师说心语 | Mr. Cowsill：教师必须尽一切努力培养那些有能力成为伟人的人的创造力
Although it ruffles some feathers to say so, I'm a maths teacher that primarily teaches to the Cambridge A-Level exams. It is my opinion that exam scores (based on the content we are learning in class) are the most accurate, objective measurement of my students' in-class learning, and therefore my teaching as a whole, that is currently available.
我是一名数学老师，主要教剑桥大学A-LEVEL课程。尽管这样说可能会让有些人感到不适，但我认为考试成绩（基于我们在课堂上学习的内容）是对我的学生在课堂上学习的最准确和客观的衡量。因此我的教学体系，目前来看是有效的。
So why the ruffled feathers? There are (well-founded) concerns that focussing too much on exam questions produces students that only know how to answer exam questions, but fail to apply much further thought.
那为什么这会让人觉得很恼火呢？人们有充分理由担心过于关注考试会使学生只知道如何回答考试问题，却无法展开更多的思考。
I want my students to do extremely well in their exams, but their mathematics education should also foster creativity, and general problem solving skills.
我希望我的学生能在考试中取得优异的成绩，另外，通过数学教育，他们也能培养出创造力和解决问题的能力。
The United Kingdom Mathematics Trust (UKMT) is a charity organization with the goal of fostering such creativity in mathematics students all over the world. They offer a fantastic variety of creative, fun, challenging maths problems, that encourage our students to use different sets of problem solving skills than they are used to in their standard lessons.
英国数学协会（UKMT）是一个慈善组织，旨在培养全世界数学学生的创造力。他们提供各种各样的创造性、有趣的、具有挑战性的数学问题，鼓励我们的学生使用不同于他们在标准课上使用的技能来解决问题。
All of our A-Level centre students here at Chengdu ShiShi are entered in the UKMT Senior Mathematical Challenge (SMC). In their A-Level maths, our students are required to use deeply-developed theory to solve problems - with the focus being on the knowledge and application of that specific theory.
所有在成都石室中学剑桥课程中心学习的学生都参加了UKMT高级数学挑战赛（SMC）。他们的A-LEVEL数学，需要学生使用深入发展的理论来解决问题，重点是特定理论的知识和应用。
In contrast, the questions in the SMC require very little in terms of developed theory. They take fairly simple ideas and ask the students to develop these simple ideas to solve a more complicated problem.
相比之下，SMC的考题仅仅需要很少的复杂理论。他们提出相当简单的想法，要求学生发散思维，拓展这个想法来解决一个更加复杂的问题。
Here is an example of a Cambridge P1 mathematics question about functions (Summer 2016 paper 12 – part of question 11):
这是一道来自剑桥大学数学 PureMath1里面关于函数的一道题（2016年夏季12卷第11题）：
To solve it, one must use developed theory about quadratic functions and their graphs, inverse functions and perform a sequence of complicated steps that they have mostly been directly taught.
要解决这一问题，必须运用完整的的二次函数及其图像、反函数的理论，然后执行一系列复杂的演算，而这些步骤大多是直接教给学生的。
Here is an example of a UKMT SMC question about functions:
这是一道UKMT SMC中关于函数的例题：
To solve it, one needs to know very little theory. One just needs to know what is meant by f(x).The rest of the working is based on simple counting principles that we learn much earlier than high school. However, it is perhaps not as clear where to go next.
要解决这个问题，只需要知道很少的理论。我们只需要知道f（x）是什么意思。剩下的步骤是基于简单的计数原则，这是我们在进入高中以前学习到的知识。不过，下一步该怎么计算或许还不太清楚。
I have always believed these two styles of problems complement each other brilliantly.
我一直认为这两种类型的问题是相辅相成的。
The A-Level maths exams lay a strong foundation of theoretical knowledge and machinery. The UKMT SMC questions encourage creativity and abstract thinking.
A-LEVEL数学考试为理论知识和力学奠定了坚实的基础。UKMT SMC的问题鼓励创造性和抽象思维。
Without a strong foundation to build on, creativity and abstract thinking are arguably useless. You can be as creative as you like, but if you lack the tools with which to create, what can you create?
没有坚实的根基，创造性和抽象思维是毫无用处的。你可以随心所欲地创造，但如果你缺乏创作的工具，你能创造什么？
Conversely, even with the strongest of foundations, a lack of creativity and abstract thought will probably allow one to be competent, but prevent them from achieving true greatness.
相反，即使是最强大的协会，缺乏创造性和抽象思维可能会让人有能力，但会阻止他们实现真正的伟大。
As teachers, it is important we do everything we can to foster that creativity in those who are truly capable of greatness.
作为教师，我们必须尽一切努力培养那些真正有能力成为伟人的人的创造力。
As previously mentioned, every year all of our students at Chengdu ShiShi A-Level centre are entered in the UKMT SMC, and every year they do extremely well.
如前所述，我们成都石室中学剑桥课程中心的所有学生每年都参与UKMT SMC，而且每年都表现得非常出色。
I hate to brag (just kidding, I LOVE to brag about our students' success) but here's how we have done previously in this competition:
我不喜欢吹嘘（只是开玩笑，我喜欢吹嘘我们学生的成功），但下面是我们之前在这场比赛中的表现：
In 2018, 28% of our students achieved gold, 28% silver and 20% bronze.
2018年，我们的学生当中有28%得到金牌，28%得到银牌，20%得到铜牌。
In 2017, 27% of our students achieved gold, 24% silver and 28% bronze.
2017年，我们的学生当中有27%得到金牌，24%得到银牌，28%得到铜牌。
In 2016, 22% of our students achieved gold, 31% silver and 31% bronze.
2016年，我们的学生当中有22%得到金牌，31%得到银牌，31%得到铜牌。
In 2015, 24% of our students achieved gold, 34% silver and 26% bronze.
2015年，我们的学生当中有24%得到金牌，34%得到银牌，26%得到铜牌。
Worldwide, the top 10% of students achieve gold, the following 20% achieve silver, and the following 30% achieve bronze.
而在世界范围内，前10%的学生获得金牌，后20%获得银牌，后30%获得铜牌。
This shows that our students at Chengdu ShiShi A-Level center are achieving far above the world average. Not only that, but we seem to be improving every year!
这说明我们成都石室中学剑桥国际课程中心的学生成绩远远高于世界平均水平。不仅如此，我们每年都在进步！
Each year, some of our top-scoring students are eligible to go on to round 2, the British Math Olympiad.
每年，我们的一些高分学生会得到晋级第二轮英国数学奥林匹克竞赛的资格。
Last year, 7 of our students were eligible and all but one competed. Round 2 consists of more challenging, open-answer questions(as opposed to multiple choice). It is designed to test and challenge the truly mathematically-inclined students.
去年，我们有7名学生获得参赛资格，其中6名学生参加了比赛。第二轮的题目包括更具挑战性的开放式回答问题（与多项选择相反），它旨在测试和挑战真正有数学倾向的学生。
In conclusion, it really is a wonderful thing that the United Kingdom Mathematics Trust are doing, and it is an absolute pleasure for us to take part.
总之，英国数学协会正在做的事情真是太棒了，我们非常高兴参加高级数学挑战赛（SMC）。
I would recommend competitions like this as a healthy supplement to a well-rounded mathematics education, for ALL students.
我建议所有学生参加这样的竞赛，以此作为全面的数学教育的良好补充。
Written by Mr. Nick Cowsill
Translated by Hu Jiacheng AS 1
