佛山市诺德安达学校——让学生爱上不一样的数学课 | Find Fun in Studying Mat

数学学科组长

诺德安达中国双语学院中学数学负责人

1. 经过两个月的学习，你认为目前的数学课程中，最特别之处是什么?

学生：双语教学，学数学的同时还学了英语;同学可以跟老师平等相处。在课堂上老师鼓励同学互相讨论数学问题，这种轻松愉悦的氛围和自主的学习模式，很容易让学生全身心投入到学习中去。

Ivan老师：我认为教师应该是传授客观真理的专家，通过设计不同的教学互动，鼓励学生发挥学习积极性;在我的课堂上，学生与老师平等相处是教学的前提和关键。

2. 经过两个月的学习，你认为孩子在学习数学过程中，出现了哪些改变?

家长：孩子的自主学习能力和克服困难的毅力提高了，比以前投入更多时间钻研数学，数学学习兴趣也提高了许多。

Ivan老师： 当作为权威的老师提出问题或发起讨论的时候，多数学生都不会特别积极地参与其中。学生或许认为向老师提出不一致的观点是失礼的表现，所以长久以来，学生的角色大多数是倾听者和跟随者，而老师则是课堂的中心，是学生知识的主要来源，导致学生缺乏主动性和创新意识。数学课程的改革应该将老师的定位从课堂的权威、课堂教学步骤的决定者和主要执行者，变为学生学习的指导者、答疑解惑者，调动起每一位学生的学习积极性和主动性。我们鼓励数学阅读，激发孩子对数学的兴趣。我们每学期鼓励学生阅读4本数学课外书。本学期开学初，同学们完成《不可思议的数》的读书任务，并在班上分享了自己的读书笔记。

(课外阅读书籍)

3.就你个人而言，你认为学习数学需要大量做题吗?

学生：有针对性的做是必要的，搞通搞透是目标;盲目大量刷就不值得。

Ivan老师：应试策略以题海战术为重点，通过反复训练考点，提高对解题速度。但是，题海战术难以提高解题的准确度。这个道理，就好比一个不懂游泳的人，企图通过不断换游泳池来提高技巧。如果我们希望学生获得启发，能够有创意地解决问题并克服事物的复杂性，那么，知道事实还不够——其关键在于概念性理解。概念为本 (concept-based curriculum) 的课程重新攫取学生与生俱来对世界的好奇心，并提供吸引心神投入的惊喜感受。

4. 就你的个人而言，数学老师符合你当初的期望吗?

学生：入学时没有特别想过这个问题。

家长：“严格要求”这方面超出期望，本来以为国际学校这方面可能会偏松。现对数学教学感到放心，比较有体系，各科目中首先引入分层教学的。

5.你对未来国际高中的数学学习有信心吗?

学生：觉得自己达到良好水平的问题不大，但要达到优秀尚需大大的努力。

家长：对数学学科这块与国际高中课程的衔接比较有信心。

Ivan老师培养了很多A level 和AP数学考试的高材生。在此文末尾，Ivan老师给大家推荐一个数学“烧脑”游戏 – 汉诺塔。有兴趣的家长可以与孩子一起通过游戏学习数学，让我们共同帮助孩子们爱上数学!

汉诺塔(The tower of Hanoi )问题源自印度一个古老传说：大梵天创造世界时做了三根金刚石柱子，一根柱子从下往上按照大小顺序摞着64片黄金圆盘。大梵天命令婆罗门把圆盘从下面开始按大小顺序重新摆放在另一根柱子上。并且规定，在小圆盘上不能放大圆盘，在三根柱子之间一次只能移动一个圆盘。

如下图所示，从左到右有A、B、C三根柱子，其中A柱子上面有从小叠到大的n个圆盘，现要求将A柱子上的圆盘移到C柱子上去，期间只有一个原则：一次只能移到一个盘子且大盘子不能在小盘子上面，求移动的步骤和移动的次数。

感谢Ivan老师为本文提供内容

Students and parents have complicated feeling towards learning Mathematics, one of the main subjects in our curriculum. It is an essential subject in modern society, yet many students find it challenging. Facing those difficult mathematics questions and exam papers, some students might even feel bored or reluctant to continue. Here, our subject leader and NAE China Bilingual Academy secondary school community Manager Mr. Ivan Chen would like to show you how we help students learn math in NAS Foshan.

Math Subject Leader

NAE China Bilingual Academy secondary school community Manager

1.What’s so special in mathematics learning in NAS Foshan?

Student: The specialty here is bilingual mathematics. We use both English and Chinese to learn the subject. Mr. Ivan Chen encourages and motivates us to discuss math questions in class.

Mr. Ivan Chen: I think teachers should design activities that are student-centered. Equality is the key in my class.

2. What has been changed since your child joined NAS Foshan, in terms of math learning?

Parent: My child is now willing to spend more time in learning.

Mr. Ivan Chen: When a teacher is being seen as an authority, many students might be reluctant to participate in class discussion. Students are listeners and followers in traditional classes. However, I believe that teachers should be facilitators and classes need to be student-centered, in order to motivate students to learn. I encourage math reading. Secondary students have already finished one book so far and three more to go for this semester.

(Extracurricular Reading Books)

3. What do you think of practicing exam skills?

Student: It’s necessary to practise exam skills but it must come with a purpose. We need to understand the reason behind each math question.

Mr. Ivan Chen: Practising exam skill helps improve the speed of finishing exam, but it’s not enough to improve accuracy. It’s essential to understand the concept of the subject, in order to arouse curiosity.

4. Do you think math learning in NAS Foshan is at your expectation?

Student: I haven’t really thought about that.

Parent: I’m actually quite surprised about its high standard and teachers being strict to students. I thought international education tended to have lower requirement for math learning.

5. What do you think of your future study in NAS Foshan?

Student: I think it should be relatively easy for me to pass but I'll need to work harder to achieve higher grade.

Parent: I'm quite confident that my child could achieve exellence in our school.

Mr. Ivan Chen would like to show parents and students a mathematics game here and hope that we can all enjoy math learning through games. Enjoy the following exercise!

According to the legend of the Tower of Hanoi (originally the "Tower of Brahma" in a temple in the Indian city of Benares), the temple priests are to transfer a tower consisting of 64 fragile disks of gold from one part of the temple to another, one disk at a time. The disks are arranged in order, no two of them the same size, with the largest on the bottom and the smallest on top. Because of their fragility, a larger disk may never be placed on a smaller one, and there is only one intermediate location where disks can be temporarily placed. It is said that before the priests complete their task the temple will crumble into dust and the world will vanish in a clap of thunder. Does this make mathematical sense?

In the classic math problem, there are three posts. Disks of different sizes (call the number of disks "n") are placed on the left-hand post, arranged by size with the smallest on top. You are to transfer all the disks to the right-hand post in the fewest possible moves, without ever placing a larger disk on a smaller one. One move is considered to be moving one disk from one post to another post.