Maths Flashcards
what are the different areas of domain general symbolic abilities?
General intelligence: ability to learn new things; Language abilities; Working memory: ability to manipulate information in mind eg. Adding up numbers while holding the numbers in mind; Spatial abilities: understanding the spatial relationship between objects or space
what are the different areas of domain general non-symbolic abilities?
number sense. Ability to discriminate between amounts very quickly without counting: Subitizing: small numbers up to 3 or 4. Object tracking: ability to keep track of small numbers. ANS: larger amounts, relies on ratio, the size and the distance between numbers. Also present in newborns and animals
describe approximate number sense
Animals and preverbal infants have the ability to discriminate between quantities, using a non-symbolic system that relies upon approximate number representations; Approximate ‘fuzzy’ representation; Abstract; Universal; Support arithmetic; Biological basis; Connected to verbal representations
describe parallel individuation system
Tracking small numbers (Hyde)
what did Xu & Spelke (2000) find about infant habituation?
habituated to a number of dots. 50% less looking time over 3 consecutive trials relative to 1st three trails or until 14 trials
what did McCtink & Wynn (2004) discover about addition and subtraction?
9 month olds. infant who saw addition looked longer at 5 than 10 and infants who saw subtraction looked longer at 10 than 5
what did Starkey & Cooper (1980) discover about sensitivity to number?
5 to 6 month-old infants showed sensitivity to number. infants look longer when number changes
what did Clearfield & Mix (1999) discover about numerical cues etc?
6-8 month infants shown displays of 2 or 3 objects varying in contour length looked longer at change in contour length than number. discriminate using perceptual non-numerical cues. use cues that naturally co-vary with number eg. volume, area, length. can’t represent discrete number and instead represent continuous quantities in terms of overall amount
what did Feigenson & Carey (2005) discover about object tracking?
12.5 months old can object track with 2 objects, 3 objects, but not 4
what did Wynn (1992) discover about infant arithmetic?
those who saw 1+1 looked longer when 1 doll was revealed than 2. those who saw 2-1 looked longer when 2 dolls were revealed than 1. they expected correct result of the transformation
what did Wakeley, Rivera & Langer (2000) discover about infant arithmetic, contrary to the previous research by (Wynn, 1992)?
maybe infants expected a change. Showed infants: 3-1=1 and 3-1=2, 1+1=3 and 1+2=3. No difference in looking times
what did Piffer, Agrillo & Hyde (2012) discover about other species having ANS and tracking systems?
Guppies prefer to be closer to more guppies rather than less
o 5 vs 10: yes (ANS)
o 3 vs 4: yes (tracking)
o 3 vs 5: no (across systems)
what did Uller, Urquhar, Lewis & Bernsten (2013) discover about infant’s understanding of number density?
10 month old infants given some more cookies to play with. they prefer more cookies more dense in chocolate chips
what did Piaget (1953) discover in his counting experiments?
Use counting words without understanding what they mean.
DO NOT understand cardinal number, one-to-one correspondence.
Do NOT understand the logic of number and counting until at least age 6
what did Gelman and Neck (1983) discover about puppet counting?
most 3-4 year old children judged the puppet counted correctly for correct trials and pseudo-error trials
most 3-4 year old children judged the puppet counted incorrectly for one-to-one violations, stable-order violate trials, cardinal violations
showed sensitivity to counting
what were the different errors the puppet could make (Gelman and Neck, 1983)?
o Stable-order principle violated
o Cardinal principle violated
o Pseudo-error trial
what did Wynn (1990) discover about counting?
- Asked to give 1, 2, 3, 5, and 6 objects
- 2 year olds only correct on 1 and 2 – did not count
- Majority of 3 year olds were correct
what did Posid & Cordes (2015) discover about counting?
- Tested 3-4 and 5-6
- All proficient counters on “Find me a ___” (up to 6) – Wynn, 1992
- Asked to give 6 or 12
- Better when the same
what did Bryant, Christie & Rendu (1999) discover about the predictors of maths? such as logic?
understand inverse relations to understand addition and subtraction
to understand the ordinal nature of number, they realise that adding a number and subtracting the same number moves the number up and down a scale by the same amount
what were the 6 different trials in Bryant, Christie & Rendu (1999) when looking at the predictors of maths?
♣ Concrete/identical: plastic bricks (told how many so couldn’t count) – same end
♣ Concrete/nonidentical: added to one end and subtracted from the other
♣ Invisible/identical: no concrete material (told were adding men); hand movements
♣ Invisible/nonidentical: no concrete materials and added from other side; hand movements
♣ Word problems
♣ Abstract
what did Muldoon, Lewis & Towse (2005) discover about sharing?
• 3-4 year olds
• Set comparisons
• If told same in other,3 year olds would count, 4 year olds would not
• Age, counting proficiency, sharing proficiency -> cardinal inferences
• 52 months, 58 months at time 3 (3 times)
• Procedural skills:
o Sharing 10-14 items
o Counting 10/20 items
• Children improve over time
• Sharing predicts time 1 and time 2 cardinal inference
what did Nunes et al. (2011) discover about what predicts deaf children’s working memory?
• WM (8 6) (repeats 4 digits in backwards order)
• Intelligence (8 6) (WISC)
• Arithmetic (8 6) (A shop had 25 cartoons of milk and sold 14. How many are left?)
• Reasoning (8 9)
• Maths – KS2 (11) and KS3 (14)
All predict
What predicts low-income children’s abilities on high-stakes maths? (Fyfe, Rittle-Johnson & Farran, 2018)
• Nursery: o Repeating patterns o Non-symbolic quality (which has more?) • Year 1: o Symbolic mapping (2 to 2 dots) o Calculation
what did Starr, Libertus & Brannon (2013) discover about predictors of maths in children?
o Individual differences in ANS predict number counting of up to 6 items, basic calculation, number comparisons at 3.5 years
what did Navarro, Braham & Libertus (2018) discover about parents’ acuity?
- 56 1-3 year old (ANS)
- Parents also completed ANS (select how many have more dots quickly)
- Correlation of .32
what did Van Herwegen et al (2017) discover about whether we can teach ANS?
- 2-4 year olds
- Pre-tested and post-tested on ANS (which side has more)
- Played number games for 5 weeks at nursery or read books with researcher
- Children improved in ANS
what did Hannula, Lepola & Lehtinen (2010) discover about spontaneous focusing on numerosity (SFON)?
6.5 and 8.5 years. Looked at maths and reading as outcomes. Predicts arithmetic skills but not reading skills in grade 2
what did Braham, Libertus & McCrink (2018) discover about SFON?
- 54 children and parents
- 2.97 to 5.27 years (M = 4.14 years, SD = 7.29 months)
- Visit Manhattan Children’s Museum
- SFON
- Two conditions
what did Saxe (1988) discover in the Brazilian candy sellers study?
- Numbers: standard orthography numbers (2000 versus 15000): urban nonsellers
- Numbers occluded on bills: Urban sellers and non sellers
- Adding/subtracting bills (if you started the day with this money, how much is it?): urban sellers
- Ratios using money
