NC3 Flashcards by Sophie Rennison

Wynn (1992)

5 month old infants have arithmetic

Expectations

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Wynn (1992)

5 month old infants have

Arithmetic expectations

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Wynn (1992)

_____ infants have arithmetic expectations

5 month old

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Wynn (1992)

How did they know that the infants had arithmetic expectations?

Babies look longer at unexpected events

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McCrink + Wynn (2004)

Method:

Occluder rises to cover objects, which were either _______ or __________

Added to

Subtracted from

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McCrink + Wynn (2004)

Found that ___ olds also have arithmetic expectations

9 month

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Huttenlocher et al., (1994) found __________ arithmetic skills in preschool children

Non-symbolic

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Huttenlocher et al., (1994)

Evidence of non-symbolic arithmetic skills in __________

Preschool children (2-4)

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Huttenlocher et al., (1994)

Conclusion

Preschool children display

Mental model for arithmetic before formal schooling

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Huttenlocher et al., (1994)

Non-symbolic arithmetic skills increased

With age

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Huttenlocher et al., (1994)

_________ increased with age

Non symbolic arithmetic skills

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Huttenlocher et al., (1994)

Found a decrease in performance with

Increasing problem size (1+1 easier than 4+1)

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(Rasmussen + Bisanz, 2005)

________ memory relates to non-symbolic calculation

Visuospatial working

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Jordan et al., (2007)

Non-verbal calculation predicts

Later math achievement

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Levine et al., 1992

RQ: What are the effects of

Different formats in children 4 to 6 1/2

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Levine et al., 1992

What were the 3 formats of math problem presented

Non verbal

Word problems

Abstract symbolic problems

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Levine et al., 1992

Findings (older children)

More accurate in all formats

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Levine et al., 1992

Findings (addition)

All children were more accurate in non-verbal format

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Levine et al., 1992

Findings (subtraction - what were children most accurate in?)

Children were more accurate in NON-VERBAL format (e.g. dots)

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Levine et al., 1992

Findings (subtraction) what were children least accurate in?

Abstract symbolic

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Levine et al., 1992

Spontaneous use of ____________ when children had to solve word/abstract problems

Fingers

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Levine et al., 1992

What was found in terms of HOW the children tackled the math problems (verbal & abstract)

Spontaneously used fingers

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Hembree (1992) conducted a meta analysis on…

The effect of MANIPULATIVEs and PROBLEM FORMAT on arithmetic skills

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Hembree (1992) (Meta-analysis on problem format/manipulatives)

Up to 7 years old…

Providing manipulatives improves accuracy

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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 1. Problems refer to real situations/objects 2. Familiar contexts 3. ____________

Use of pictures

How to solve word problems? 4 steps (CESP)

1. Create representation 2. Extract relevant info 3. Select appropriate operation 4. 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)

1. 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

1. Start with procedural strategies 2. Every time, association between prob. and answer strengthened 3. If strength of association exceeds the threshold, answer is retrieved

Siegeler et al., 1988 Distributions of associations network Analysis of the performance...(2)

1. 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

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)

1. D-S mathematical knowledge | 2. Domain-general executive function and language

3 examples of Executive function skills

1. Working memory 2. Inhibition 3. 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)

1. 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