DEVELOP Reading and Maths Flashcards
(16 cards)
What is the order of maths learning?
Maths order:
-non-symbolic, learning the count, symbolic, arithmetic operations, rational numbers, algebra.
Outline Starkey and Cooper (1980) study into Innate number sense?
72 infants, 16-30 weeks old.
Habituation- dishabituation-of-looking procedure- duration of first fixation.
Infants habituated to arrays containing particular number of dots then presented post-habituation array containing different number of dots. Small + large conditions with same ratios.
Dishabituation for small but not large condition. In small condition. infants looked at display with new number of dots for long time. Small number conditions, infants discriminate among small arrays that were identical in length not number + density but not number.
=Infants recognise change in number, are subitizing for small number condition.
Outline Cleafield + Mix (1999) study into Innate number sense?
16 infant ppt 6-8months.
Infants habituate to display 2 or 3 black squares on page. Test with alternating displays of either familiar number of squares with novel contour length of a novel number of squares with familiar contour length.
=Infants dishabituated to display that changed in contour length. Infants did not dishabituate to display that changed in number. Conclusion: infants base discrimination on contour length ( or some other continuous variable) not number.
Outline Wynn (1992) study into innate number sense?
Trying to understand adding and subtracting in babies as young as 5 months old. Puppet show with addition and subtraction.
Initially they make sense e.g. 2-1=1.
Then follow up study had 1+1=3.
=infants looked longer at wrong outcomes.
= 5 month olds can calculate results of simple arithmetical operations on small number of items
=infants posses true numerical concepts.
=Humans innately endowed with arithmetic abilities.
Outline Wakeley et al study into innate number sense?
Replicated Wynn’s study. Failure to replicate across all condition- babies did not longer at the incorrect than the correct outcomes.
What is symbolic number mapping?
Symbolic mapping are abstract and exact representations of numerosity.
Human invention to describe numerosity’s.
-> 2 forms: number words + Arabic digits.
Words for small numbers are among the first
Describe what number word acquisition is?
Kids learn the count sequence by rote before understanding the numerical meaning of number words and Arabic numerals.
Rote counting-reciting the number words in sequence.
Acquire meaning of ‘one’ at a young age, but they do not automatically grasp the meaning of ‘two’.
-> english-speaking children: 24-36 months.
->culture-dependent (e.g. plural markers of nouns).
-> morphological bootstrapping hypothesis.
What are the counting principles in kids learning mathematics?
The one-to-one principle:
-each object can only be counted once.
-each number word paired with one and only one object.
-each object can only be paired with one number word.
-all objects paired with a number word.
What is the stable order principle, in counting principles in kids?
The number words are recited in a fixed order.
What is the abstraction stable order principle, in counting principles in kids?
Any array or collection of sets can be counted.
We count the collection of sets the same way regardless of their characteristics.
What is the order irrelevance principle, in counting principles in kids?
The order in which objects are counted does not matter.
Each order lead to same result.
What is the cardinality principle, in counting principles in kids?
Last number in count sequence also describes how many objects there are in total set.
Not only describes the order of the object but also the quantity of whole set.
How do we test the cardinality principle?
Give-N-task (Wynn, 1990).
Grabbers, pre-number-knowers.
Subset- knowers (one-knower, two-knower, three-knower, four-knower).
Cardinal principle- knower.
Childrne typically become CP-knowers around 3-4 years of age, larger inter-individual variations.
What is the Arabic digit acquisition?
-also represent exact numericities.
-Children acquire meaning of Arabic digits slightly later than meaning of number words.
-correlated with onset of schooling- children learn to write the numbers and connect the number names with written symbols.
-> E.g. Jimenes Lira et al (2017).
2-to 4-year old children.
=kids knowledge of non-symbolic exact quantities, spoken number words, and digits predicted their ability to map between symbolic and non-symbolic exact quantities.
=children’s knowledge of the mappings between digits and non-symbolic quantities (i.e., of spoken number words or written digits) predicted symbolic number comparison.
Explain how Hurst et al (2017) connected spoken number words, Arabic digits & quantity?
Design 3-to-4 year-old children.
Given 6 mapping tasks.
