Deck 8: Numerical Development

Question 1

Based on the results of a conservation of number experiment, Piaget concluded that:

A)Many adults find mathematics difficult
B)We are born with some understanding of numbers, that is, we have some kind of innate numerical sense
C)Children who are only a few months old seem to understand addition and subtraction
D)Children have no sense of numbers and numerical relations until they are about 7 years old
E)Understanding numbers is achieved with the development of formal operations

Answer 1

Children have no sense of numbers and numerical relations until they are about 7 years old

Question 2

In the test presentations developed by Robert Cooper (1984) infants saw one of three different relations which were either: (I) the reversed relation; (II) a relation representing equal quantity; (III) a novel representation of the same relation as at habituation; (IV) ratio and percentage; or (V) proportion and fraction.

A)I, II, III
B)I, II, V
C)II, III, IV
D)I,III, IV
E)II, III, V

Answer 2

I, II, III

Question 3

Which of the statements below is false about Starkey and Cooper's (1980) study?

A)Infants who were just 2 to 3 months old can compare numbers
B)A habituation paradigm was used
C)The visual aspect and numerical aspect were controlled in the experiment
D)Infants were sensitive to a change in the fine numerical display from 3 to 2 or 2 to 3
E)The participants were less than 12 months of age

Answer 3

Infants who were just 2 to 3 months old can compare numbers

Question 4

Which of the below statements reflect the principal findings of Robert Cooper's (1984) study? (I) 10-month-old infants dishabituated to the "equal to" only; (II) 10-month-old infants dishabituated to the "reversed relation" only; (III) 14-month-olds dishabituated to "less than" and understand relational reversals; (IV) 14-month-olds dishabituated to the "equal to" only.

A)I, II
B)I, III
C)I, IV
D)II, III
E)III, IV

Question 5

Which is not true about Karen Wynn's (1992) study?

A)The aim was to test whether infants can calculate the results of simple arithmetic operations
B)It employed a violation-of-expectation paradigm
C)The results suggest that even 3-month-old infants can add and subtract small numbers
D)The dependent variable was the time infants looked at the possible versus impossible outcomes
E)Mickey Mouse served as a prop in the experimental procedure

Question 6

Which of these statements is true about Karen Wynn's (1992) second experiment?

A)Infants performed as well as adults in calculating the answers to simple mathematical problems
B)Infants had the longest looking time for (1 + 2 ) = 3, compared to (1 + 1 = 2) or (1 + 1 = 1)
C)Infants had the longest looking time for (3 - 1 ) = 1, compared to (2-1 = 1) or (1-1 = 1)
D)Wynn speculated that infants have very precise expectations of the results of these subtractions
E)Wynn speculated that infants have very precise expectations of the results of these additions

Question 7

In the study by Simon, Hespos, and Rochat (1995), it was found that: (I) Wynn's original interpretation was supported; (II) infants seemed to pay longer attention to the swap in identities; (III) impossible arithmetic elicited shorter looking times; (IV) numerical ability emerges very early in childhood.

A)I, II
B)I, III
C)I, IV
D)II, III
E)II, IV

Question 8

Clearfield and Mix's (1999) study suggested:

A)Infants actually discriminate on the basis of abstract number knowledge
B)Infants were only sensitive to a change in contour length
C)Wynn's original interpretation was supported
D)Numerical ability emerges very early in childhood
E)Their findings are not relevant to Wynn's (1992) study

Question 9

Which statement below is untrue about Xu and Spelke's (2000) study?

A)There was no significant difference in looking time between the displays
B)The aim was to test whether infants have the ability to represent approximate numerosities
C)The results suggest that infants at 6 months of age have a sense of numerosity
D)8 dots and 16 dots were used as stimuli in this study
E)A habituation procedure was employed

Question 10

Which of the following characterize this concept of "number sense": (I) it is a faculty possessed by human infants and animals; (II) it is a specialized mental mechanism for processing numbers; (III) it is present in adults; (IV) it relies on verbal encoding.

A)I, II
B)I, III
C)I, IV
D)II, IV
E)II, III

Question 11

Dehaene explained nonverbal number sense in a metaphor, which is called:

A)The Decelerator
B)The Divider
C)The Accelerator
D)The Accumulator
E)The Terminator

Question 12

Which of those listed below is NOT a principle of counting identified by Gelman and Gallistel (1978)?

A)Cardinal principle
B)One on one principle
C)Stable order
D)Abstraction
E)Order relevance

Question 13

What is the meaning of "cardinal principle" as stated by Gelman and Gallistel (1978)?

