mathematical thinking Flashcards
(11 cards)
Why is maths still important to learn despite modern technology
Math gives us an understanding of:
Transitivity
Cardinality
Ordinality
Additive relations
What is transitivity
Basically deduction:
If A = B and B = C then C = A
What is cardinality
Enables us to work out the exact number in a set, even when the number is too large to estimate. When two sets of items are equal and value of one of the sets is known, can then figure out the value of the other set is the same.
What is ordinality
Use of numbers to indicate their order in relation to another. Knowing 6 is greater than 4, and so a set of 6 will always be bigger than set of 4.
What is additive relations
Quantities stay the same if nothing is added or subtracted or if same number is added and then subtracted
What are the two systems of number cognition
Approximate magnitude
Precise representations of distinct individuals
Explain signature limits
a 6 month old can do 1:2 ratios but not 2:3 but this improves with age
What are the 3 mathematical systems suggested by Carey (2004)
Analogue system
Parallel individuation system
Set- based quantification
Explain the parallel individuation system
Allows children to learn how to connect number with the counting system
Learn association between quantity and counting
Recognise and represent small numbers exactly.
Only up to 3 items
Explain set-based quantification
Understanding singular/plural distinction
Understanding of quantifiers (“a” and “some”)
Dependent on language
What is language important and not important for in maths
Important for exact calculations (parallel individuation)
not important for approximate ones (approximate magnitude)