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  Scientifically based instruction vs. Philosophy based instruction

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)

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?

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

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

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

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

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

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

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

2003: U.S. Ranked 24 th out of 29 OECD Countries in Mathematics Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at

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

Washington--WASL Grade LevelMath 3rd Grade 69.6% 4th Grade 58.1% 5th Grade 59.5% 6th Grade 49.6% 7th Grade 54.6% 8th Grade 49.8% 10th Grade 50.4%

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)

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

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

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

Teacher Knowledge  Findings:  Teachers’ mathematical knowledge directly affects their students’ mathematical learning.

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

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

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

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

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

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

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

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)

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

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

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

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)

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