Task 7 Flashcards

1
Q

What are the three uses of numbers?

A

Cardinal numbers are used to represent the quantities of numbers

Ordinal/ranks are used to order numbers

Labels are used for labelling e.g. phone numbers

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2
Q

What are two issues that learners face regarding the uses of numbers?

A
  1. distinguish between the uses of numbers
  2. ensure that numbers are correctly mapped to their symbol (word-digit)
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3
Q

What is the distance effect?

A

Distance effect is the phenomenon where there is a shorter response time for numbers that have larger distances (e.g. 2-8) compared to those with shorter distances (2-3).

It can be both symbolic (i.e. digit) or non-symbolic (e.g. dots)

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4
Q

What is the problem size effect?

A

It is the phenomenon when responses are slower and less accurate when numbers are larger (e.g. it is easier to detect 3 dots that 36 dots)

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5
Q

Describe the development of number processing in infancy and childhood

A

Infants have some innate number processing abiltiies. e.g. in dishabituation paradigm they can detect changes in small numerosity of 2 & objects. Activation of right parietal lobe

Primary and middlehood = both symbolic and non-symbolic distance effect observed from 1st grade. Activation of left IPS and right PFC

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6
Q

Describe number processing in adulthood and neural correlates.

A

Both symbolic and non-symbolic distance effect are present.

Close numbers evoke more activation in the bilateral IPS than distant numbers for both symbolic and non symbolic.

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7
Q

What is the function of the intraparietal sulcus (IPS) and how does its activation differ in child hood and adulthood?

A

Its function is for magnitude representations denoted by number symbols.

It is bilaterally activated in adulthood and only activated on the left for children

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8
Q

What are the neural underpinnings of number processing in childhood?

A

PFC, left anterior ACC, Bilateral MFG - executive functions

Retrieval from declarative memory = fronto-temporo areas (left IFG, MTL, Hippocampus)

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9
Q

What are the neural underpinnings of number processing in adulthood?

A

IPS - Magnitude processing
Left frontal gyrus - visual symbol processing
Left supramarginal gyrus - retrieval of verbally coded information

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10
Q

What are the 3 main areas involved in number and arithmetic?

A

IPS
Left angular gyrus
Posterior superior parietal lobule

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11
Q

What is the function of IPS?

A

Magnitude representations that number symbols denote

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12
Q

What is the function of the left angular gyrus?

A

Retrieval of previously learned number facts

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13
Q

What is the function of the posterior superior parietal lobule?

A

Relating space to numbers (e.g. counting invisible objects?

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14
Q

How and when do numerical magnitude representations become automated?

A

Automation starts in 3rd grade.
This is when he numerical information starts to interfere regardless of the distance of numbers

How?
Automation is observed when an irrelevant dimension of a task interferes with one’s response by making respond slower.

E.g. in study 1 when determining which digit was larger in magnitude, the physical dimension which was irrelevant interfered when it was incongruent because it was processed automatically.

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15
Q

What is size congruity?

A
  • The slower RT that is produced by incongruent trials compared to neutral ones
  • Faster RT that is produced by congruent trials compared to neutral ones.
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16
Q

What is interference and when does it occur?

A

It is the slow reaction times produced by the incongruency of an irrelevant dimension.

  • Incongruent physical size (irrelevant dimension) can interfere with numerical comparisons (relevant dimension)
  • Incongruent numerical size (irrelevant dimension) can interfere with physical comparisons (relevant dimension)
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17
Q

What is facillitation?

A

Faster reaction times when relevant dimensions are congruent

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18
Q

When numerical comparison is relevant, what is its irrelevant dimension?

A

Physical size

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19
Q

When physical size is relevant, what is its irrelevant dimension?

A

Numerical size

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20
Q

What were the three predictions from Girelli’s study?

A
  • Since physical size is part of the perceptual dimension, it will be highly automatic earlier on. Thus, it will have a greater influence on the numerical task.
  • A link between number and their quantity representations is expected to develop more slowly and correspond to the improvement of numerical skills.
  • Autonomous activation is the result of a strong association between the numeral and its quantity representation.
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21
Q

Describe the method in study one from Girelli’s paper

A

Participants were undergrads and postgrads students

Conditions =
Laterality:
- unilateral were numbers were either small (less than 5) or large (6-9) and had numerical distance of 1. e.g. 1-2.
-the bilateral condition were one small and one large number with a numerical distance of 5 (e.g. 1 & 6)

Congruity:
- congruent: numerically larger numbers were also larger in size
- neutral: same size, or same numbers but different size
-incongruent: numerically larger number was smaller

Task:
Numerical comparison: which number is bigger in quantity?
Physical comparison: which number is bigger in size?

