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Intro to block 2 mathematics - Coggle Diagram
Intro to block 2 mathematics
children learning maths
Skemp(1989)
two types of maths
instrumental understanding
learning mathematical procedures and being able to carry them out
relational understanding
see the relationships between different areas of mathematics, and being able to apply knowledge and understanding to new situations.
those who successful at maths can do both
skemp work built on by Chinn and Ashcroft (1998) and Poustie (2000)
leading to two basic types of cognitive style: the grasshopper and the inchworm.
Compton et al. (2007) summarised
grasshopper
Are intuitive thinkers
Like ‘the big picture’
Make estimates
Look for patterns
Like to verify information
Solve problems mentally
Make flexible use of methods which change
Adjust numbers for ease of calculation
Enjoy investigations
inchworm learners
Are prescriptive
Like facts
Write information down
Look for formulae
Avoid verifying
Follow procedures
Use a single method
Use numbers exactly as given
Enjoy analysis
Counting and understanding number
Counting
1978, Gelman and Gallistel
identified five counting principles, all of which children need to master in order to count successfully.
Compton et al. provided a helpful summary of these principles
Stable order principle.
number names remain in a constant order. earn the number order, particularly through songs and rhymes.
One-to-one correspondence.
Each item is to be counted only once. This is often done by touching, pointing, nodding towards or moving each object.
Cardinal principle.
he final number spoken indicates the number of items in a set. Children begin to realise that the last number spoken is the answer to ‘How many?’ questions and tells you how many there are.
Abstraction principle.
Anything can be counted even if the items are not exactly alike. This is the appreciation that counting the number of objects is not affected by size or position or whether or not the items are of the same type
Order-irrelevance principle.
Objects can be counted beginning with any item, whatever its position within the set.
number lines