Archeologists excavating sites in the ï¿Fertile

Archeologists excavating sites in the “Fertile
Crescent” region of the Middle East have
found huge amounts of small clay tokens.
These tokens varied greatly in size and
5 shape and had fairly detailed pictographs
pressed into them. Anthropologists fiercely
debated the function of the tokens. Many
researchers thought the tokens had religious
significance; after all, the region had a rich,
10 well-documented spiritual tradition, as
evidenced by the splendidly designed temple
at Uruk. Other scholars believed that the
tokens were a sort of game piece or toy.
However, neither explanation was wholly
15 satisfying to the anthropological community.
Finally, in 1970, Denise Schmandt-Besserat
unlocked the secret of the tokens. They
were accounting tools, with the quantity and
type of the good indicated by the pictograph
20 on the piece.
Cognitive scientists have since shown
that all humans, and even some animals,
possess the ability to subitize—that is, to
recognize instantly the difference between
25 one, two, and three objects, although
Kaufman et al have established that this
ability differs from actual counting. In order
to move from mere subitizing to actual
counting and arithmetic requires the ability
30 to employ metaphor, according to Lakoff
and Nunez. Arithmetic began, contend
Lakoff and Nunez, when early humans used
metaphor to map from the domain of
concrete physical objects to the domain of
35 abstract or symbolic numbers. Lakoff and
Nunez have shown that by starting with a
tangible collection of objects and then
adding or subtracting from that collection
allows all of the abstract arithmetic axioms
40 to be construed. The ancient Sumerian
tokens, which used symbols to represent
actual quantities of items, represent perhaps
the first instance of this sort of metaphorical
mapping. Indeed, many credit ancient
45 Sumerians with the invention of
mathematics.



1:
Which of the following best states the main idea of the passage?

A The discovery of ancient Sumerian tokens depicting quantities of goods provides compelling evidence that the ability to subitize is universal.

B The ability to metaphorically map concrete objects as abstract symbols first occurred in ancient Sumerian civilizations.

C Discoveries in cognitive science concerning the nature of mathematical thought coupled with archeological evidence indicate that the Sumerians were one of the founders of mathematics.

D Mathematics would not have developed without the emergence of a metaphorizing capacity.

E Counting and arithmetic differ from subitizing in that subitizing is a universal phenomenon while counting and arithmetic are localized.



2: The author’s claim about the ability to subitize would be most strengthened by the discovery of which of the following?

A Wedda man from a Sri Lankan tribe who represents the number of coconuts in his collection by assigning a corresponding clam shell to each coconut

An individual who, after sustaining a serious head injury, loses the ability to add and subtract numbers

A numbering system from an early Chinese civilization that closely resembles a system developed by a Meso-American culture

A tribe with lifestyles and customs unchanged since the Stone Age whose language contains words which designate only between “few” and “many”

A nomadic people who keep track of the days of their wandering by making notches in a thighbone

3:
The author of the passage would most likely agree with which of the following statements:

A The discovery of the ability in some chimpanzees to count would not cause cognitive scientists to rethink their position on the nature of mathematics.

B Cognitive scientists should expect human infants to be able to differentiate up to three objects.

C The ability to subitize requires the same mental faculties as the ability to count and perform arithmetic.

D The earliest known use of the metaphorizing capacity in humans involved the mapping of goods onto clay tokens.

E Arithmetic axioms, rather than being accepted as inherently true, can be proven by the manipulation of concrete collections of objects.