Flashcards in Understanding of Mathematics Deck (22)
What are domain general abilities?
General intelligence, language abilities, working memory, spatial abilities.
Not specific to maths.
What are domain specific abilities in maths?
Symbolic abilities (e.g. knowing the order of the counting names).
Non-symbolic abilities (e.g. ability to discriminate between amounts very quickly without counting).
What is approximate number sense?
The innate ability to discriminate between quantities - using a non-symbolic system that relies upon approximate number presentations.
Abstract. Universal. Support arithmetic. Biological. Connected to verbal representations.
What is the parallel individuation system?
Tracking small numbers.
Is the ANS innate? What is the evidence for this?
Xu & Spelke (2000) - can infants discriminate between 8 and 16 dots on a screen?
Habituated to these.
Infants become interested in the new number, therefore, infants can tell the difference between the 2:1 ratio - innate evidence.
McCrink & Wynn (2004) - 9mo infants. Infants who saw addition looked longer at 5 than 10 and infants who saw subtraction looked longer at 10 than 5 - innate evidence.
Coubart, Izard, Spelke, Marie & Streri (2014) - newborns. When looking at 4vs12 and 3vs9 they did look longer at the different number - but this was not seen for 2vs3. Ratios need to be large.
What is the subitising task? What has it shown us?
Chesney & Haladjian (2011) - how many dots can you see? Starkey & Cooper (1980) - Object tracking - 6mo. Sensitivity to number - infants look longer when number changes.
Clearfield & Mix (1999) - infants looked longer at change in contour length than number. Infants discriminate stems using perceptual non-numerical cues like area and length. These just happen to co-vary with numbers. Goes against Starkey's study but still shows that infants see a change in some way.
How many objects are 5-12mos able to track?
Feigenson & Carey (2005) - 3 max.
What is the evidence for infant arithmetic?
Wynn (1992) - 5mos. Some may be innate but not completely.
Doll and screen task - infants expected the correct result of the transformation.
Wakeley et al (2000) - suggest that infants may simply expect a change.
How many objects can the tracking system subitise?
What evidence has been used to show that other species have ANS and tracking systems?
Piffer et al (2012) - Guppies!
Have an ANS and a tracking system. But can't merge system - don't know the difference between 3vs5.
What comprises the tracking system?
Subitising + tracking of objects.
At what age did Uller et al (2013) show that infants can understand number density?
Infants prefer more dense.
What did Piaget (1953) believe about counting?
Constructed a counting experiment (1953) - asked to count one set + infer number of second or asked to count both and asked if they're equal.
Children use counting words without understanding what they mean.
They do not understand cardinal number or one-to-one correspondence.
They do not understand the logic of number and counting until at least 6.
What did Gelman believe about counting?
Suggested that younger children may be able to count if Piaget's task was simpler.
Use puppet counting (Gelman & Mack, 1983). Examples included correct trial, one-to-one principle violation, stable-order principle violation, pseudo-error trial, cardinal principle violation.
What did Gelman discover?
Majority of 3-4yos judged that the puppet counted correctly in correct + pseudo-error trials.
Majority judged that the puppet counted incorrectly for the violations.
Conclusion: children showed sensitivity to counting - against Piaget's theory!
What other studies (apart from Gelman) went against Piaget's counting theory?
Wynn (1990) - majority of 3yos were correct when counting.
Posid & Cordes (2015) - tested 3-4yos and 5-6yos - all proficient counters up to 6. They were better at counting when the object was the same and when it was up to 6 instead of 12.
How is logic a predictor of maths?
Bryant et al (1999) - children must understand inverse relations to understand addition + subtraction. 5-6yos. Given inversion + control problems.
Concrete trials were done better (where they had actual material).
Non-identical problems were harder.
Logic is important.
What are other predictors of maths (apart from logic)?
Muldoon (2005) - sharing proficiency, age + counting proficiency. Children also improve overtime. Sharing can predict cardinal inferences.
Nunes (2010s) - WM, intelligence, arithmetic, reasoning and maths at KS2 and KS3.
Fyfe et al (2018) - repeating patterns, non-symbolic quality, symbolic mapping + calculation all predict maths at 4-6th grades.
Starr et al (2013) - individual differences in ANS predict maths abilities like basic calculation.
Navarro et al (2018) - parents' acuity (ANS scores). r = .32.
Can we teach ANS?
Van Herwegen (2017) - 2-4yos. Pre-test + post-test. Children improved in ANS.
What can spontaneous focusing on numerosity (SFON) predict?
Hannula et al (2010) - arithmetic but not reading skills.
Can we increase SFON?
Braham et al (2018) - budget or healthy eating condition.
Children did better on the SFON task in the budget condition.
PA - talk about numbers more at home + in school to improve SFON.