NC3 Flashcards
Wynn (1992)
5 month old infants have arithmetic
Expectations
Wynn (1992)
5 month old infants have
Arithmetic expectations
Wynn (1992)
_____ infants have arithmetic expectations
5 month old
Wynn (1992)
How did they know that the infants had arithmetic expectations?
Babies look longer at unexpected events
McCrink + Wynn (2004)
Method:
Occluder rises to cover objects, which were either _______ or __________
Added to
Subtracted from
McCrink + Wynn (2004)
Found that ___ olds also have arithmetic expectations
9 month
Huttenlocher et al., (1994) found __________ arithmetic skills in preschool children
Non-symbolic
Huttenlocher et al., (1994)
Evidence of non-symbolic arithmetic skills in __________
Preschool children (2-4)
Huttenlocher et al., (1994)
Conclusion
Preschool children display
Mental model for arithmetic before formal schooling
Huttenlocher et al., (1994)
Non-symbolic arithmetic skills increased
With age
Huttenlocher et al., (1994)
_________ increased with age
Non symbolic arithmetic skills
Huttenlocher et al., (1994)
Found a decrease in performance with
Increasing problem size (1+1 easier than 4+1)
(Rasmussen + Bisanz, 2005)
________ memory relates to non-symbolic calculation
Visuospatial working
Jordan et al., (2007)
Non-verbal calculation predicts
Later math achievement
Levine et al., 1992
RQ: What are the effects of
Different formats in children 4 to 6 1/2
Levine et al., 1992
What were the 3 formats of math problem presented
Non verbal
Word problems
Abstract symbolic problems
Levine et al., 1992
Findings (older children)
More accurate in all formats
Levine et al., 1992
Findings (addition)
All children were more accurate in non-verbal format
Levine et al., 1992
Findings (subtraction - what were children most accurate in?)
Children were more accurate in NON-VERBAL format (e.g. dots)
Levine et al., 1992
Findings (subtraction) what were children least accurate in?
Abstract symbolic
Levine et al., 1992
Spontaneous use of ____________ when children had to solve word/abstract problems
Fingers
Levine et al., 1992
What was found in terms of HOW the children tackled the math problems (verbal & abstract)
Spontaneously used fingers
Hembree (1992) conducted a meta analysis on…
The effect of MANIPULATIVEs and PROBLEM FORMAT on arithmetic skills
Hembree (1992) (Meta-analysis on problem format/manipulatives)
Up to 7 years old…
Providing manipulatives improves accuracy
Hembree (1992) (Meta-analysis on problem format/manipulatives)
Children are more accurate when problems refer to….
Real situations and objects
Children are more accurate when problems refer to real situations and objects, as opposed to more ___________ or _________
Forms
Non-familiar contexts
Children’s accuracy can be improved by
- Problems refer to real situations/objects
- Familiar contexts
- ____________
Use of pictures
How to solve word problems? 4 steps (CESP)
- Create representation
- Extract relevant info
- Select appropriate operation
- Perform the operation
Three major classes of word problems
Easy
Moderate
Hard
Children spontaneously develop _____________
Invented strategies
Children spontaneously develop invented strategies, e.g. (2)
- Count all
2. Count from first
Children’s “invented strategies” were studied using
Micro-genetic designs
(Siegler et al., 1988)
Distributions of ________
Associations network
(Siegler et al., 1988)
__________ associations
Distributions of
3 steps of Siegler et al., (1988)s Distributions of Associations Network
- Start with procedural strategies
- Every time, association between prob. and answer strengthened
- If strength of association exceeds the threshold, answer is retrieved
Siegeler et al., 1988
Distributions of associations network
Analysis of the performance…(2)
- More errors with LARGER operands
2. Incorrect answers are often related to the operands rather than completely unrelated
Siegeler et al., 1988
Distributions of associations network
Incorrect answers are often related to the
Operands rather than being completely unrelated
Siegler et al., 1999
Overlapping ______ model
Waves
Siegler et al., 1999
______________ model
Overlapping waves
Siegler et al., 1999
Overlapping waves model suggests
Strategies overlap - children may select from any one of these
Siegler et al., 1999
Overlapping waves model
Strategies overlap, rather than being a
Staircase model
Staircase model
Sudden transitions ‘steps’
There are four dimensions of strategy use… (4 S’s)
Strategy repertoire
Strategy distribution
Strategy efficiency
Strategy selection
A strategy repertoire is
The range of strategies one may use
Strategy distribution is
Relative frequency of use
Strategy efficiency is
Accuracy/speed in implementing a strategy
Strategy selection is
Whether or not one makes appropriate choice based on a strategies efficiency
Strategy repertoire/distribution/efficiency/selection
These are the
Four dimensions of strategy use
Choice/no choice paradigm
Method:
Participants either told to choose a strategy or are instructed to use a strategy
Choice/no choice paradigm
In the no choice paradigm…
Good performance with small additions
Not with subtractions
Choice/no choice paradigm
In the choice paradigm
Uses retrieval for small additions
Counts for subtractions
In the NO CHOICE paradigm, children used retrieval for small additions but counted for subtractions. This shows they made
An adaptive strategy choice
In order to succeed in domain-specific mathematical problems, you must employ (2)
- D-S mathematical knowledge
2. Domain-general executive function and language
3 examples of Executive function skills
- Working memory
- Inhibition
- Shifting
Working memory
Ability to monitor/manipulate info in mind
Inhibition
Ability to suppress irrelevant info/ignore distractions
Shifting
Capacity for flexible thinking/shifting of attention between different tasks
Two types of working memory
Verbal
Visuospatial
Example of a Verbal working memory test
Backward digit span
Example of a visuospatial working memory test
Corsi task
Cross-sectional/longitudinal studies have revealed that VERBAL WM is a STRONG PREDICTOR OF
Word arithmetic (written/verbal; word problem solving)
Szucs et al., 2014
Verbal WM __ Visuospatial WM
>
Clinical studies show children with math learning difficulties have
Reduced Verbal WM capacity
(Cragg et al., 2017)
WM is required to access…..
Arithmetic facts LONG term
Inhibition
Distraction might be _______ or __________
Internal
External
Gragg et al., 2017
Inhibition might be relevant to (2)
- Inhibiting irrelevant info
2. Suppressing retrieval of incorrect number facts
Conflicting research as to whether _________ is related to math achievement (Szucs et al., 2013; Lee et al., 2012)
Inhibition
“Switching attention flexibly from one task to another, or considering multiple perspectives at the same time”
Shifting
Yeniad et al., (2013)
Shifting is __________ to math achievement
Correlated
How is language related to arithmetic?
Children need good language skills to learn verbal number words & understand instructions/word problems
