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Mathematics in a Responsiveness to Instruction Framework

Mathematics in a Responsiveness to Instruction Framework. Susan Davis, Personnel Development Consultant North Carolina Department of Public Instruction Exceptional Children Division November 2008. What is this?.

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Mathematics in a Responsiveness to Instruction Framework

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  1. Mathematics in a Responsiveness to Instruction Framework Susan Davis, Personnel Development Consultant North Carolina Department of Public Instruction Exceptional Children Division November 2008

  2. What isthis?

  3. We’ve got to stop asking children to solve problems they don’t know how to solve and, instead, teach them math.

  4. Responsiveness to Instruction The practice of providing high quality instructionmatched to student need, monitoring progress frequently to make decisions about changes in instruction or goals and applying child response data to important educational decisions. Response to Intervention Policy Considerations and Implementation, NASDSE

  5. Responsiveness to Instruction (RtI) … a school-wide system of support

  6. Core Components of RtI • Screening (Formative Assessment) • A continuum of services available to all students (from universal to intensive) • Research-Based Interventions • Progress Monitoring (Formative Assessment) • Data-based Decision Making

  7. SO WHAT ABOUT MATH in an RtI framework?

  8. National Assessment of Educational Progress (“NAEP”) • 40% of students at or above proficient (Grade 4) • 7% of students at or above advanced (Grade 4) • 32% of students at or above proficient (Grade 8) • 7% of students at or above advanced (Grade 8)

  9. "Arithmetic is being able to count up to twenty without taking off your shoes." –Anonymous

  10. 5 Strands of Mathematical Proficiency • Understanding • Computing • Applying • Reasoning • Engagement Source: National Research Council. (2002). Helping children learn mathematics. Mathematics Learning Study Committee, J. Kilpatrick & J. Swafford, Editors, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

  11. NC Standard Course of Standard Strands (or goals): Number and Operations Measurement Geometry Data Analysis and Probability Algebra Problem Solving

  12. Three General Levels of Math Skill Development (Kroesbergen & Van Luit, 2003) ** Number Sense ** Basic math operations ** Problem-solving skills Source: Kroesbergen, E., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs. Remedial and Special Education, 24, 97-114..

  13. Number Sense Basic math operations Problem-solving skills Common Threads in Research and Practice Understanding Computing Applying Reasoning Engagement Number and Operations Measurement Geometry Data Analysis and Probability Algebra Problem Solving

  14. Two more … • FLUENCY (Automaticity) • LANGUAGE

  15. Fluency (Automaticity) • There is a strong correlation between poor retrieval of arithmetic combinations (‘math facts’) and global math delays • Automatic recall of arithmetic combinations frees up student ‘cognitive capacity’ to allow for understanding of higher-level problem-solving Source: Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293-304

  16. Language What does equal mean? 1=1³ Is this a correct statement?

  17. How can CSI help? • C = Core • S = Strategic • I = Intensive

  18. What investigative tools should be used?

  19. Formative Assessment Universal Screening Benchmark assessment Targeted progress monitoring

  20. Tier I • Direct/Explicit • Components of Number Sense • Appropriate LANGUAGE

  21. Components of Number Sense Quantity and Magnitude Numeration Equality Base Ten Form of a Number Proportional Reasoning Algebraic and Geometric Thinking

  22. Activity … • If Mark has 6 brown socks and 3 white socks in a drawer, how many socks will he need to blindly pull from the drawer before he is guaranteed to pull out two socks of the same color?

  23. Tier II • Direct/Explicit • Components of Number Sense • Appropriate LANGUAGE • Targeted instruction

  24. Tier III • Direct/Explicit • Components of Number Sense • Appropriate LANGUAGE • Targeted instruction • Smaller group/individualized, more intense and frequent

  25. Cover, copy, compare allows students practice at visualizing and computing through a sequence of easy to remember steps.

  26. Math Vocabulary • Preteach Math Vocabulary • Model the relevant vocabulary • Ensure that students learn standard, widely used/accepted labels for math terms and operations

  27. Other Instructional Strategies Teaching … use of known number combination (2 + 2 = 4, so 2 + 3 =5) relations among operations (6 + 4 =10, so 10 −4 = 6) commutative and associative properties problem interspersal technique or incremental rehearsal

  28. Resources: • http://www.ed.gov/about/bdscomm/list/mathpanel/index.html • www.interventioncentral.com • http://www.k8accesscenter.org/training_resources/math.asp • http://mathforum.org/math.topics.html

  29. CASE SOLVED … death by inadequate instruction

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