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EDSPE 523

EDSPE 523. Week One. 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

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EDSPE 523

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  1. EDSPE 523 Week One

  2. 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

  3. 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 one’s own efficacy (National Research Council, 2001, p. 5)

  4. 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?

  5. Student Performance (NAEP) • National Assessment of Educational Progress (NAEP) given at 4th, 8th, & 12th grades • “The Nation’s Report Card”

  6. NAEP 8th Grade Math (2003) Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

  7. NAEP 8th Grade Math (Race/Ethnicity) Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

  8. NAEP 8th Grade Math (Family Income) Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

  9. 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

  10. 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

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

  12. 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/

  13. 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/

  14. Washington--WASL 2006-07

  15. 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)

  16. 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

  17. 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

  18. Teacher Knowledge • Liping Ma compared Chinese and U.S. teachers’ knowledge of mathematics and mathematics instruction. Ma, 1999

  19. Teacher Knowledge • Findings: • Teachers’ mathematical knowledge directly affects their students’ mathematical learning.

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

  21. 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

  22. Teacher Knowledge • Ma’s recommendations: • refocus teacher preparation • enhance teacher study of mathematics “on the job” • use well-constructed textbooks

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

  24. 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

  25. 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

  26. Scientifically Based Instruction • Reading [math] programs based on scientifically based research incorporate the findings of rigorous experimental research. Slavin, 2003

  27. 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)

  28. 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

  29. Reviews of Research on Mathematics for Students with Learning Disabilities • Twenty-six high quality studies in three categories: • Curricular and broad instructional approaches—use of diagrams and visual scaffolding, use of explicit instruction including self-verbalization • Progress monitoring • Tutoring

  30. Other Critical Instructional Elements • Highlight Big Ideas • Address Prior Knowledge • Content and Example Sequencing • Example Selection • Diagnosis and Error Correction • Practice and Review

  31. 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)

  32. 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

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