[問題]PP-test2 第二篇Q12.15(reading)

[elizabeth88]

Some people believe that mathematics is
a difficult, dull subject that is to be pursued only
in a clear-cut, logical fashion. This belief is
perpetuated because of the way mathematics is
presented in many textbooks. Often mathematics
is reduced to a series of definitions, methods to
solve various types of problems, and theorems.
Theorems are statements whose truth can be
established by means of deductive reasoning
and proofs. This is not to minimize the importance
of proof in mathematics, for it is the very thing that
gives mathematics its strength. But the power of
the imagination is every bit as important as the
power of deductive reasoning.
The long history in the development of a
concept or any of the unproductive approaches
that were taken by early mathematicians is not
always addressed in mathematics courses. The
fact is that the mathematician seeks out relationships in
simple cases, looks for patterns, and only then
tries to generalize. It is often much later that the
generalization is proved and finds its way into an
actual textbook.
One way we can learn much about mathematics
and in the meantime find enjoyment in the process
is by studying numerical relationships that exhibit
unusual patterns. For example, children may find it
easier to learn their multiplication tables by exploring
the patterns that the numbers display. Even
complicated arithmetic problems can sometimes be
solved by using patterns. Given a difficult problem,
a mathematician will often try to solve a simpler, but
similar, problem. This type of reasoning---first
observing patterns and then predicting answers in
complicated problems ---is an example of inductive
reasoning. It involves reasoning from particular facts
or individual cases to a general statement that may
be true. The more individual occurrences that are
observed, the better able we are to make a correct
generalization. For instance, we can predict the
exact time of sunrise and sunset each day. This is an
example of inductive reasoning since the prediction is
based on a large number of observed cases. Thus
there is a very high probability that the prediction will
be successful.

12. What is the main idea of the
passage?

A.Inductive reasoning should be
included in the study of math.
B.Mathematics can be studied
only in a logical manner.
C.Proving theorems should be the
central focus of mathematics.
D.Mathematics courses should
concentrate on deductive
reasoning.
答案是A.
15. The author believes that
many mathematics textbooks
underestimate the importance of

A.imagination
B.logic
C.multiplication
D.formulas
答案是A.
想請問為何Q12及Q15答案為A,如何推出,謝謝.

[sparkchen]

This is not to minimize the importance
of proof in mathematics, for it is the very thing that
gives mathematics its strength. But the power of
the imagination is every bit as important as the
power of deductive reasoning.

ans is A