Math Intervention for Special Education Students

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Math Intervention for Special Education Students

• Pamela Higgins
• Fall 2008

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Domains of Skills in Math
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Factors that Influence Math Ability

• Cognitive ability
• Attention
• Organization
• Persistence
• Self-esteem
• Attitudes toward Math
• Quality/Amount of Instruction

• Perceptual Skills
• Perseveration
• Language
• Reasoning
• Memory
• Symbolism

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• Impact in Math

• Perceptual Skills

• Measurement
• Estimation
• Problem Solving
• Geometry

• Spatial relationships
• Distances
• Size relationships
• Sequencing

• Instructional Need
• Practice estimating size and distance
• Verify estimates

Bos and Vaughn p 334
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Perseveration
Bos and Vaughn p 334
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Language
Bos and Vaughn p 334
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Reasoning

• Strategies
• Use concrete materials and real-life a
• applications until a concept is understood.
• Use Think Alouds to illustrate mental processes
• Allow students to explain their thinking
• Recognize and correct errors in thinking

Bos and Vaughn p 334
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Memory

• Teaching Strategies
• Reduce the amount of new information
• Increasing the number of exposures to the new
  material.
• Allow students to verbalize and demonstrate new
  material.
• Bos and
  Vaughn p 334-335

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Symbolism Difficulty
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NCTM Standards www.nctm.org/standards

• Number and Operations
• Instructional programs from prekindergarten
  through grade 12 should enable all students to--
• understand numbers, ways of representing numbers,
  relationships among numbers, and number systems
• understand meanings of operations and how they
  relate to one another
• compute fluently and make reasonable estimates.

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• Algebra
• Instructional programs from prekindergarten
  through grade 12 should enable all students to--
• understand patterns, relations, and functions
• represent and analyze mathematical situations and
  structures using algebraic symbols
• use mathematical models to represent and
  understand quantitative relationships
• analyze change in various contexts.

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• Geometry
• Instructional programs from prekindergarten
  through grade 12 should enable all students to--
• analyze characteristics and properties of two-
  and three-dimensional geometric shapes and
  develop mathematical arguments about geometric
  relationships
• specify locations and describe spatial
  relationships using coordinate geometry and other
  representational systems
• apply transformations and use symmetry to analyze
  mathematical situations
• use visualization, spatial reasoning, and
  geometric modeling to solve problems.

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• Measurement
• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• understand measurable attributes of objects and
  the units, systems, and processes of measurement
  
• apply appropriate techniques, tools, and formulas
  to determine measurements.

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• Data Analysis and Probability
• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• formulate questions that can be addressed with
  data and collect, organize, and display relevant
  data to answer them
• select and use appropriate statistical methods to
  analyze data
• develop and evaluate inferences and predictions
  that are based on data
• understand and apply basic concepts of
  probability

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• Problem Solving
• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• build new mathematical knowledge through problem
  solving
• solve problems that arise in mathematics and in
  other contexts
• apply and adapt a variety of appropriate
  strategies to solve problems
• monitor and reflect on the process of
  mathematical problem solving.

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• Reasoning and Proof
• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• recognize reasoning and proof as fundamental
  aspects of mathematics
• make and investigate mathematical conjectures
• develop and evaluate mathematical arguments and
  proofs
• select and use various types of reasoning and
  methods of proof.

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• Communication
• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• organize and consolidate their mathematical
  thinking through communication
• communicate their mathematical thinking
  coherently and clearly to peers, teachers, and
  others
• analyze and evaluate the mathematical thinking
  and strategies of others
• use the language of mathematics to express
  mathematical ideas precisely.

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• Connections
• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• recognize and use connections among mathematical
  ideas
• understand how mathematical ideas interconnect
  and build on one another to produce a coherent
  whole
• recognize and apply mathematics in contexts
  outside of mathematics.

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• Representation
• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• create and use representations to organize,
  record, and communicate mathematical ideas
• select, apply, and translate among mathematical
  representations to solve problems
• use representations to model and interpret
  physical, social, and mathematical phenomena.

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Use Data to Drive Instruction

• Data available
• ARMT/SAT 10 Data
• Quarterly Assessments
• Eligibility Information
• Informal Curriculum Based Assessments
• Present Level of Performance on IEP Goal Pages

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Communication with Regular Education Teacher

• Be aware of Data available to the Regular
  Education Teacher
• Participate in data meetings for students if
  possible
• Collaborate with regular education teacher to be
  aware of students strengths and weaknesses

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Who needs intervention?

• Students scoring Levels 1, 2, and 3 on ARMT/SAT
  10
• Look at actual scores. For example, a 3 may
  really be almost a 2. That student needs to be
  watched closely to determine his/her needs.
• Does the student have a Math Goal on the IEP?

