What Have Students With Significant Cognitive Disabilities Learned in Grade 8 Mathematics

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What Have Students With Significant Cognitive
Disabilities Learned in Grade 8 Mathematics?

• Dan Wiener
• Massachusetts Department of Education
• CCSSO, San Francisco
• June 2006

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How MCAS-Alt Works

• Portfolio
• Work samples and data are collected during
  classroom activities based on the strands
  required by the state for assessment.
• Teachers design and conduct tasks/activities and
  submit products to the state for scoring.

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Which Students Took 2005 MCAS-Alt?
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Students taking MCAS-Alt, Grade 8 Mathematics (n
837)
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Portfolio Requirements forMathematics (2005)

• Of five possible strands (Number Sense, Geometry,
  Data, etc.), teacher selects three for portfolio
• Core set of evidence
• Data chart of students performance of skill over
  time
• Work samples, video, photos based on same skill
• Additional supporting evidence, at teachers
  discretion
• Self-evaluation, context, descriptions

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Mathematics Strands

• Number Sense and Operations
• Simple operations Ordering, Comparing, and
  Rounding numbers Money, Fractions, Estimating
• Patterns, Relations, and Algebra
• Sorting, repeat patterns, count by 2s, 5s, and
  10s Unknown variable/inequalities/how changes
  in variables affect one another Equations
  Equivalent amounts
• Geometry
• 2-D and 3-D shapes Lines (parallel and
  perpendicular), points, planes, angles Relative
  positions of objects next to, above, etc.
  Symmetry and transformations
• Measurement
• Time, Length, Weight, Area/Volume
• Data, Statistics, and Probability
• Classify objects Gather data through
  observation, survey Represent information in
  different ways Describe/draw conclusions Predict

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Math Data Analysis, Statistics, and
Probability
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How Are MCAS-Alt Portfolios Scored?

• Criteria
• Completeness of portfolio
• Level of Complexity (difficulty standards)
• Demo of Skills Concepts (accuracy)
• Independence (cues/prompts/assistance)
• Self-Evaluation (monitor and reflect)
• Generalization (instructional approaches)

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MCAS-Alt Scoring Rubric
Level of Complexity
Demonstration of Skills Concepts (i.e.,
Accuracy)
Independence
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Additional Rubric Dimensions

• Self-Evaluation
• Choices, reflection, goal-setting
• Generalized Performance
• Context and approaches used

These do not count toward the Performance Level
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MCAS-Alt Performance Levels(alternate
achievement standards)
Performance How MCAS-Alt Results Are Reported

• Incomplete Insufficient information
• Awareness Very little understanding
• Extensive prompting, primarily inaccurate
• Emerging Simple understanding
• Limited and inconsistent performance
• Progressing Partial understanding
• Primarily accurate and independent

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MCAS-Alt Performance Levels(grade-level
achievement standards)
How MCAS-Alt Results Are Reported

• Needs Improvement Partial understanding at
  grade level
• Proficient Solid understanding at grade level
• Advanced Comprehensive and in-depth
  understanding at grade-level

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How Did Students Perform on the Grade 8 Math
MCAS-Alt?
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Percent of Domain Scores Across Grade 8
Mathematics Learning Standards
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Three Math Strands Are Required Which Did
Teachers Choose to Submit?
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How Students Performed on Each Assessed Math
Strand
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How Students Performed on Each Assessed Math
Strand
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How Students Performed on Each Assessed Math
Strand
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How Students Performed on Each Assessed Math
Strand
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How Students Performed on Each Assessed Math
Strand
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Examples from 19 selected portfolios (59 strands)

• Examination of portfolios at four performance
  levels, based on specific score combinations, to
  look specifically at content
• 2 at Needs Improvement (LC 5, DSC 3-4, Ind 4)
• 9 at Progressing (LC 3, DSC 3-4, Ind 4)
• 3 at Emerging (LC 2-3, DSC 2-4, Ind 2-3)
• 5 at Awareness (LC 2-3, DSC 1-4, Ind 1-2)

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Depth of Knowledge
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Categorical Concurrence and Typical Activities
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What Have We Learned?

• Students with significant cognitive disabilities
  can and are learning challenging math skills
• Exceeding expectations typical learning, at
  their own pace
• Teachers selection of strands may limit
  students access to entire Math curriculum
• Teachers selection of tasks may limit
  opportunities to learn higher-level skills
• Expert teachers must lead the way, their work
  publicized as exemplary
• Need to find and make available new resources for
  teaching math to students with significant
  disabilities

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Teaching Math to This Population Concerns and
Considerations

• Teachers data collection skills
• Charts show progress over time on a new skill
• But must be based on solid, assessable goals
• Depth of knowledge of portfolio tasks
• Inconsistent depth across classrooms and
  portfolios
• Expectations, skills of teacher, available
  resources
• Tasks can include either
• Recall and recognition (1 step), applying skills
  (2 steps), problem-solving, comparing/contrasting,
  projects
• Teachers comfort level teaching math
• Selection of strands to assess
• Choice of tasks and activities

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What Changes Have We Made?

• Require data charts based on specific outcomes
• Learn new skills increase number of tasks
• Require specific strands in each grade
• Trained 3000 teachers to enhance depth of
  knowledge of instructional activities and tasks
• Adding open response, creating, explaining,
  comparing, interpreting
• Writing more challenging, measurable academic
  goals
• LOOKING AHEAD Scoring progress in
  addition to performance?

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Contact Information

• MCAS-Alt on the web at
• www.doe.mass.edu/mcas/alt
• Contact
• dwiener_at_doe.mass.edu or nhanson_at_doe.mass.edu