22
Q

Describe the two tasks used in Girelli’s study

A

Numerical comparison where participants started the number that was bigger in quantity/magnitude

Physical comparison where participants stated the number that was bigger in size

23
Q

Describe the congruency conditions

A

Congruent trials: numbers that were numerically larger also appeared larger in size

neutral: numbers were either the same size or they were the same numbers (e.g. 3 3) but different size

incongruent trials: the numerically larger number was smaller in size

24
Q

Describe the laterality condition in Girelli’s first study

A

Unilateral consisted of either small numbers (1-4) or large numbers (6-9) and the numerical distance was one (e.g. 1-2, or 6-7)

Bilateral trial consisted of one small (3) and one large (8) number adn the numerical distance was 5 (e.g. 3-8, 1-6, 4-9)

25
Q

What were the results regarding error rates from Girelli’s first experiment?

A

Error rates
* Generally low for both tasks
* More errors in incongruent for both tasks, but especially in the numerical task.

26
Q

What were the results regarding reaction times in Girelli’s first experiment?

A

RT was slower in numerical comparisons compared to physical comparisons

27
Q

What were the results regarding congruity from Girelli’s first experiment?

A
  • All congruity conditions were significantly different from one another
  • But the effect of congruity depended on the task
  • Irrelevant dimension for each was automatically activated
28
Q

What were the congruity results in the numerical comparison from Girelli’s first experiment?

A
  • All differed.
  • Both interference & facilitation determined by the interaction of the two dimensions.
29
Q

What were the congruity results in the physical comparison task from Girelli’s first experiment?

A
  • Congruent & neutral were the same
  • Incongruent was different from the other two.
  • Interference effect
30
Q

What were the laterality results from Girelli’s first experiment?

A
  • Significant main effect + interaction with congruity
  • Unilateral (smaller distance) = slower than bilateral (larger distance)
  • Greater effects of congruity in bilateral (larger distance)
31
Q

What were the conclusions from Girelli’s first experiment?

A
  • The congruity effects observed in both tasks suggests that the irrelevant dimensions are automatically activated for both tasks.
  • The physical comparisons yielded only interference effect while the numerical task had both facilitation and interference effect.
  • Larger distances between numbers enable faster RT, especially for physical comparisons
  • RT is generally faster for physical comparisons
32
Q

Girelli replicated the first experiment to children in 1st, 3rd and 5th grade. What were the conclusions from the study?

A

*Generally, all children were faster for the physical comparisons.
Laterality: all were faster for bilateral (larger distance) pairs. The effect was less prominent with increasing age.
* Congruity effect: all groups showed facilitation effect, but the emergence of interference was at third grade onwards. Thus, younger children were less likely to be interfered by the irrelevant task.
* All children were disturbed by irrelevant numerical information regardless of the distance of the numbers.
* Automacity of magnitude representation of numbers seems to develop around third grade.
* Younger children do access the semantic representations of numbers but have slow processing speed.
* Practicing one dimensions should increase its automacity.

33
Q

WHen does number processing become automated?

A

in third grade when numerical size interferes during physical size comparisons of numbers

34
Q

Describe the sample from Temple’s study

A

Adults and 5 year olds

35
Q

What was the task from Temple’s study?

A

two conditions:
Dots & digits both of which were either close (1-4) to 5 or far (6-9) from 5 and had to press a button to indicate whether the presented stimuli was larger or smaller than 5. Reaction times were measured.

36
Q

What were the results and conclusions from Temple’s study?

A
  • The results from Temple show that 5 year olds and adults both show similar distance effect which activates bilateral inferior parietal brain regions.
  • The slight delay observed in children can be accounted for by confounding variables such as the fact that they had to look when pressing the button.
  • The larger amplitudes can be explained by their thin skull which enables more electrical activity to be recorded.
  • Close digits and not far digits produced a reversal in polarity during transition to P2P from N1.
  • This reversal in polarity was observed in children for both dots and digits, especially in the dots condition for close dots. It was proposed that this is due to sensory issues.
37
Q

What was Libertus’ study aim and how was his study different from Temple’s?

A
  • Libertus wanted to test the proposal that the reversal in polarity observed for the dots condition was due to sensory issues. He used Temple’s experiment on university students but controlled for surface area of dots and randomized their display.
38
Q

What were the results from Libertus’ experiment one?

