Transcript Document 7755870

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)
100%
80%
60%
27
40
40%
20%
Prof/Adv
Basic
Below Basic
33
0%
Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)
NAEP 8th Grade Math (Race/Ethnicity)
100%
80%
7
32
11
36
36
60%
40%
20%
61
16
53
42
38
Prof/Adv
43
35
21
23
Basic
Below Basic
46
0%
Black Latino Native White
Asian
Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)
NAEP 8th Grade Math (Family Income)
100%
80%
11
37
36
Prof/Adv
60%
41
40%
20%
53
Basic
Below Basic
22
0%
Poor
Not Poor
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
Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at
http://www.oecd.org/
ark
300
St ates
Spa in
Port ug
al
Ita ly
Greec
e
Tu rke
y
Mexi c
o
Unit ed
Fra nc
e
Swed
en
Austria
Germ
any
Ire lan
d
OECD
Avera
ge
Slo va
ck Re
pub lic
Norwa
y
Lu xem
bo urg
Pol an
d
Hung a
ry
Denm
Icela n
d
Cana d
a
Bel giu
m
Switze
rla nd
New Z
e ala n
d
Austra
l ia
Cze ch
Re pub
lic
Japan
Kore a
Neth e
rla nds
Fi nlan
d
Average Scale Score
2003: U.S. Ranked 24th out of 29
OECD Countries in Mathematics
550
500
450
400
350
m
0
Port ug
al
Greec
e
M exi c
o
Spa in
Tu rke
y
Ita ly
Pol an
d
Lu xem
bo urg
Hung a
ry
Unit ed
St ates
Ire lan
d
Neth e
rla nds
New Z
e ala n
d
Switz e
rla nd
Aus tra
l ia
Cana d
a
Cze ch
Re pub
lic
Ic ela n
d
Denm
ark
Swed
en
OECD
Avera
ge
Aus tria
Germ
any
Fra nc
e
Slo va
k Rep
ubl ic
Norwa
y
Fi nlan
d
J apan
Kore a
Bel giu
Percent of Students
U.S. Ranks Low in the Percent of Students in the Highest
Achievement Level
10
8
6
4
2
Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at
http://www.oecd.org/
Washington--WASL
2006-07
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%
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
review)
with Learning Disabilities (Gersten et al., under
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