Presentation on theme: "Mathematics in a Responsiveness to Instruction Framework Susan Davis, Personnel Development Consultant North Carolina Department of Public Instruction."— Presentation transcript:
Mathematics in a Responsiveness to Instruction Framework Susan Davis, Personnel Development Consultant North Carolina Department of Public Instruction Exceptional Children Division November 2008
Weve got to stop asking children to solve problems they dont know how to solve and, instead, teach them math.
Responsiveness to Instruction The practice of providing high quality instruction matched 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
Responsiveness to Instruction (RtI) … a school-wide system of support
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
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)
"Arithmetic is being able to count up to twenty without taking off your shoes." –Anonymous
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.
NC Standard Course of Standard Strands (or goals): Number and Operations Measurement Geometry Data Analysis and Probability Algebra Problem Solving
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..
Common Threads in Research and Practice Understanding Computing Applying Reasoning Engagement Number Sense Basic math operations Problem-solving skills Number and Operations Measurement Geometry Data Analysis and Probability Algebra Problem Solving
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
Language What does equal mean? 1=1³ Is this a correct statement?
Tier I Direct/Explicit Components of Number Sense Appropriate LANGUAGE
Components of Number Sense Quantity and Magnitude Numeration Equality Base Ten Form of a Number Proportional Reasoning Algebraic and Geometric Thinking
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?
Thats the right answer to a different problem … Come up with the problem that answer goes with
Tier II Direct/Explicit Components of Number Sense Appropriate LANGUAGE Targeted instruction
Tier III Direct/Explicit Components of Number Sense Appropriate LANGUAGE Targeted instruction Smaller group/individualized, more intense and frequent
Cover, copy, compare allows students practice at visualizing and computing through a sequence of easy to remember steps.
Math Vocabulary Preteach Math Vocabulary Model the relevant vocabulary Ensure that students learn standard, widely used/accepted labels for math terms and operations
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