Mathematics in a Responsiveness to Instruction Framework

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Mathematics in a Responsiveness to Instruction
Framework

• Susan Davis, Personnel Development Consultant
• North Carolina Department of Public Instruction
• Exceptional Children Division
• November 2008

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What isthis?
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ITS A CRIME!!!!!!
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Weve got to stop asking children to solve
problems they dont know how to solve and,
instead, teach them math.
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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

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

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SO WHAT ABOUT MATH in an RtI framework?
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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)

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

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NC Standard Course of Standard Strands (or goals)

• Number and Operations
• Measurement
• Geometry
• Data Analysis and Probability
• Algebra
• Problem Solving

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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..
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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
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Two more

• FLUENCY (Automaticity)
• LANGUAGE

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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

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Language

• What does equal mean?
• 11³
• Is this a correct statement?

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back to the CRIME
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This is a job for CSI!
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How can CSI help?

• C Core
• S Strategic
• I Intensive

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What investigative tools should be used?
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Formative Assessment

• Universal Screening
• Benchmark assessment
• Targeted progress monitoring

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Analysis of the problem
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Interventions

• http//ejaypaz.multiply.com/video/item/10

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Tier I

• Direct/Explicit
• Components of Number Sense
• Appropriate LANGUAGE

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Components of Number Sense

• Quantity and Magnitude
• Numeration
• Equality
• Base Ten
• Form of a Number
• Proportional Reasoning
• Algebraic and Geometric Thinking

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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?

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Thats the right answer to a different problem

• Come up with the problem that answer goes with

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Tier II

• Direct/Explicit
• Components of Number Sense
• Appropriate LANGUAGE
• Targeted instruction

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Tier III

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

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Cover, copy, compare

• allows students practice at visualizing and
  computing through a sequence of easy to remember
  steps.

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Math Vocabulary

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

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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

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Resources

• http//www.ed.gov/about/bdscomm/list/mathpanel/ind
  ex.html
• www.interventioncentral.com
• http//www.k8accesscenter.org/training_resources/m
  ath.asp
• http//mathforum.org/math.topics.html

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CASE SOLVED

• death by
• inadequate instruction