development 22 Maths

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  • Created by: CaliFish
  • Created on: 14-05-17 19:48
when we talk about the development of maths what are we really talking about
numerical understanding
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what is the most basic numerical understanding
numerical equality
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define numerical equality
the realisation that all sets of N objects have something in common
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how old infants show sense of numerical equality
5-month-old
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at least at how many sets
1-3 objects
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they have an idea of what
what is larger than something else
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but when do children really have a understanding of numerical equality
3-4 years
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what type of studies test if infants understand arithmetic
violation of expectancy paradigm
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what does this involve
show them something that shouldn't happen, and if the infant looks longer, it indicates surprise/shock
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however what 3things
the findings have not always been replicated and the location of objects has shifted therefore thats what they're looking at and there is an extent to the amount of sets they can do
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therefore, the infants ability reflects ______ rather than ____ processes
perceptual, arithmetic
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infants rely on what
subitizing
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define subitizing
look at a few objects and know how many are present, therefore they are not doing arithmetic they are just seeing there is less than last time or more
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however infants have limits to subitizing because what must the ratio be for babies to understand something is bigger than the other
2:1
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by what age can most children count to 10
3 years
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what are the 5 basic principles of counting (and understand them)
1 to 1 correspondance, stable order, cardinality, order irrelevance, abstraction
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where is there a difference in counting
culturally
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why
the language
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who does better than US
china
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why
numbers in the teens follow a constant pattern in terms of language
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what does the balance scale problem measure
reasoning and strategies
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what type of description does the balance scale give
qualitative, descriptive
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what are the 4 ages of that you see difference in
pre school, school, adolescence, adolescence + torque
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how do the preschoolers problem solve
focus on weight only
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how do the schoolers problem solve
focus on weight only, until weight is equal, then will focus on distance
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how do the adolscents problem solve
consider both weight and distance, if both are unequal then confused, might connect torque
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what is torque
the longer the lever, the less weight you need,
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sielger wanted to know what
how do children move through these stages
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what else was made in accordance with the balance scale taks
a balance scale connectionist model
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what is another name of a connectionist model
a neural network
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what is a connectionist model
computer model of the brain
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the model is given what
weight problems that are frequent, to the real world
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what does the connectionist model do
show same development as children
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therefore their learning is from the what
input
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therefore what might be an answer to singlets question
hebbian learning
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what is hebbian learning
growth of synapses, making new connections, connectionism, associations
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gradual changes in _________ can lead to stage-like changes in behaviour
synaptic weights
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what is there a lot of when studying maths
variability and selection
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finish the sentence, in challenging situations...
children generate a variety of problem solving strategies
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finish the sentence, with repeated experience...
strategies that work best 'survive'
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what math strategy is this obviously shown in
the min strategy
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what is the min strategy
to save effort, when adding up you will start from the biggest number
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what type of method is used
microgenetic design
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how
give loads of trials so that you witness the development
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what strategies did they use
fingers, retrieval, min
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sometimes they would use different strategies when
in the same experiment
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therefore there was a lot of what
variability
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how variable
never attempted strategies that violated principles of addition, distinguish good from bad, variablity was not random
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what are the stage of conclusions about their use of strategies
inflexible > variable > flexible
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what is this called
overlapping waves of strategy choice
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this led to what
overlapping waves
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what does the overlapping waves theory state
at any one time, children use multiple strategies
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finish the sentance, with age and experience..
they rely increasingly on more advanced strategies
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so development actually involves what
discovering, changing and selecting strategies
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what is this limitation of the theory
its descriptive only
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what variability does seigler identify
within an individual on related problems, within an individual on the same problem twice, within a single trial
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some may consider variablity to be wha
a nuscence factor
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but variability actually does what
contribute to cognitive growth
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what is evidence for this
before children discover min strategy they get super variable
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Other cards in this set

Card 2

Front

what is the most basic numerical understanding

Back

numerical equality

Card 3

Front

define numerical equality

Back

Preview of the front of card 3

Card 4

Front

how old infants show sense of numerical equality

Back

Preview of the front of card 4

Card 5

Front

at least at how many sets

Back

Preview of the front of card 5
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