A)It is easier to count objects that are colored red than colored green
B)Each item should only be tagged with one unique number tag
C)Number words must be ordered in the same sequence across trials
D)Any objects can be counted
E)The last number represents the cardinal of the whole set

Question 14

Based on the findings of a study by Robert Cooper (1984), what is the earliest evidence that young children have the fundamental ability to represent numerical relations?

A)10-month-old infants dishabituated to the "less than" condition only
B)10-month-old infants dishabituated to the "equal to" condition only
C)10-month-old infants dishabituated to the "more than" condition only
D)14-month-old infants dishabituated to all three conditions
E)14-month-old infants habituated to the "equal to" condition only

Question 15

Wynn's (1992) study on whether young infants have an understanding of quantity revealed that:

A)Infants can add and subtract large numbers
B)Infants looked longer at possible events rather than impossible events
C)There is no difference in the time taken to look at possible and impossible events
D)Infants looked longer at impossible events rather than possible events
E)Infants are scared of impossible events

Question 16

Simon et al.'s (1995) alternative explanation for Wynn's (1992) results is that:

A)Infants are frightened when they see an impossible event
B)The impossible conditions in the experiment are unrelated to the rules of the physical world
C)The source of children's surprise is the violation of specific numeral principles
D)Infants paid more attention to the swap in identities
E)The impossible conditions in the experiment violated the rules of the physical world

Question 17

Clearfield and Mix (1999) observed that:

A)Infants were not sensitive to any changes in contour length
B)The contour size of the objects in the display does not vary systematically
C)Area and contour length covered by stimuli is not related to number
D)The contour size of the objects in the display varied systematically with the number
E)Infants were not paying attention during the task

Question 18

In Antell and Keating's (1983) study, which presented infants with displays testing their abilities to discriminate between changes in dot numbers, it appeared that:

A)Infants have no understanding of numbers but solve the task by perceptual features
B)Infants have an understanding of numbers and did not rely on perceptual features
C)Infants dishabituated to the change in numbers in the larger number groups
D)Infants dishabituated to the change in number in both small and large number groups
E)After habituating to perceptual features, infants were able to count numbers

Question 19

Xu and Spelke's (2000) study as to whether infants have the abilities to represent numerosities found that:

A)There was no significant difference in looking time between displays
B)Infants at 6 months of age do not have a sense of numerosity
C)Infants at 6 months of age have a sense of numerosity
D)Infants do not respond to perceptual qualities of a display
E)Infants at 3 months have a sense of numerosity

Question 20

Wynn's (1996) study on whether infants could enumerate actions that are marked as countable items by the temporal quality of action showed that:

A)Infants do not have a sense of number and that this enumeration system is specific
B)Infants do not have a sense of number and that this enumeration system is general
C)Infants have a sense of number and that this enumeration system is general
D)Infants have a sense of number and that this enumeration system is specific
E)Infants can count actions but not objects

Question 21

Based on information presented in the Chapter, it would be fair to conclude that infants display an understanding of numerical quantities and relations from the age of:

A)3 months
B)5 months
C)10 months
D)18 months
E)24 months

Question 22

What was the explanation for Clever Hans' mathematical abilities?

A)Clever Hans was sensitive to subtle cues that were unwittingly transmitted by the trainer
B)Clever Hans could make simple arithmetical calculations
C)It serves as an evidence that animals are intelligent
D)Clever Hans was given prior mathematical training
E)Animals have a numerical sense

Question 23

Which of the following is not true about the innate number sense proposed by Dahaene (1997) and Gallistel and Gelman (1992)?

A)It is an imprecise and fuzzy system
B)It is a specialized mental mechanism for processing numbers
C)It is based on language or knowledge of a precise number system
D)This number sense is known as the Accumulator
E)It is a preverbal system

Question 24

Which of the following principles by Gelman and Gallistel (1978) distinguishes between counting and labeling?

A)Cardinal principle
B)Order irrelevance
C)Abstraction
D)Stable order
E)One on one principle

Question 25

Based on the information presented in the Chapter, how many systems are involved in one's numerical understanding?

A)0
B)One: an innate system of number sense
C)One: a formal system of mathematics conveyed by rough education
D)Two: One innate system of number sense and one formal system of mathematics conveyed by rough education
E)Three: One innate system of number sense, one formal system of mathematics conveyed by rough education and one sense of inversion, otherwise known are the reversibility of mathematical operations