The development of maths skills Flashcards
maths definition
study of quantitative relations
-expressed numerically these relations can be understood and manipulated in precise ways
Young children and learning maths
- formal teaching required for advanced maths
- early maths skills thought to be innate knowledge, experience, informal learning and imitation (+rely on broad array of skills)
- maths understanding is ‘cumulative’ = early learning sets foundation for later learning
maths skills are important because..
-central dimension to human experience (need it to understand: time, distance and speed)
we also need it for: stats, money, health info
early maths skills predict?
overall school success
Study: UK, US and canada (Duncan et al, 2007) found maths skill at school predicted maths achievement throughout school, above and beyond general cog. ability and social skills
-maths skill predicts reading achievement more than literacy skill
Also, predicts success in other areas:
-associated with successful financial decision
-understanding health info = better health
-predicts college completion and socio-economic status age 42 (after controlling for IQ and yrs in school)
Individual differences:
-kids maths skills are often v poor eg. 64% of 10yr olds don’t have proficient maths skills
- understanding what enables skills to develop = can design and test effective interventions to support kids
Early number milestones
-typical development from 0-6yrs
typical development of whole number competencies:
0 - can discriminate on basis of small numerosities
11 months - can discriminate increasing from decreasing numbers
2yrs - sequence of counting words begins, can do 1-1 correspondence in sharing tasks
2-6yrs - recognises no. of words mean more than one
3 yrs - counts small number of objects
3-6yrs - can use cardinality principle (eg, number of items in a set eg. 2,4,6 has a cardinality of 3)
4yrs - uses fingers to aid adding
Number sense in infancy
4 month olds looked longer at quantities that were different from ones presented before= recognise change in quantity (only worked with no.s of 4 or less)
= infants can only discriminate between quantities less than 4
-Feigenson et al - 2 crackers in one box, 3 in another, 10-12 month olds crawl to box with 3 crackers
early general magnitude system evidence
- infants may have general magnitude system for: time, space and number
- infants seem to associate more means more across dimensions (big size = more quantity = lasts longer)
- infants may be born with it or it may develop v early on (a sense of quantity or magnitude across dimensions)
- -may be why spatial skills emerge as an important predictor of main skills
Development of early maths skills
4 informal maths skills develop before school?
- non-symbolic quantity understanding
- numerical equality
- counting
- numerical magnitude estimation
Informal maths skill before school no.1:
non-symbolic quantity understanding
=knowledge of a set of items without the need to use verbal or symbolic names
- provides foundation for learning verbal labels and arithmetic
- ability to know number of a set of objects without counting them = ‘subitizing’
- 3 and 4 yr olds ability in this skill predicts math achievement score 6 months later
Informal maths skill before school no.2:
numerical equality
=understanding that sets of different objects that have the same number have something in common eg. ‘twoness’ eg. football and basketball
-emerges v early in development (6months)
Informal maths skill before school no.3
Counting
by age 3, most can count to 10. Begin to understand these counting principles:
- 1-to-1 correspondence = each object must be labelled by a single number word
- stable order = numbers should be recited in order
- cardinality = no. of objects in a set of corresponds to the last no. stated
- order irrelevance = objects can be counted in any order
- abstraction = any set of objects or events can be counted
- counting skill at age 5 predicts maths achievement at 8 yrs old
Informal maths skill before school no.4
numerical magnitude estimation
=understanding quantities are ordered along a less-to-more dimension
-this ability predicts maths achievement
Role of working memory, inhibitory control and modality specific skills
cognitive model of maths (Geary, 2004)
CHECK NOTES FOR MODEL
-in the model the idea is that deficits in mathematical domain (at the top) are caused by cognitive deficits further downstream
-central executive skills support conceptual and procedural skills (called ‘executive functions)
- modality-specific systems (lang and visuospatial) represent the info.
1) central executive skills - describes high level cog skills involved in co-ordinating and executing goal-directed behaviour - they involve:
- working memory - the system allowing us to process and maintain info
- inhibitory control - system allowing us to supress distracting info
- -> these cog skills support maths learning, help construct math knowledge and facilitate solving math problems
2) language systems and visuospatial skills
- modality - specific systems supporting the maintenance and processing of info specific to either verbal or visuospatial info
- child may have good executive function but have limitations in these 2 systems = limits ability to represent a particular type of info
1) poor visual-spatial skills affect:
- column arithmetic
- visual attention and monitoring
- number magnitude and estimation
- respresenting numbers in a spatial format
2) poor verbal skills affect:
- counting
- remembering number facts eg. times tables
- math word problems
Dyscalculia
=mathematical learning difficulty
=specific learning disorder characterised by impairments in learning basic arithmetic facts, processing numerical magnitude and performing accurate and fluent calculation
-poor at maths, but average (or above) IQ and reading scores
- 5-8% of school kids have it
- much less research for this compared to dyslexia(+less widely recognised)
causes??
1) -problem of numerosity highlighted in study that showed kids with dyscalculia counted to 3 rather than subitizing(Seeing and knowing number) – this problem isn’t likely to be due to schooling as these skills usually attained before = more likely a weak inituitive group of numbers – with this deficit= immature strategies. In extreme cases this can lead to the ‘reverse distance effect’ where it takes kids longer to decide 9>2 than that 9>8
– seems to be due to kids with dyscalculia using a counting strategy (takes longer to count from 2 - 9 than 8 - 9)
2) children may use immature strategies (eg. finger counting) because they can’t successfully represent this info in working memory
- may retrieve wrong maths strategy or info due to poor inhibitory control
- memory span usuaully lower, which is correlated with maths difficulties
