2. 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

3. 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

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

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

6. More information about explicit instruction……. http://www.nifdi.org/ www.k8accesscenter.org/training_resources/DirectExp licitInstruction_Mathematics.asp www.k8accesscenter.org/training_resources/DirectExp licitInstruction_Mathematics.asp http://www.specialconnections.ku.edu/cgi- bin/cgiwrap/specconn/main.phy?cat=instruction&sec tion=main&subsection=di/math http://www.specialconnections.ku.edu/cgi- bin/cgiwrap/specconn/main.phy?cat=instruction&sec tion=main&subsection=di/math http://www.nichcy.org/research/ee/learning- strategies/sp http://www.nichcy.org/research/ee/learning- strategies/sp

7. 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

8. More information on self- instruction….. http://www.sciencedaily.com/releases/2007/03/07032 6095349.htm http://www.sciencedaily.com/releases/2007/03/07032 6095349.htm http://onlinelibrary.wiley.com/doi/10.1111/j.1540- 5826.2007.00232.x/abstract http://onlinelibrary.wiley.com/doi/10.1111/j.1540- 5826.2007.00232.x/abstract http://k8accesscenter.org/training_resources/MathPrb lSlving_upperelem.asp http://k8accesscenter.org/training_resources/MathPrb lSlving_upperelem.asp

9. 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.

10. More information on peer- tutoring: http://kc.vanderbilt.edu/pals (PALS) http://kc.vanderbilt.edu/pals http://teachingld.net/pdf/teaching_how- tos/classwide_peer_tutoring.pdf http://teachingld.net/pdf/teaching_how- tos/classwide_peer_tutoring.pdf http://cecp.air.org/Peer_Tutoring.pdf http:ies.ed.gov/ncee/wwc/reports/beginning_reading/ cwpt/index.asp

11. 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

12. More information about Visual Representations: http://www.k8accesscenter.org/training_resources/CR A_Instructional_Approaches.asp http://www.k8accesscenter.org/training_resources/CR A_Instructional_Approaches.asp http://specialconnections.ku.edu/cgi- bin/cgiwrap/speccon/main.php?cat=instruction&secti on=main&subsection=math/cra http://specialconnections.ku.edu/cgi- bin/cgiwrap/speccon/main.php?cat=instruction&secti on=main&subsection=math/cra http://www.coedu.usf.edu/main/departments/sped/m athvids/strategies/cra.html http://www.coedu.usf.edu/main/departments/sped/m athvids/strategies/cra.html

13. Effective Math Intervention Strategies What Works Clearinghouse http://ies.ed.gov/ncee/wwc/ Best Evidence Encyclopedia (BEE http://www.bestevidence.org Center on Instruction http://centeroninstruction.org/index.cfm

14. 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: http://www.nap.edu/catalog.php?record_id=9822 http://www.nap.edu/catalog.php?record_id=9822 Steedy, K., Dragoo, K., Arefeh, S., & Luke, S. (2008). Effective mathematics instruction. Evidence for Education, 3(1), 1 – 13.