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HD FS 631:
Learning and Cognitive
Development
November 18, 2002
Schooling & Cognition:
Reading and Mathematics
Susan Hegland
1
1. Discuss the development
of reading: cite evidence to
support. In what way does
reading development
correspond to general
changes in cognitive
ability?
2
Reading
• What develops?
• How does cognitive development influence
reading?
• What sex differences exist in reading and
verbal abilities?
• How does the environment influence
reading?
3
What develops?
•
•
•
•
Jeanne Chall (1979): Five stages
Stage 0: pre-first grad
Stage 1: grade 1: learning to read
Stage 2: grades 2 & 3:
learning to read fluently
• Stage 3: reading to learn
• Stage 4: truly proficient reading:
drawing inferences
• Apply Atkinson & Schiffrin Model:
how does working memory,
automatization, control strategies affect
5
4
Atkinson-Schiffrin Model
Response
Generator
Sensory
Register
Automatization
Working
memory
Long
term
memory
Control
Processes
6
1
How does cognitive
development influence
reading?
DIBELS
• Dynamic Indicators of Basic Early Literacy
Skills
• Used widely in Iowa
• Brief (3-5 minute probe)
• Guides instruction planning
• Early Reading Skills
• Phonological Recoding
• Comprehension
7
8
Early Reading Skills
Phonological Recoding
Phonemic awareness -> reading (
Stanovich) !
• Knowledge that words consist of
separable sounds:
• c……..a………t
• Liberman: No 4’s perform this
accurately!
• Rhyme detection
• Kindergarten & first graders given
training in phonemic awareness show
better early reading (Cunningham)
• Translating written symbols into sounds
and words
– Proficient reading requires direct retrieval
of whole word from memory
– But phonological recoding needed for
reading ability to advance
• Automatization critical: frees up
resources to focus on comprehension!
• Remember Siegler’s strategy choice
model:
– first choice: whole word retrieval
– second choice: phonological recoding
9
Siegler’s strategy
choice model
10
Dyslexia
Use
Strategy
Strategy
Strategy
Strategy
Strategy
Age
11
1
2
3
4
5
• Stanovich: Faulty phonological processing
may be main cognitive factor behind
dyslexia (reading disability)
• Phonological recoding appears to be
modular, independent of IQ
• Phonological processing skills remain
stable over childhood (Wagner)
• Early intervention critical
12
2
Pseudoword accuracy
by age and dyslexia
Reading Comprehension
• Set of integrated processes requiring all
components of information processing
system
• Individual words recognized, linked to
previously learned letters or words
• Held in working memory and combined
with other words
• Automatization frees working memory
for control processes
• Control processes call for predicting,
clarifying, summarizing, questioning
Number of Pseudowords
60
40
20
Normal
Dyslexic
0
'7 - 8'
'9 - 10'
'11 - 12'
'13 - 14'
Age in Years
Siegel, 1993
13
14
Influence of working memory
capacity
Working memory task:
recalling last words
15
Influence of long term memory
• Reading is a constructive process
• Reading “a process in which information
from the text and the knowledge
possessed by the reader act together to
produce meaning” R. Anderson “A
Nation At Risk” 1984
• Children who know more about a given
topic show better reading
comprehension (Pearson)
• Increasing background knowledge
increase reading comprension
(Omanson)
17
6
Number of Pseudowords
• Danemann: listening span correlates with
comprehension from preschool through
college students
• Listening span: number of successive
short sentences recalled verbatim
• Working memory limits listening span for
young children and less-proficient readers
• Working memory capacity differentiates
dyslexic and non-dyslexic readers
5
4
3
2
Normal
Dyslexic
1
0
'7 - 8'
'9 - 10'
'11 - 13'
Age in Years
Siegel, 1993
16
Influence of Control Structures
Case: executive control structure:
problem situation---goal ---strategy
Brown: reading comprehension affected by
• ability to monitor understanding
• adjust reading strategies accordingly
Comprehension monitoring strategies
• improve with age (control strategies)
• improve with instruction (Palinczar &
Brown)
18
3
Influence of Interest Level
on Reading
Sex differences in reading?
• Getting smaller in last 25 years!
– Favor females
• U.S.: Girls > Boys in elementary reading
– Great Britain: no sex differences
– Germany: girls more likely to be illiterate
• Boys more likely to be reading disabled
(Hyde)
– Reading disabilities traced to basic
cognitive abilities that are early and stable
– Substantial biological component in
19
reading disabilities
Reading Comprehension
Interest Level and Reading
Comprehension in 5th graders
• Stories in children’s readers (basal
readers)
are not inherently interesting to children
• Topic interest has more influence on
reading and academic performance
– for boys than
– for girls (Asher, Renninger)
20
Meta-analyses of sex differences
• Compares effect sizes (differences in standard
deviation units) across studies
– .2 = small effect
– .5 = moderate effect
– .8 = large effect
• Hyde: sex differences in verbal ability
– effect size = .24
Girls
Boys
– sex accounts for 1% in variance in verbal performance
• Getting smaller over time!
