A great discovery solves a great problem but there is a bit of discovery in the solution for any problem. Your problem may be minor; but if it challenges your curiosity and inspires your creativity, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a young age may create a taste for mental work and leave their lasting impression on the mind and character for a lifetime.
Thus, a teacher of mathematics has (1)[a great opportunity]. If he fills his time with drilling his students in routine operations, he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems in proportion to their knowledge, and helps them solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.
Also a student whose college curriculum includes some mathematics has (2)[an excellent opportunity]. This opportunity is lost, of course, if he regards mathematics as a subject which he must take and which he should forget as quickly as possible after the final examination. The opportunity may be lost even if the student has some natural talent for mathematics because he, as everybody else, must discover his talents and tastes; he cannot know that he likes raspberry pie if he has never tasted raspberry pie. He may manage to find out, however, that a mathematics problem may be as much fun as a crossword puzzle, or that vigorous mental work may be an exercise as desirable as a fast game of tennis. Having tasted the pleasure of mathematics, he will not forget it easily, and then there is a good chance that mathematics will become something for him: a hobby, or a tool of his profession, or his profession, or a great ambition.
I remember the time when I was a student myself, a somewhat ambitious student, eager to understand a little mathematics and physics. I listened to lectures, read books, tried to take in the solutions and facts presented, but (3)[there was a question that disturbed me] again and again: “Yes, the solution seems to work, it appears to be correct; but how is it possible to invent such a solution? Yes, this experiment seems to work, this appears to be a fact; but how can people discover such facts? And how could I invent or discover such things by myself?” Today I am teaching mathematics in a university; I hope that some of my more eager students ask similar questions and I try to satisfy their curiosity. Trying to understand not only the solution of this or that problem but also the motives and procedures of the solution, and trying to explain these motives and procedures to others, I was finally led to write the present book. I hope that it will be useful to teachers who wish to develop their students’ ability to solve problems, and to students who are keen on developing their own abilities.
問1 本文中の(1)[a great opportunity] とは,教師にとってどのような機会であると筆者は考えていますか。(50～60文字)
問2 本文中の(2)[an excellent opportunity] とありますが,筆者は,どのような場合にこれが失われてしまうと考えていますか。(40～50文字)
問3 本文中の(3)[there was a question that disturbed me] とありますが,筆者を悩ませたのはどのような疑問ですか。 (50～60文字)
【あなたへの指示：はじめ】
上の英文は, ある数学者が自分の著書に付した序文の一部です。私はこれを読んで、問1、問2、問3に対し、それぞれ下記のように、答1、答2、答3として答えました。あなたは私の英語の先生になって、それぞれの答について本文や問と見比べ、抜けている要素は減点、過剰な要素も減点、無関係な要素も減点、関係ある要素は加点、要約が適切なら加点、ほか、高校生レベルといえるかも考慮しつつ、適切な回答かどうかを考え、根拠と共に、0点～100点で点数化して、それぞれの答が何点ずつか、点数をつけてください。文字数が足りないものは40点満点まで点数を比例圧縮して減らすこと。
答1：
答2：
答3：
【あなたへの指示：おわり】
