arithmetic development

Question 1

what is the most basic numerical understanding?

Answer 1

numerical equality

Question 2

what is numerical equality?

Answer 2

the realisation that all sets of N objects have something in common

Question 3

at what age do infants show sensitivity to numerical equality?

Answer 3

around 5 months (for sets of 1-3 objects)

Question 4

do infants understand large numbers precisely?

Answer 4

no - they have an approximate sense of larger numbers

Question 5

when do children show precise representations of sets larger than 3?

Answer 5

around 3-4 years of age

Question 6

do all researchers agree infants understand arithemtic?

Answer 6

no - some argue infants rely on perceptual processes rather than true arithmetic

Question 7

what perceptual process may explain infants’ numerical abilities?

Answer 7

subitizing

Question 8

what is subitizing?

Answer 8

rapidly and accurately recognising small quantities (without counting)

Question 9

what is the ‘seemingly impossible’ task?

Answer 9

infants watch objects added or removed behind a screen

Question 10

how do 5 month old infants typically respond?

Answer 10

they look longer at impossible outcomes

Question 11

what does longer looking suggest (according to some researchers?

Answer 11

surprise or violated expectations (e.g. expecting 2 dolls but seeing 1)

Question 12

who conducted the original ‘impossible task’ study?

Answer 12

Wynn (1992)

Question 13

have these findings been consistently replicated?

Answer 13

no - replication failures include Wakeley et al (2000) and Cohen & Marks (2002)

Question 14

what is a key limitation of infants’ arithmetic competence?

Answer 14

limited to small sets and may rely on perceptual processes

Question 15

at what age can most children count to 10?

Answer 15

3 years old

Question 16

what are the five principles of counting and what are they?

Answer 16

1. one to one correspondence : one number word per object
2. stable order : number words are always recited in the same order
3. cardinality : last number counted represents the total quantity
4. order irrelevance : objects can be counted in any order
5. abstraction : any set of objects can be counted

Question 17

what is the ‘min’ strategy?

Answer 17

starting counting from the larger of two numbers e.g. 5+2 (start at 5 and count up 2)

Question 18

who studied the min strategy?

Answer 18

Siegler & Jenkins (1989)

Question 19

what method did Siegler & Jenkins use?

Answer 19

microgenetic study

Question 20

how many children were in the min strategy experiment?

Answer 20

98 4-5 year olds

Question 21

how long were children followed in the min strategy study?

Answer 21

11 weeks

Question 22

what was measured in the min strategy study?

Answer 22

speed, accuracy and reported strategies

Question 23

what strategies did children use and how variable were they in the min strategy study?

Answer 23

finger counting, retrieval and the min strategy - they used different strategies on ~1/3 of trails for the same problem

Question 24

what is the overlapping waves theory?

Answer 24

children use multiple strategies at the same time during development

Question 25

when is behaviour most variable?

Answer 25

just before discovering a new strategy

Question 26

how does development occur according to this theory?

Answer 26

through changes in strategy use and discovery of new strategies

Question 27

what happens to effective strategies over time?

Answer 27

used more frequently ('survive')

Question 28

is finger counting an effective strategy?

Answer 28

yes - smart and useful one and should be encouraged to help with arithmetic difficulties

Question 29

what cognitive ability supports finger counting and the min strategy?

Answer 29

working memory

Question 30

what did Dupont-Boine & Thevenot (2017) find?

Answer 30

finger counting was linked to better arithmetic performance and working memory

Question 31

how was reading for pleasure related to maths achievement?

Answer 31

children who read weekly at age 10 scored ~10% higher in maths at 16

Question 32

how strong was the reading effect compared to parental education?

Answer 32

nearly 4 times stronger

Question 33

why might reading improve maths ability?

Answer 33

supports understanding and learning of new concepts

Question 34

who conducted the reading for pleasure study?

Answer 34

Sullivan & Brown (2015)

Question 35

what intervention improved maths in year 1 children and what app was used?

Answer 35

completing maths problems as part of bedtime routines and an adapted version of the bedtime math app

Question 36

who benefitted the most from the math-before-bed study, and who conducted it?

Answer 36

children of high maths-anxious parents and Berkowitz et al (2015)

Question 37

how do storybooks influence maths learning?

Answer 37

through extratextual maths-related talk during reading

Question 38

what is the difference between implicit and explicit maths storybooks?

Answer 38

implicit : maths only in illustrations explicit : maths in both text and illustrations

Question 39

what condition in the storybook study led to more maths-related talk and what types of maths talk increased?

Answer 39

explicit condition, counting, cardinality, comparisons, shapes, patterns, spatial talk

Question 40

who conducted the storybook study?

Answer 40

Wang, Vasilyeva & Laski (2024)

Question 41

how do boardgames support numerical understanding and who researched this?

Answer 41

numbers correspond to distance moved, time elapsed and number words spoken, involved 20 games (~3 mins each) over 2-3 weeks, researched by Geetha Ramani & Robert Siegler

Question 42

what is a key rule in the Great Race, and what should not be counted? what did the control group do?

Answer 42

children name the number squares they land on, should not count the moves themselves and the control group named colours instead of numbers

Question 43

why is number line estimation difficult for children?

Answer 43

children struggle to understand numbers as linear

Question 44

which group showed improvement on number line tasks and who reported these findings?

Answer 44

number boardgame group, Siegler & Ramani (2008)

Question 45

did the benefits persist over time in the board game study?

Answer 45

yes - remained after 9 weeks

Question 46

do circular boardgames improve number understanding?

Answer 46

no - very little improvement

Question 47

which type of boardgame is most effective?

Answer 47

linear boardgames

Question 48

why aren't boardgames used more in schools?

Answer 48

- lack of resources / training - curriculum pressure - concern play overshadows learning - decline of play after preschool