Number

Question 1

Do infants demonstrate numerical equivalency?

Answer 1

yes

• babies pay attention to aspects of quantity
• correspondence about quantity across presentation modality

Question 2

What did Spelke’s study show?

Answer 2

that infants have numerical understanding as young as 5 months

-babies prefer to look longer at the image that matches the number of sounds

Question 3

know Wynn’s (1992) experiment

Answer 3

1. object placed in case
2. screen comes up
3. second object added
4. hand leaves empty

2 possible outcomes:

• possible outcome: screen drops revealing 2 objects
• impossible outcome: screen drops revealing 1 object

Question 4

describe alternative explanations, weakness in Wynn’s interpretation of results

Answer 4

• unexpected outcome vs initial learning
• not necessarily precise counting
• evidence may not be conclusive about ability to count, but it seems that infants pay attention to “quantity”

Question 5

What strategies do children use to add and subtract ?

Answer 5

• 4 to 5: fingers, retrieval from memory

- 1st graders: counting from the larger addend, decomposition

Question 6

describe the results from Wynn (1992)

Answer 6

*children stare more at the impossible outcome

Question 7

three principles of counting

Answer 7

one-to-one, stable-order, cardinality

Question 8

one-to-one

Answer 8

there must be one and only one number name for each object counted

Question 9

stable-order

Answer 9

number names must always be counted in the same order

Question 10

cardinality

Answer 10

the last number name denotes the number of objects being counted

Question 11

are there cultural differences in children’s ability to count

Answer 11

• yes, some cultures emphasize math achievements while others on understanding of concepts vs procedures
• U.S. students lag behind students in most other industrialized nations, chiefly because of cultural differences in the time spent on schoolwork and homework and in parents’ attitudes toward school, effort, and ability.

Question 12

What kinds of strategies do children use to add and subtract? How do the kinds of strategies change over development?

Answer 12

• counting on their fingers (aloud)
• counting mentally
• retrieval from memory

Question 13

How do changes in information processing capacity influence numerical cognition?*

Answer 13

j

Question 14

What is the number line?

Answer 14

• give kids a line and say this is a line that goes from 1 to 10, now tell me where would you put a 2, 5, 8, 9
• kids leave more space in the first half of the line, then in the second half

Question 15

What are implicit theories about intelligence?

Answer 15

• entity theory

- incremental theory

Question 16

How does it apply to numerical cognitive achievement?

Answer 16

beliefs about intelligence affect math achievement

Question 17

What do the results of Blackwell et al., (2007tell us about implicit theories and mathematical achievement?

Answer 17

people with incremental beliefs about intelligence achieve better in math in comparison to people with entity beliefs

Question 18

entity theory of intelligence

Answer 18

belief that intelligence is something people are born with and can’t change

Question 19

Why and how has this concept been integrated in intervention programs (e.g., Siegher’s work)?

Answer 19

-for disadvantaged children, by introducing board games to improve numerical understanding

Question 20

number line study predicts

Answer 20

the extent to which children can distribute the numbers correctly on the line predicts their numerical understanding, competence in math