A
  • At a behavioural level, digits were processed faster. The distance effect was present for both dots & digits.
  • Digits: No difference in N1 for the distances in the digits group + Distance effect at inferior parietal & temporo occipital.
  • Smaller distances are processed slower when transitioning to P2P + there is a reversal in polarity (more positive for both distances). More right than left hemisphere activation.
  • Dots: N1 is smaller for larger distances, so faster reaction times. Both distances become more positive (reverse polarity) when transitioning to p2p. But this time, smaller distances are processed faster.
  • Dots – smaller vs. larger values: no difference in larger values. Difference in smaller, with 4 being slower than 1. Transition to P2P= both values are positive (reverse). 4 & 6 are both faster.
39
Q

Which condition was processed faster in Libertus’ first experiment? Digits or dots?

A

Digits

40
Q

What were the results regarding the distance effect in Libertus’ first experiment?

A

Distance effect was present for both dots and digits

41
Q

What was the result regarding N1 in the digits condition from Libertus’ first experiment?

A

No difference of N1 for both close and far digits

42
Q

At which brain regions was the distance effect present in the digits condition from Libertus’ first experiment?

A

inferior parietal and temporo occipital

43
Q

Explain the results pertaining to processing of distance during transition to the P2P in the digits condition from Libertus’ first experiment?

A
  • Smaller distances are processed slower when transitioning to P2P + there is a reversal in polarity (more positive for both distances). More right than left hemisphere activation.
44
Q

What were the results for the dots condition in Libertus’ first experiment?

A
  • Dots: N1 is smaller for larger distances, so faster reaction times. Both distances become more positive (reverse polarity) when transitioning to p2p. But this time, smaller distances are processed faster.
  • Dots – smaller vs. larger values: no difference in larger values. Difference in smaller, with 4 being slower than 1. Transition to P2P= both values are positive (reverse). 4 & 6 are both faster.
45
Q

What was the discussion/conslusion from Libertus first experiment?

A
  • The differences observed in the dots condition can be attributed to sensory processing, especially for small numerical values that initially start during the N1 but the interact with numerical distance effect when it transitions to p2p.
46
Q

What were the results from Temple’s study?

A

Results:
* P1, N1 & P2P observed for both groups. Larger effects for children (due to thinner skull).
* Children also slight delay which could be accounted for by the fact that pressing the button was not automatic so it made them take more time.
* Adults showed a reversal in polarity when transitioning from N1P2P for close digits. Close digits became positive while far digits remained negative. Dots also remained negative regardless of distance.
* Children showed the reversal of polarity for both dots & digits.

47
Q

What were the discussion/conslusion from Temple’s study?

A

Conclusions:
* The distance effect (i.e. larger distance processed faster) was the same for both dots & digits in both groups.
* Bilateral activations of the inferior parietal brain area in both adults & children
* There was a reversal in polarity in the distance effect for the close digits condition in adults, and both digits & dots elicited the reverse (more positive) in children.
* It was proposed that it could be accounted by sensory processing, but this was not further tested.

48
Q

What was the aim of Libertus’ first study?

A

Libertus et al. wanted to explore the idea about sensory processing to account for the reversal in polarity. They first replicated the above study and examine the cause for the reverse polarity seen when transitioning from N1 to P2p. Surface area and individual dot size was controlled for, and the dots were randomized.

49
Q

How was the second experiment from Libertus’ study different from the first?

A
  • There was no digit task, only dots.
  • There no small numbers (e.g. 1-4), only large ones.
  • Participants had to indicate if the numerosity of numbers presented were smaller or larger than 15.
  • there were three trial variations: constant size, constant surface area, and perimeter was constant across numerosities
50
Q

What were the behavioural results from Libertus’ study 2?

A

Behavioural
* Main effect of distance
* Main effect of trial type: no sig diff between area dots & size dots, but slower on peri dots than size and area.
* RT in exp 1 & 2 did not differ in the dots condition.

51
Q

What were the ERP results from the second experiment in Libertus’ study?

A

No difference in N1. Larger distances slightly faster when transitioning to P2p. Transition becomes more positive

52
Q

What were the results and conclusions from Libertus’ second experiment?

A
  • No difference in N1. Larger distances slightly faster when transitioning to P2p. Transition becomes more positive
    Conclusion:
  • The distance effect is not tied to any notation (dots or digits)
  • Results from Temple were indeed due to sensory processing.
  • When these confounding are eliminated as done in this study (using larger numerics), then the notation-independent effect is found.