Passage Summary
Para1: With the excavation of archeological evidence, several possible theories pose to explain the token found, and made the conclusion on its use as “counting tool”
Para2: The author explain the reason to the proposed explanation in para1 by using Sumerian to illustrate how the process in human intelligence at ancient time evolve from the simple subtilizing to develop the capacity to comprehend counting and the abstract arithmetic concept
Q1) 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.
In order to move from mere subitizing to actual counting and arithmetic requires the ability 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 abstract or symbolic numbers. …. The ancient Sumerian tokens….
………from sentence in Para2, we only know ancient Sumerian is an “early” civilization, whether its first or not we don’t know for sure
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.
Correct, Para 1 states the possible explanation to the archeological evidence found, then in para2, using cognitive science to explain how the primitive mathematical thought evolve from subitizing to abstract arithmetic understanding, as could be seen in the Sumerian civilization, (C) perfectly cover the whole context
D) Mathematics would not have developed without the emergence of a metaphorizing capacity.
Lakoff and Nunez, when early humans used metaphor to map from the domain of concrete…..this statement is in Para 2, (D) only concern Para 2 and doesn’t cover the whole passage
E) Counting and arithmetic differ from subitizing in that subitizing is a universal phenomenon while counting and arithmetic are localized.
Same as (A), subitizing is just used as a medium to illustrate the actual counting-invention of mathematic, not the main focus for the passage
Q2) The author’s claim about the ability to subitize would be most strengthened by the discovery of which of the following?
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 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 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 abstract or symbolic numbers.
A) 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
As the sentence clearly says subitizing ability is not counting and needs the more abstract-metaphor understanding, from (A) we only need the ability to match and actual counting for the number of coconut, its subtlety in discussion is of different context, also assign the items to a number of subjects its not the subitizing ability, won’t strengthen or weaken subitizing ability
B) An individual who, after sustaining a serious head injury, loses the ability to add and subtract 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 to be construed.”
…..from sentence in para 2, the ability to adding and subtracting numbers is the subitizing ability, however, (B) states that an individual “lose” the ability, so it weakens, not strengthen this ability
C) A numbering system from an early Chinese civilization that closely resembles a system developed by a Meso-American culture
…..numbering system is an abstract arithmetic development, fit perfectly to para2, strengthen the subitizing ability
D) A tribe with lifestyles and customs unchanged since the Stone Age whose language contains words which designate only between “few” and “many”
……“few” and “many” is too primitive for the abstract subitizing ability to develop, thus weaken
E) A nomadic people who keep track of the days of their wandering by making notches in a thighbone
….. same as (A), won’t affect the subitizing ability
Q3) The author of the passage would most likely agree with which of the following statements:
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 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 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 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 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 Sumerians with the invention of mathematics.
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.
counting ability is the base to the development of abstract mathematic or arthimetic, they always relate to each other, so essentially what (A) states is wrong
B) Cognitive scientists should expect human infants to be able to differentiate up to three objects.
"the ability to subitize—that is, to recognize instantly the difference between one, two, and three objects", so infants can differentiate objects is indeed the subitizing ability
C) The ability to subitize requires the same mental faculties as the ability to count and perform arithmetic.
From sentence “In order to move from mere subitizing to actual counting and arithmetic requires the ability 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 abstract or symbolic numbers.”, .....we just know that to evolve from subitizing to actual counting we need the metaphorical ability, not that these two need "the same mental faculties"
D) The earliest known use of the metaphorizing capacity in humans involved the mapping of goods onto clay tokens.
“, when early humans used metaphor to map from the domain of concrete physical objects to the domain of abstract or symbolic numbers.”
….the statement to choice (D) is of differ from the original sentence in para 2 says, so wrong
E) Arithmetic axioms, rather than being accepted as inherently true, can be proven by the manipulation of concrete collections of objects.
no proof to arithmetic axioms ever discuss in the passage