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)

33

40

27

0%

20%

40%

60%

80%

100%

Prof/Adv

Basic

Below Basic

Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

NAEP 8th Grade Math (Race/Ethnicity)

61 53 46

21 23

3236

38

43 35

7 11 1636 42

0%

20%

40%

60%

80%

100%

Black Latino Native White Asian

Prof/ Adv

Basic

Below Basic

Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

NAEP 8th Grade Math (Family Income)

53

22

36

41

11

37

0%

20%

40%

60%

80%

100%

Poor Not Poor

Prof/Adv

Basic

Below Basic

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

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 24th out of 29 OECD Countries in Mathematics

300

350

400

450

500

550

Ave

rag

e S

cale

Sco

re

Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results , data available at http://www.oecd.org/

U.S. Ranks Low in the Percent of Students in the Highest Achievement Level

0

2

4

6

8

10

Per

cen

t o

f S

tud

ents

Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at http://www.oecd.org/

Washington--WASL

Grade Level Math

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%

2006-07

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, 1999Ma, 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, Schmidt, Houang, & Cogan, 20022002

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