Low Interest
High Interest
– Less stereotyping?
Interest Level
Asher & Markel, 1974
– Changes in tests?
21
22
How environment influences reading:
Goodman: children do acquire reading “as
naturally as they acquire language”
Current evidence suggests otherwise:
Some
– acquire reading with minimal instruction
– require systematic assessment and
instruction
– find it hard to learn to read without massive
interventions (i.e., Reading Recovery)
• Systematic, quality instruction is
successful:
23
2. Discuss sex differences in
mathematics ability: What
are the directions of the
differences? How
important are the
differences? How have the
differences changed?
24
– phonemic awareness & phonological
recoding
4
What develops and how?
Children’s Number Concepts
• Children’s Number Concepts
• Conservation of Number and
Mathematical understanding
• Young Children’s Knowledge of Number
• Children’s Arithmetic Concepts
• Math Disabilities
• Sex Differences in Mathematical Ability
• Cultural Differences in Math Learning
• How does the Environment affect Math
Learning?
• Develop from protoconcepts (Starkey)
and primitive procedures (Wynn) to
abstract concepts and procedures
• Some understanding of numerical
processes appears to be universal
Conservation of Number and
Mathematical understanding
Classification of children’s number
concepts and counting ability: 4-6 yr
olds
25
– Gelman: Children have a L.A.D. (Language
Acquisition Device)
– And a M.A.D.
• Hegland: L.A.D.’s require L.A.S.S’s;
– M.A.D.’s require M.A.S.S.’s (Math
Acquisition Supporting System)
• Piaget: Number reflected in conservation
• Gelman, Wang, Clements: number and
conservation develop independently
– Success in class inclusion predicts success in
missing addend problems:
(J. and T. have 12 cars altogether. J. has 5. 27
How many does T. have?) (Clements)
Young Children’s Knowledge of
Number: Gelman
• One-one principle
• Stable-order
principle
• Cardinal principle
• Abstraction
principle
• Order-irrelevant
principle
• Each item: one and
only one number name
• Number names in
stable, repeatable
order
• Final number =
quantity of set
• Apply to any array of
entities
• Order in which things
counted irrelevant 29
25
Nonconservers
Conservers
20
Number of children
– 7 - 8: children master conservation-of-number
tasks
– Concrete operations: reversible, mental, and
linked
26
15
10
5
0
Prequantitative
Quantitative
Counting Ability
Saxe, 1979
28
Preschoolers & the 5 Principles
• One-one: arrays of fewer than 5 objects
– 3’s, 4’s, and 5’s successful (Gelman)
• Stable order (Gelman)
– 90% 4’s and 5’s
– 80% 3’s
• Cardinal (Fuson)
– 3’s and 4’s usually gave last word for quantity
• Order irrelevant (Briars & Siegler)
– only 40% of 5’s successful
30
5
Strategy use in 4’s & 5’s
Children’s Arithmetic Concepts
Unknown
• Piaget: Addition and subtraction require
concrete operations (inversion
reversibility)
• Recent research: young children use a
variety of arithmetic strategies (Resnick)
Correct
Use
Count on: 1st
Guessing
Min
Finger recognition
Shortcut sum
– counting all
– counting from the first
– counting from the largest (by age 6)
Retrieval
Sum
0%
• Most children construct these strategies
20%
40%
60%
80%
100%
Siegler & Jenkins, 1989
31
32
– Used because of efficiency!
Siegler’s strategy
choice model
Development of Mental Arithmetic
1
2
3
4
5
Apply Atkinson-Shiffrin model:
• Shift from counting-based to fact retrieval
(Ashcraft)
Use
Strategy
Strategy
Strategy
Strategy
Strategy
– from procedural to declarative knowledge
• Processes become automatic;
– less monitoring and effort involved
• Are control procedures involved?
Age
– depends on nature of instruction!
33
34
Effortful processes
•
•
•
•
•
•
Automatic processes
Require mental effort
Take up working memory space
Available to consciousness
Interfere with other processes
Improve with practice
Vary with individual differences
•
•
•
•
•
•
35
require no mental effort
not available to consciousness
do not interfere with other processes
permit more complex tasks
do not improve with practice
do not vary with individual differences
in intelligence, motivation, or
education
• Example: Baratta-Lorton: children are
ready for adding when counting is
36
6
Procedural & conceptual
knowledge
Danger of premature
automatization!!!
