carcass wrote:
Students can learn mathematics only by exploring it on their own, with generous room for trial and error. For what matters, in the long run, is not acquiring particular computational skills (since without constant use skills rapidly fade), but knowing how to find and use suitable mathematical tools whenever they become necessary.
If the position expressed above is correct, then each of the following can be true EXCEPT:
The beauty of this question is that we need to find something that is DEFINITELY FALSE OR AGAINST author's conclusion. Other options might be aligned to author's conclusion, might be irrelevant or might have remote chances of being true. But as long as the are not definitely against author's conclusion, we are not interested.(A) Mathematics teachers are often afraid that someone will ask a question that they cannot answer, and this insecurity frequently leads to authoritarianism in the classroom.
This can be true based since the argument doesnt provide any details on this. But we cannot say that this is against author's conclusion
(B) Prospective teachers should themselves learn mathematics as a process of constructing and interpreting patterns, of devising strategies for solving problems, and of discovering the beauties and applications of mathematics.
This is aligned to the conclusion that maths comes by experimenting. Although the passage is talking about students but it CAN apply to teachers also
(C) Political leaders must accept responsibility for coordinating a nationwide plan for all levels of instruction if mathematics education is to improve.
This can be true based since the argument doesnt provide any details on this. But we cannot say that this is against author's conclusion
(D) The most effective method for teaching students mathematics is for teachers to state the definitive rule for solving exercises of a given type and then to insist on rote practice in its proper application.
This is definitely against author's conclusion. The author's method of learning Maths is exactly opposite of this option. So this is the answer that we are looking for(E) Most current teaching presents mathematics as established doctrine, stressing the production of right answers rather than the ability to communicate reasons.
Again this can be true as the passage doesnt give ay details on the same. But we cannot say that this is against author's conclusion
_________________
Please consider Kudos if my post is helpful. Feel free to point out mistakes in my post