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The Concept of Number and the Counting Process

Keywords: the concepts of size, shape, number, prehistoric times, anthropologists

Humanity's primal efforts to systematize the concepts of size, shape, and number are usually regarded as the earliest mathematics. However, the concept of number and the counting process developed so long before the time of recorded history (there is chaeological evidence that counting was employed by humans as far back as 50,000 years ago) that the manner of this development is largely conjectural. Imagining how it probably came about is not difficult. The argument that humans, even in prehistoric times, had some number sense, at least to the extent of recognizing the concepts of more and less when some objects were added to or taken away from a small group, seems fair, for studies have shown that some animal possess such a sense.

With the gradual evolution of society, simple counting became imperative. A tribe had toknow how many members it had and how many enemies, and a shepherd needed to know if the flock of sheep was decreasing in size. Probably the earliest way of keeping a count was by some simple tally method, employing the principle of one-to-one correspondence. In keeping a count of sheep, for example, one finger per sheep could be turned under. Counts could also be maintained by making scratches in the dirt or on a stone, by cutting notches in a piece of wood, or by tying knots in a string.

Then, perhaps later, an assortment of vocal sounds was developed as a word tally against the number of objects in a small group. And still later, with the refinement of writing, a set of signs was devised to stand for these numbers. Such an imagined development is supported by reports of anthropologists in their studies of present-day societies that are thought to be similar to those of early humans.

11. What does the passage mainly discuss?

(A) The efforts of early humans to care for herds of animals

(B) The development of writing

(C) The beginnings of mathematics

(D) Similarities in number sense between humans and animals

12. The word "conjectural" in line 5 is closest in meaning to

(A) complex

(B) based on guessing

(C) unbelievable

(D) supported by careful research

13. Why does the author mention animals in line 9?

(A) To support a theory about the behavior of early humans

(B) To identify activities that are distinctly human

(C) To illustrate the limits of a historical record of human development

(D) To establish that early human kept domesticated animals

14. The word "it" in line 11 refers to

(A) evolution

(B) counting

(C) tribe

(D) shepherd

15. What is the basic principle of the tally method described in the second paragraph?

(A) The count is recorded permanently.

(B) Calculations provide the total count.

(C) Large quantities are represented by symbols.

(D) Each marker represents a single object.

16. The word "employing" in line 13 is closest in meaning to

(A) using

(B) paying

(C) focusing

(D) hiring

17. Which of the following is NOT mentioned as an early method of counting?

(A) Cutting notches

(B) Bending fingers

(C) Piling stones

(D) Tying knots

18. The word "maintained" in line 15 is closest in meaning to

(A) justified

(B) asserted

(C) located

(D) kept

19. The word "assortment" in line 17 is closest in meaning to

(A) instrument

(B) variety

(C) surplus

(D) symbol

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20. It can be inferred that research in other academic fields relates to research in the author's field in which of the following ways?

(A) It contributes relevant information.

(B) It is carried out on a simpler level.

(C) It is less reliable than research in the author's field.

(D) It causes misunderstandings if applied to the author's field.

21. Which of the following conclusions is supported by the passage?

(A) Counting processes did not develop until after writing became widespread.

(B) Early counting methods required herds of animals.

(C) Mathematics has remained unchanged since ancient times.

(D) Early humans first counted because of necessity.

22. Where in the passage does the author mention the ability of animals to recognized small and large groups?

(A) Lines 1-2

(B) Lines 6-9

(C) Lines 10-12

(D) Lines 17-18

参考答案：CDACC DDDDB DB

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