S2 L3 - Reading and Mathematical Development 1 Flashcards
(32 cards)
How far has maths attainment declined in the UK?
Decreased by 13 points since the 2018 Pisa and 16 points on OECD
Large gap between disadvantaged and advantaged pupils
What % of adults in the UK have numeracy below that needed to function in every day life? (eg understanding food prices, pay household bills)
24%
What is the Approximate Number System?
Our minds come equipped with a rich and flexible sense of number
Several researchers will argue that humans are born with the ability to reason mathematically
What is the Habituation-dishabituation-of-looking procedure?
Duration of first fixation
72 infants between 16-30 weeks of age
Infants habituated to arrays containing a particular number of dots than presented a post-habituation array containing different number of dots
Small and large number conditions with same ratios
Infants can recognise a change in number
Infants are subitising for small-number condition
Another innate number sense test by clearfield and mix?
16 infants between 6-8 months
Infants habituated to displays of either 2 or three black squares on a page
Tested w alternating displays of either a familiar number of squares with a novel contour length of a novel number of squares with a familiar contour length
results-
infants dishabituated to the display that changed in contour length
infants did not dishabituated to the display that changed in number
infants base their discrimination on contour length (or some other continuous variable that correlates with it), not on number
What did Wynn find
infants looked longer at wrong outcomes
5 month old infants can calculate the results of simple arithmetical operations on small number of items
infants possess true numerical concepts
humans innately endowed with arithmetic abilities
humans innately endowed with arithmetic abilities
what did wakeley find?
failure to replicate across all conditions - wynns study - babies did not look longer at the incorrect than the correct number
What are Symbolic Numbers?
Abstract and exact representations of numerosity
Human intervention to describe numerosities
^Typically two forms - Number words and Arabic digits
Words for small numbers are among the first words learnt
whereas arabic digits are learned slightly later
What is rote counting? And they learn this before understanding what?
Reciting the number words in sequence
The numerical meaning of number words and arabic numerals
children get the meaning of “one” at a young age but they dont automatically get the meaning of “two”
english speaking children - 24-36 months
culture-dependent (eg plural markers of nouns)
-Morphological Bootstrapping Hypothesis
Children learn the skills of counting first (Counting Principles)
What are the principles?
The one-to-one principle
The stable order principle
The abstraction principle
The order irrelevance principle
The cardinality principle
Children need to understand all of these to understand counting
What is the One-to-one principle?
Each object can only be counted once
each number word has to be paired with one and only one object
Each object can only be paired with one number word
All objects are paired with a number word
What is the stable order principle
The number words are recited in a fixed order
(Number words are recited)
What is the Abstraction Principle?
Any array or collection of sets can be counted
We count the collection of sets in the same way no matter their characteristics (the size or shape or what they are eg colour circles, dogs, cats, shapes, different circle sizes grouped together)
What is the Order Irrelevance Principle?
The order in which objects are counted does not matter and will lead to the same result
9same number of objects)
What is the Cardinality Principle?
The last number in the count sequence also describes how many objects there are in the total set (the cardinal value)
Not only describes the order of the object but also the quantity of the whole set
How can we test for the Cardinality principle? (the last number in the count sequence being how many objects there are in the total set)
The Give-N-Task
- Grabbers
-Pre-number knowers (number given is unrelated to the requested number)
(different levels of knowers been proposed
-Subset knowers - for some numbers theyre unreliable
(one-knower, two-knowers, three-knowers, four-knowers)
Then they become Cardinal Principle (CP) knower
can reliably give you the number of j=objects for example youve asked for
Do children acquire the meaning of Arabic digits before or after learning the meaning of number words?
Slightly later (after)
correlated w the onset of schooling when children learn to write the numbers and connect the number names with written symbols
What do Arabic digits represent?
Exact numerosities
What is the connecting spoken number words, Arabic digits, and quantity by Jimenez Lira 2017?
2-4year old children
Mapping task (which of the 2 stimuli matched the target stimulus)
a) Quantity - to - number word
b) Number word to quantity
c) Number word to digit
d) Digit to number word
e) Quantity to digit
f) Digit to quantity
found that childrens knowledge of non-symbolic exact quantities, spoken number words, and digits predicted their ability to map between symbolic and non-symbolic exact quantities
childrens knowledge of the mappings between digits and non-symbolic quantities ie number of spoken words or written digits predicted symbolic number comparison
What did Hurst design?
3-4 year old children
6 mapping tasks
Word-Numeral Dyad
Quantity-Numeral Dyad
Quantity-Word Dyad
mapping between quantities and numerals were more difficult than mapping between numerals and number words and number words and quantities
the ability to map a quantity to a word predicted their spoken word to numeral which then predicted their ability to map a quantity to a numeral dyad - mediation (something occureicie?)
numerals are mapped to quantities indirectly via direct words
may first map numerals to number words
and only through this mapping can they then tie to abstract quantity representations
What is Ordinality?
The relation between items in a sequence
ordinality develops later than cardinality
ordering numbers smallest to largest
grade 1 and kindergarten children have a strict definition of order that is tied to knowledge of count sequence (ie can order adjecent but not non-adjacent sequences)
by 7-12 years of age, children quite accurate for both adjacent and non-adjacent sequences
How can you assess ordinality development?
Number ordering tasks (more appropriate for children)
Judgement Tasks
Performance on the two tasks are highly correlated and they tap into the same cognitive skill
What is a number ordering task?
ask children to tap the numbers displayed in order going from smallest to largest
take into account speed and accuracy
theyre good at adjacent sequences but not non-adjacent sequences so theyd have difficulty with that
What is the Order-Judgement task?
display numbers
put either a tick or cross if they go in ascending order
