Cognitive and educational neuroscience of math learning: implications for interventions in learning disabilities Vinod Menon Department of Psychiatry & Behavioral Sciences Department of Neurology & Neurological Sciences Symbolic Systems Program Program in Neuroscience Stanford University
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– Fine-grain developmental differences during critical stages of skill acquisition
• Development of memory-based knowledge – Learning to use efficient strategies
– Crucial role of associative memory system
– Core memory systems play an important role in knowledge acquisition
• Training and brain plasticity – Normalization of brain response with training in children with learning disabilities
– Changes in functional and structural circuits
– Brain-based predictors of learning
• Implications for educational neuroscience and interventions in learning disabilities
Levels of Mathematical Information Processing
• Basic Number Processing– Symbol mapping
– Magnitude Judgment
• Fact Retrieval – Calculation vs. Automatic Retrieval
• Complex Mathematical Computation– Involves many other cognitive functions
• Working Memory
• Attention
• Visuospatial Processing
Which is bigger?
3 5
6 x 6 = 36
17 - 8 = ?
Basic number processing and fluent fact retrieval are key bottlenecks in dyscalculia.
3
Canonical brain areas involved in numerical
problem solving
Results of meta-analysis - 44
studies of arithmetic in adults
(Neurosynth, Yarkoni et al.
2011)
Ashkenazi et al., 2012 JLD.
Neurobiological basis of math and
reading disabilities
Distributed systems involved in math cognition and
learning
Menon (2013) Handbook Math Cogn.
Fias et al. (2013) Trends in Neursci Ed.
Cannot assume that same brain systems are
similarly involved in different stages of learning
Mathematical Skill Development
Developmental of Arithmetic skills
8 10 12 14 16 18 20
0
1
2
3
4
Nu
mb
er
of su
bje
cts
AgeRivera (2005) Cerebral Cortex
• Aim: Examine neurodevelopmental changes in mental arithmetic (ages 8-19)
• Task: Single-digit addition and subtractiona + b = ca – b = c
• Analysis: Age-related increases and decreases in
brain activation
Developmental changes: Behavior
• Accuracy: asymptotes by age 9
• RT: changes continue through adolescence
8 10 12 14 16 18 20
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
Accura
cy
Age
8 10 12 14 16 18 20
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
Accura
cy
Age
8 10 12 14 16 18 20
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1400
1600
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2200
2400
Reaction t
ime (
msec)
Age
8 10 12 14 16 18 20
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1400
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2000
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2400
Reaction t
ime (
msec)
Age
Experimental trials Control trials
Anterior to Posterior Shift in Arithmetic
Processing with Age
Rivera et al., 2005
Increases with age
Decreases with age
Addition & Subtraction
Combined
Age range: 8 – 19 years
Developmental changes: Children vs. Adults
PFC, MTL and basal ganglia are more
engaged in children
8 10 12 14 16 18 20
-3
-2
-1
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L S
FG
Age
8 10 12 14 16 18 20
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L M
FG
Age
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L I
FG
Age
8 10 12 14 16 18 20
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L V
entr
al str
iatu
m
Age
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uta
me
n
Age
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G/P
HG
Age
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L H
ipp
oca
mp
us
Age
But also - Basal ganglia,
hippocampus and
parahippocampal gyrus
Prefrontal cortex
Effortful processing Procedural and declarative memory systems
L Parietal and Lateral occipital cortex activation increases with age
8 10 12 14 16 18 20
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-2
-1
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L S
upra
ma
rgin
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yru
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Age
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L I
nf.
Occip
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yru
s
Age
Parietal and LOC are more engaged in adults
Summary: Neurodevelopmental changes in
mental arithmetic
• Older individuals showed greater activation in the left parietal cortex, along the supramarginal gyrus and adjoining anterior intra-parietal sulcus
• By contrast, younger subjects showed greater activation in the prefrontal cortex, including dorsolateral and ventrolateral prefrontal cortex and the anterior cingulate cortex – Reflects comparatively more working memory and attentional resources to
achieve similar levels of mental arithmetic performance
• Increased functional specialization of the left parietal cortex in mental arithmetic, a process that is accompanied by decreased dependence on memory and attentional resources with development
• Younger subjects also showed greater activation of the hippocampus and dorsal basal ganglia – Reflects greater demands placed on both declarative and procedural
memory systems
How does a child solve 7 + 8 ? Decoding
brain activity patterns associated with
counting and retrieval strategies
Counting Fingers
Sum
Max
Min
Verbal Counting
Sum
Max
Min
Counting-based
Memory-based
Decomposition
Retrieval
Increasing maturity
Dec
reas
ing
reac
tion t
imes
and c
ogn
itiv
e re
sourc
es
Geary (1994)
How does a child solve 7 + 8 ? Decoding brain activity
patterns associated with counting and retrieval strategies
Strategy session fMRI session
Cho (2011) Developmental Science
Performance Matched
How does a child solve 7 + 8 ?:
Decoding Children’s Brain Activity Patterns
during Counting versus Retrieval
• Participants
2-3 grade children (7-10 years)
• Behavioral task
1) strategy assessment session (e.g., 3 + 4 = ?)
- % of trials retrieved, % of trials counted, etc.
2) fMRI session
- standard addition (both addends greater than 1; e.g., 3 + 4 = 8 ?)
- plus 1 addition control (one of the addend is 1; e.g., 7 + 1 = 8 ?)
• Functional image analysis
- univariate approach based on GLM
- multivariate approach using searchlight classification