• Procedural: knowledge how
• Conceptual: knowledge that
Math bugs (van Lehn)
• Math procedures that produce erroneous results
• Very hard to change once they’re automatized!
• 1/3 + 1/2 = 1/5
• 300
19
19 + 12 = 31
- 297
+ 12
197
211
• Clinical interviews can detect (Labinowicz)
– Horizontal and vertical (abstract level
networks)
Between
hi & lo
Central
tendency
Average
Moves with
range
37
Development of conceptual
and procedural knowledge
“ Facts”
Commutativity
Cardinal principle
Stable order of counters
Conceptual knowedge
Affected
by
outliers
38
But
Fact retrieval
• Too often, children do not link conceptual
and procedural knowledge
• “Plug and chug” without reflecting on
outcomes
• If buses hold 30 children, how many buses
for 75 children? 2.5 buses!
Counting on: largest
Counting on: first
– J. and T. have 12 cars altogether. J. has 5.
How many does T. have? 17!!!
– Key word: altogether means: add!!!
Counting all
Procedural Knowledge39
– Point math:
Math Disabilities
3
40
Type 1: Poor Procedural Skills
• Identified early in kindergarten
• Two types
• Typically catch up before third grade
• Possibly developmental?
• Typically from homes with
– 1: Poor procedural knowledge
• more immature mix of strategies
• Poorer knowledge of rules of counting
– low income,
– lower parent education (including drop-outs)
– little adult stimulation,
– little value of education
– 2: Poor memory retrieval
41
42
7
Sex Differences in Math
Learning
Type 2: Deficits in memory
retrieval
• Use fact retrieval less often than other kids
• Practice at fact retrieval does not improve
performance
• Tend not to catch up with peers over time
• Overlap with reading disabilities children
• Single deficit: representation and retrieval
of semantic information from long term
memory?
– No single cause, but intriguing hypothesis43
Geary
More males at extreme of math
performance distribution
• Traditionally, boys excel girls in math,
on average, at all levels
– Recently: no differences before high school
• Hyde: meta-analysis
– Sex differences small and often nonsignificant in elementary school (but favor
girls!)
– Differences favoring males begin in high
school and increase in college and
adulthood
– Magnitude of effect sizes have halved in
44
last 25 years!
– Sex differences greatest at highest ability
Why more males at extremes?
• Biological differences (Benbow)
Males
Females
– Math bright males
• Near-sighted
• Allergic
• Left-handed
45
Cultural Differences in Mathematical
Performance
46
Compared with Americans, Asians
• Value achievement in school more
• Spend more time on homework
• Have more demanding curricula
Research by Stevenson, Stigler, Ginsburg, Lee
Research in kindergarten through fifth grade:
Compared with Asians, American kids and
parents:
• Have nationally established curricula
• Have more high-level interactions and teacher monitoring in
class
• satisfied at lower levels of math achievement
• Have more whole group instruction in math (less seatwork,
less small group instruction)
• attribute success/failure to ability, not effort
• spend less time on math in class
• on task for smaller proportion of time (fewer breaks)
• less energetic teachers (more time in class, less time for
preparation)
• show more nervous, anxious behaviors in class
• Male and female brains show different
patterns of use during math problems
• Perhaps prenatal testosterone “bath” that
creates males introduces more complexity
and more variance?
47
• Have more manipulatives in class
• Spend more time on word problems
• Relate math to real life more often
• Get more questions on math concepts and math strategies
48
8
How does the Environment
influence Math Learning?
Interpreting cross-cultural math
comparisons
• Differences begin early and increase with time
and schooling
• Asian math instruction (Taiwan, Japan, Korea) is
more consistent with standards of National
Council of Teachers of Mathematics
• However, specific practices (e.g., homework)
may be culturally bound and not transferable
P.S. Hatano found that long-term use of abacus
results in internal abacus!
• Long-lasting impact of direct instructional
techniques that increase
– link between procedures and concepts
(through communication & multiple
representations)
– planning & reflection in problem solving
(Bransford: Jasper series)
• No evidence for radical constructivism
– Some direct instruction needed!
• Starkey:
49
50
– Head Start programs neglect mathematics!!
SES and school achievement:
Summer vacations
Discuss the effects of
academic preschool
programs. Are the effects long
lasting? How does parental
attitude interact with the
curriculum of the preschool
program to affect children’s
development?
500
400
300
Middle income
Low income
200
100
4th
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Math Achievement
600
Grade
Alexander & Entwisle, 1996
51
52
9