EDSPE 523

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EDSPE 523

• Week One

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Reading/Math Parallels

• Explicit Instruction vs. Whole Language
• Decoding vs. Comprehension
• Phonemic Awareness
• Scientifically based instruction vs. Philosophy
  based instruction

• Teacher-Directed vs. Guided Discovery
• Computation vs. Problem Solving
• Number Sense
• Scientifically based instruction vs. Philosophy
  based instruction

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Proficiency in Math

• Conceptual understanding
• Comprehension of mathematical concepts,
  operations, and relations
• Procedural fluency
• Skill in carrying out procedures flexibly,
  accurately, efficiently, and appropriately
• Strategic competence
• Ability to formulate, represent, and solve
  mathematical problems
• Adaptive reasoning
• Capacity for logical thought, reflection,
  explanation, and justification
• Productive disposition
• Habitual inclination to see mathematics as
  sensible, useful, and worthwhile, coupled with a
  belief in diligence and ones own efficacy
• (National Research Council, 2001, p. 5)

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Agenda

• How are we doing in math?
• In general
• For students with special needs
• How prepared are teachers?
• How good are our curricula (texts)?
• What does the research tell us about effective
  practices in math?

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Student Performance (NAEP)

• National Assessment of Educational Progress
  (NAEP) given at 4th, 8th, 12th grades
• The Nations Report Card

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NAEP 8th Grade Math (2003)
Source USDOE, NCES, National Assessment of
Educational Progress (NAEP)
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NAEP 8th Grade Math (Race/Ethnicity)
Source USDOE, NCES, National Assessment of
Educational Progress (NAEP)
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NAEP 8th Grade Math (Family Income)
Source USDOE, NCES, National Assessment of
Educational Progress (NAEP)
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Student Performance (TIMSS)

• The Third International Mathematics and Science
  Study (TIMSS), a cross national comparative
  achievement test for students (approximately) 9
  and 13 years old

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TIMSS

• TIMSS
• (9 year olds)
• 2 countries scored significantly higher than
  U.S. students

• TIMSS
• (13 year olds)
• 24 countries scored significantly higher than
  U.S. students

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Student Performance (PISA)

• Program for International Student Achievement
  (PISA) cross-national study of 15-year olds in 32
  industrialized countries

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2003 U.S. Ranked 24th out of 29 OECD Countries
in Mathematics
Source Organization for Economic Cooperation and
Development (OECD), PISA 2003 Results, data
available at http//www.oecd.org/
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U.S. Ranks Low in the Percent of Students in the
Highest Achievement Level
Source Organization for Economic Cooperation and
Development (OECD), PISA 2003 Results, data
available at http//www.oecd.org/
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Washington--WASL
2006-07
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Math and Students with Special Needs

• Not as much information
• Adolescents with LD may perform up to 7 years
  behind their grade level in math (Cawley
  Miller, 1989)
• Only 12 of students with mild disabilities
  participate in advanced math classes (Wagner
  Blackorby, 1996)

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Performance Deficits

• Younger Students
• Lack fluent and accurate recall of number
  combinations
• Continue to use counting strategies after other
  students have attained fluency
• However, more likely to make errors with these
  strategies
• Deficit may be stable over time (little
  improvement over 2years)
• Difficulty in quantity discrimination
• Bigger/smaller, how much bigger

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Performance Deficits

• Older Students
• Difficulty developing and applying strategies
• May use same strategies , but less efficiently
• May apply strategy correctly, but to the wrong
  problem type
• May be reluctant to give up initial strategies
  and replace with more efficient ones
• Difficulty mastering basic operations

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Teacher Knowledge

• Liping Ma compared Chinese and U.S. teachers
  knowledge of mathematics and mathematics
  instruction.

Ma, 1999
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Teacher Knowledge

• Findings
• Teachers mathematical knowledge directly affects
  their students mathematical learning.

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Teacher Knowledge

• Findings
• U.S. teachers displayed procedural knowledge with
  some algorithmic competence.
• Chinese teachers displayed algorithmic competence
  with conceptual understanding.

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Teacher Knowledge

• Factors that support the development of Chinese
  teachers Profound Understanding of Fundamental
  Mathematics (PUFM)
• their own elementary education
• their teacher preparation
• their work as math specialists

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Teacher Knowledge

• Mas recommendations
• refocus teacher preparation
• enhance teacher study of mathematics on the job
• use well-constructed textbooks

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Mathematics Curricula

• Mathematics curricular materials (textbooks)
  account for about 75 of what occurs in
  mathematics instruction in elementary and
  secondary classrooms.
• Porter 1989

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Mathematics Curricula

• U.S. textbooks compared to those of other
  countries
• much larger and heavier
• cover more topics with less depth
• fail to develop linkages between topics
• are repetitive and spiral

Schmidt, Houang, Cogan, 2002
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Mathematics Curricula

• U.S. textbooks compared to those of other
  countries
• focus more on eye catching, irrelevant
  illustrations,
• dedicate equal time to simple and difficult
  tasks,
• provide little information for teachers on
  content and methodology.

Schmidt, Houang, Cogan, 2002
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Scientifically Based Instruction

• Reading math programs based on scientifically
  based research incorporate the findings of
  rigorous experimental research.
• Slavin, 2003

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Relevant Reviews of Mathematics Research

• Teacher Effectiveness Research
• Direct Instruction Research, Follow Though and
  Beyond
• Recent Reviews of Research
• Students At Risk for Academic Failure (Baker,
  Gersten, Lee, 2002)
• Students with Learning Disabilities (Gersten et
  al., under review)

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Reviews of Research on Mathematics for Students
At Risk

• Fifteen high quality studies resulting in four
  major interventions that improved student
  achievement
• Progress-monitoring data available to teachers
  and students
• Peer tutoring
• Providing feedback to parents
• Explicit, teacher-directed instruction

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Reviews of Research on Mathematics for Students
with Learning Disabilities

• Twenty-six high quality studies in three
  categories
• Curricular and broad instructional approachesuse
  of diagrams and visual scaffolding, use of
  explicit instruction including self-verbalization
• Progress monitoring
• Tutoring

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Other Critical Instructional Elements

• Highlight Big Ideas
• Address Prior Knowledge
• Content and Example Sequencing
• Example Selection
• Diagnosis and Error Correction
• Practice and Review

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Special Education Underlying Assumptions

• Special education programs are a problem-solving
  component of the school system whose function is
  to identify and serve individuals whose
  performance is significantly discrepant from
  their peers. (Deno)

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Housekeeping

• How to read the textbook
• Study questions?
• Readings due next week
• Chapters 4 5
• Application exercises due next week
• Counting (p. 41) 1, 5
• Symbol ID and Place Value (p. 60) 6, 9
• Curriculum Evaluation presentations
• Start thinking about groups