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Who needs intervention (cont.)?

• Students demonstrating specific needs on the
  Quarterly Assessments.
• Students who demonstrate specific needs on
  Chapter Tests.

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What do I need to know?

• ARMT/SAT 10 Data
• Quarterly Assessment with item analysis
• COS and Pacing Guide
• Item specs

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• Understanding the complexity and components of
  the learning task
• AND
• Understanding the students strengths and needs
• WILL
• Inform instructional design, accommodations and
  strategies in the regular and special education
  environments.

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Use Data to Drive Instruction
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Design Specific Intervention

• Intervention should include
• Building on basic skills
• Modeling and scaffolding new skills I do, we do,
  you do
• Practice to build fluency and automaticity with
  number facts
• Specific remediation of concerns identified in
  classroom assessments and work
• Consistent review

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What does intervention look like?

• Daily Intervention
• Global math concerns
• Math goals identified
• May need resource time
• Content of intervention should parallel COS

• Periodic Intervention
• Target specific skills
• May not have Math goals in IEP
• May not need pull out
• May be done by General Education Teacher

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What Math instruction include?

• Assess students needs and choose appropriate
  goals.
• Set goals with the student.
• Review before a lesson, review within the
  lesson, review homework, review within the lesson
  and across lessons

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• Model Explicit Strategies
• Explicit/Direct instruction is a primary
  component of instruction for students with
  disabilities.
• Model problem solving strategies
• Think Aloud of thought processes as the teacher
  solves problems
• Allow the student to practice strategies
• Provide corrective feedback
• Student Teacher Interaction is dynamic and
  fluid, adjusting to the needs of the student.

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• Use Concrete Semi-concrete Abstract Sequence
• Use of manipulative objects and pictures to
  represent math facts, word problems, fractions,
  and concepts.
• Objects, pictures, drawings accompanied by
  explanations

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• Teach Concepts and Rules
• Explicitly teach relationships
• 8614 and 6814 14-86 and 14-68
• 0 x n n
• Monitor Progress and Provide Feedback
• See growth and adjust instruction
• Teach Mastery - Automaticity

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• Teach Problem Solving A complex process
• Recognize problem
• Plan a strategy
• Examine the mathematical relationships in the
  problem
• Determine knowledge needed to solve
• Represent information graphically
• Generate equation
• Estimate an answer
• Sequence computation
• Compute the answer
• Check if reasonable

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Information Available through the Text

• An Intervention System
• Diagnostic tests by grade level
• Readiness Activities and Suggested Follow-Up
• Forms to track results
• Vocabulary
• Guidelines and suggested activities/problems
  throughout the chapter
• Leveled practice suggestions throughout each
  section.
• Error intervention
• Professional Development Note in Chapters

35

• Supplemental Materials by Grade Level
• Reaching All Learners
• Reteaching Masters
• Practice Masters

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References

• Foundations for Success The National
  Mathematics Advisory Panel. Final Report. 2008.
  US Department of Education.
• Strategies for Accessing Algebraic Concepts
  (K-8). Access Center. September 20, 2006.
• The Access Center. Improving Outcomes for All
  Students K-8. Learner Accommodations and
  Instructional Modifications in Mathematics
  Classroom for Students with Learning
  Disabilities.
• Bos, Candace S. and Sharon Vaughn, Strategies for
  Teaching Studnets with Learning and Behavior
  Problems, Sixth Edition, Merrill. 2006.
  p.333-377.
• Lyndia Eich and Karrin Lewis. K-12 Mathematics
  Diagnostic-Intervention Program Review.
  Preliminary Report. 2007
• Gersten, Russell and Chard, David, Number Sense
  Rethinking Arithmetic Instruction for Students
  with Mathematical Disabilities. LD Online, 2001.
  http//www.ldonline.org/article/5838 .

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References (continued)

• Hardy, Shannon. Research Based Math
  Interventions for Middle School Students with
  Disabilities. Access Center. 2005
• Kroesbergen, E. H. and Van Luitt, J.E.H.
  Mathematics Interventions for Children with
  Special Needs. Remedial and Special Eduction
  24(2), 97-114
• Mercer, Cecil D. and Mercer Ann R., Teaching
  Studnets with Learning Problems, Seventh Edition,
  Merrill, 2005. pp.427-483.
• What is a Math Disability. https//www.msu.edu/c
  ourse/cep/886/Math

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• Strategy Sources on line
• http//www.uic.edu/depts/counselctr/ace/math.htm
• http//homepates.wmich.edu/whitten/champaign_proj
  ect/math.html
• www.pbs.org/wgbh/misunderstoodminds/math.html
• https//www.msu.edu
• www.nctm.org Go to standards
• http//illuminations.nctm.org - interactive
  activities.