What is conservation?
Knowledge of the properties of the world that are preserved under various transformations.
E.g. same volume of water in wide glass and tall glass
What was A-not-B experiment about?
If an object is put under cover A, and then, in front of the child, removed and put under cover B, the child will often look for the object under cover A. Piaget argues that this shows that the child does not understand that the object will be found under cover B.
What is object permanence in the sensory-motor stage?
The understanding that objects continue to exist even when they are no longer visible. Infants develop this concept during the first year.
How do preoperational children understand conservation of number?
They may think that changing the arrangement of objects (e.g., spreading them out) changes the number, showing they are distracted by physical appearance.
How do concrete-operational children understand conservation of number?
They recognize that quantity remains the same despite changes in arrangement or appearance.
Which kinds of neurons reflect an innate knowledge of numbers in primates?
“Number-specific neurons” are part of our evolutionary heritage. They are located in the parietal region and respond maximally to a specific number of items (can be presented visually or auditorily). The reaction decreases more the further away the amount of items is from the specific number the neuron responds to.
What kind of conservation understanding develops in the formal-operational stage?
Children can understand abstract scientific conservations, like energy and momentum, which they cannot directly experience in everyday life.
Can young children discriminate between different numbers of items (experimental evidence)?
Young children have shown the ability to discriminate between 1, 2 and 3 objects in studies on infant attention by getting bored of looking at one amount of objects and getting interested again when being presented with a different amount
Which experiment suggests that babies might be able to perform additions?
5-month-olds were presented with one object being put on a stage, letting it disappear behind a a screen afterwards. When another (second) object was added behind the screen before revealing, the infant shows surprise which is taken as evidence for them calculating 1+1=2
What is the nativists point of view on the nature-versus-nurture controversy?
The most important features of human knowledge develop due to genetic programming.
What is the empiricist’s point of view on the nature-versus-nurture controversy?
Nearly all knowledge is acquired through experience with our environment. We are capable of improving and changing fundamentally.
What is the nature-versus-nurture controversy?
A debate about the origins of knowledge between empiricists and nativists
What does the “know-better” explanation suggest?
Children learn more accurate facts and better methods, and stop relying on wrong strategies.
What happens to neurons and synapses in the first two years?
Neurons decrease, but synaptic connections increase tenfold.
What is the role of myelination in development?
It speeds up neural signal transmission and continues into early adulthood.
Which factor is more important before and after age 2?
Before 2 — neural development, after 2 — knowledge and experience.
Why doesn’t brain development after age 2 rely mainly on growth?
Because the brain already reaches about 80% of adult size — further improvement depends on learning and experience.
What happens to synapses after age 2?
The number of synapses declines.
What is the difference between “primary” and “secondary” mathematics?
“Primary” mathematics is the kind of mathematics humans have always shown and seems to be in place by age 5 (according to Geary), “ secondary” mathematics is defined as the mathematics that requires schooling
What is Case’s memory-space proposal?
He proposes that the key to solving a more-advanced cognitive problem is an increased capacity of working memory (see Noelting Juice Problems)
What are the Noelting Juice Problems? Which results did they find?
Children of different ages are shown different amounts of glasses with either juice or water. They are asked to indicate which combination of water and orange juice glasses equals a higher concentration of juice in the pitcher (which combination tastes more like juice). Children of different ages can solve the juice problems using different approaches.
Which ages of children can reliably solve which juice problems?
age 3-4: problems where all the juice goes into one pitcher
4-5: can count number of glasses -> choose the pitcher with more orange juice
(no matter how many glasses of water are added)
7-8: notice if there is more water or juice added to the pitcher (even if the amount of juice glasses is fewer than in the other pitcher)
9-10: can compute the difference between amounts -> choose pitcher with greater difference for juice (but don’t compute relative percentages yet)
Which implications does Case draw from the Juice problems at various ages?
He argues that 3-4 year olds can supposedly only hold one fact in memory (which pitcher holds the juice). 4-5 year olds seem to be able to hold 2 simple numbers in their working memory and 7-8 year olds can keep 2 subtractions. 9-10 year olds seem to be able to keep 4 facts (difference water/juice per pitcher for A and B and if it is a positive or negative difference for A and B).
Which reasons does Case give for the working memory growth?
- increased speed of neural transmission (due to myelination)
- practice trains mental operations to become more efficient (require less working memory)
