W3L2 - Behavioral and Neural Evidence for Numbers Flashcards
1.) Numbers are important and why we want to study them 2.) Number processing is distinct from language 3..) Performance on enumeration and number comparison tasks points to multiple number mechanisms in the brain 4.) Non-symbolic comparison processes are related to arithmetic 5.) The representation of numbers on a mental number line may explain some basic number phenomena 6.) Abstract coding of number in the brain allows basic calculation
Why are numbers important to study?
- Central to who we are (16,000 numbers a day)
- Basis of Civilization
- Technological advancement depends on number
- Number deficits affect people’s opportunities in society
What does sophisticated use of number depend on?
Sophisticated use of number may depend on the development of language
- Relationship is not clearly causal
- Perhaps language just generally enriches/focuses learning
What are evidences suggesting numbers are different from language. Broad Evidences
- Neuropsychological (Dyslexia vs Dyscalculia)
- Animals
- Preverbal Children
- Cultures with limited language for numbers
How do we describe numbers and language
Numbers: Foundation of Knowledge
Language: Basis of communication
Animal Studies. Why are numbers important for animals
Evolutionary Significance
What are the 6 animals discussed in W3L2
- Clever Hans (Horse)
- Jakob (Raven)
- Alex (Parrot)
- Desert Ants
- Lions
- Chimps (Ayumi)
Animals in Numbers: Clever Hans Horse
- Initially thought to be able to do math by hoof stamping (including square roots)
- But later found he was reading owner’s face
- Faces, not arithmetic
Animals in Numbers: Jakob Raven
- Could select a pot with a specific number of dots on the lid (1-7)
- Trained to open boxes and eat the seeds contained in them until a precise number of seeds had been eaten
Animals in Numbers: Alex Parrot
- Numerical ability in context of langauge
- Could squawk “1-6” how many specified colour blocks there are
- Enumerate total number of objects
- Number of “blue” blocks plate surrounded by blocks of other colour
- Specify colour of largest or smallest object
- Suggesting he had sense of greater or less than as well.
Animals in Numbers: Desert Ants
- Judge distance by counting steps
- Legs are clipped they undershoot the journey
- Given stilts, the go too far when returning from foraging
Animals in Numbers: Lions
Lions decide to attack based on the ratio of their numbers compared to the number of voices in an “intruder” pride
Animals in Numbers: Chimps Ayumi
- Number tasks that exceed the ability of humans
- When length of visible number was reduced, Ayumni could still perform while the kids performance dropped
- Superior performance on this task may reflect additional processes in addition to number
- VSTM required exceeds the 4-5 items limit of humans
Evidences that preverbal children could distingush numbers. Three studies
Numeriosity:
Preferential looking task on dot displays that differ. Reflects the novelty
- Babies looked longer at displays that had change in number 2-2 (1.9s) vs 2-3 (2.5s)
- 6mo babies can distinguish between 8 and 16 and 16 and 32 (1:2 ratio)
Arithemetic
- Babies understood 1 + 1 = 2. Stared longer when 3 dolls appeared instead of 2
What is the evidence for concept of number change over time?
Method, Results, Conclsusion
Number Line Task
Method
- Place a vertical line at the location where the above number would appear between the given number range
Result
- Children often overcompensate for the position of the given number
- Non-linear (Logarithmtic) to linear change
- Early representation represents ratio differences rather than linear separation
Conclusion
- Movement from logarithmic to linear representation over time may reflect formal education
Evidence that cultures with limited capacity for language had a sense of number
Similar number line task: Pica (2004)
- Munduruku have words that go up to 5
- Beyond 5 reflects the approximate number
- Smaller numbers are precise, larger numbers are less precise
- Progressively smaller intervals
- Logarithemtic
- Did not use numerals in a counting sequence
- Did not use numerals to refer to precise quantitites
Object Enumeration. What are the performance measures and steps
Performance Measures
- IV: Random spots/dots
- DV: Accuracy and RT
Steps
- Symbolic encoding of visual information
- Accessing that symbolic representation for combining into a total or sum
Object Enumeration. What are the results?
Evidence for 2 counting mechanims for dot enumeration
- “Sibsitising” Number Range
- Set Size <4
- Rapid and Accurate
- “Approximate Number System”
- Set Size >4
- Slow And Approximate
RT curve shows “elbow” at the 4ish number
Number comparison: What are the types
- Symbolic (8+3)
- Non-Symbolic (Dots)
- Cross-Modal (8 + Dots)
Number comparison: What are the results. Symbolic Elaboration
Number Distance Effect
Slower RT and Less Accurate for numbers closer in numerical distance
- Suggests that neural mechanisms are ordered in a functional way
- Supports mental number line
Number comparison: What are the results. Non-Symbolic Elaboration
Weber’s Ratio
- Errors depend on the ratio of the magnitudes
- Smaller Weber ratio implies Higher sensitivity to ratio differences
- Weber ratios for numerical similarity are linear on a log scale
- Imprecise in subsitising range
Cross model number comparison. Results? and Conclusion?
Results
- Cross modal number as accurate as unimodal
- Little/ No accuracy cost for comparing numerosities across stimulus format or modality
- But cross-modal is slower than unimodal in general
Conclusion
- Number comparison is a general brain mechanism, not a visual brain mechanism
- Judgements of approximate number is a due to a representation of number
