring: (PALS) tos/classwide_peer_tutoring.pdf tos/classwide_peer_tutoring.pdf cwpt/index.asp

Visual Representations Since math is such a complex process, individuals need visual representations (manipulatives, pictures, number lines, and graphs, to name just a few) to make sense of what is very difficult! CONCRETE-REPRESENTATIONAL-ABSTRAC T (CRA) or CONCRETE-SEMICONCRETE- ABSTRACT (CSA) CRA or CSA is what it is all about with respect to Visual Representations

More information about Visual Representations: A_Instructional_Approaches.asp A_Instructional_Approaches.asp bin/cgiwrap/speccon/main.php?cat=instruction&secti on=main&subsection=math/cra bin/cgiwrap/speccon/main.php?cat=instruction&secti on=main&subsection=math/cra athvids/strategies/cra.html athvids/strategies/cra.html

Effective Math Intervention Strategies What Works Clearinghouse Best Evidence Encyclopedia (BEE Center on Instruction

References Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001) Adding it up: Helping children learn mathematics. Retrieved October 7, 2013, from the National Academies Press Web Site: Steedy, K., Dragoo, K., Arefeh, S., & Luke, S. (2008). Effective mathematics instruction. Evidence for Education, 3(1), 1 – 13.