征服学术界铁人五项,国际数学竞赛获奖背后有哪些秘密武器? Maths Learning at CKWA

CHAO YANG

在今年美国学术五项全能竞赛中,8年级的Evan同学通过在5个不同学科领域的竞争,最终拿到了华北区比赛总分第五名的好成绩。

美国学术五项全能竞赛是具学术挑战性很强的比赛,所有学科由同一主题贯穿,让选手以全新的视角和系统的思维进行学习。提及这次比赛的成绩,Evan说道,“之所以获得美国学术五项全能比赛个人总分第五名,主要还是因为数学的成绩比较高。对我平时的学习程度来说,这次竞赛中数学的题做起来很简单,比较得心应手,所以拉高了整体成绩。”

与此同时,今年9月,朝阳凯文15位来自3-9年级的同学们参加美国大联盟夏季数学挑战赛,经历紧张的个人赛和速度赛后,共有林雨彤、龙峻泽、韩木子、任嘉朕等4名同学挤进排名30%获得铜奖,5位同学拿到比赛前50%成绩。美国“大联盟”(Math League)思维探索活动是美国及北美地区具有卓越影响力的中小学数学思维探索研学活动, 也是一项具有全球影响力的中小学数学思维探索研学活动。

如果说作为创校生Evan一路稳扎稳打的个人成绩只是个体,那么在美国大联盟数学挑战赛中同学们取得的成绩,则代表了朝阳凯文学校整体的数学水平。

 

而作为一所创校仅第四年的学校,朝阳凯文是否在数学教学中有什么秘籍,以此支持同学们在众多国际数学比赛中屡获佳绩的呢?

户外数学课 

全方位的数学学习

国家课程与剑桥课程结合,课堂内外结合,学科之间结合打造的全方位数学教学,是朝阳凯文的第一个秘密武器。

国家课程与剑桥课程结合

朝阳凯文在1-9年级为学生设置符合国家课标同时融入英国剑桥的数学课程。在满足国家课标的前提下进行技能和拓展,以便为同学们9-10进入IGCSE和 11-12年级的IBDP做准备。

 

国家课程的数学内容扎实、深入,剑桥的数学课程重注解题思路。两者结合,不仅可以多维度的培养孩子的能力,对于孩子找到适合自己的方法也很适用。

在5年级的课堂上,班主任Luna老师解释说,“比如同学们学到整数乘法的时候,人教版的解题思路是教孩子们列竖式,而剑桥数学的解题思路是方格式。再比如我们学时刻表时,剑桥的数学课是教孩子们画一个timeline时间轴,人教课程会更倾向于教孩子用结束时刻减去初始时刻这样的公式得出时长。两种方法都有自己的长处,我们都会教给孩子们,或者结合着进行教学,这样对于孩子找到适合自己的方法也很适用”。

 

Luna老师教孩子们认识3D图形 

课堂内外结合

教学不止课堂,教育是时时刻刻发生的。

在朝阳凯文,学校通过“课堂、课后、竞赛”三位一体全方面的教学培养,帮助学生们搭建和培养数学思维的能力。

中学部数学教师Mandy Wang老师介绍道,“中学部一直提供给同学们有关数学的课外课辅导,以夯实他们的数学基础。比如我在周一的课外课,是专门针对6-7年级参加滑铁卢高斯数学竞赛进行辅导的,Jessie Geng老师在周四有专门针对数学作业课后辅导的课外课。同学们通过课堂的学习以及作业和竞赛的辅导,提高他们的数学学术的专业知识,优化他们理性思维的水平以及解决具体问题的能力”。

学科之间结合

说起国际学校数学学习的最大难题,排在第一位的就是需要用英语去进行读题和解题。换言之,孩子们需要进行大量的数学专业名词背诵和理解,才能完成解题的第一步。

为了解决这一难题,在中学部数学组的老师们和英语组进行跨学科教学,通过沟通,帮助孩子们在英语上,加强对读懂数学题目的阅读和语法方面进行强化。在小学四年级谷谷老师的数学课上,她把孩子们需要了解和掌握的数学专业英文单词打出来给孩子们贴在本子上,时时刻刻提醒同学们进行背诵。

 

四年级同学贴有英文单词的笔记本

同时,谷谷老师为了帮孩子们更好的理解概念,也和语文进行了跨学科教学。她为孩子们阅读数学类绘本,通过在阅读绘本的过程中,提高孩子们的数学能力。

培养逻辑思维

数学能力的核心是数学思维能力,也是朝阳凯文学习的重中之重。

中学部平时的教学中,会要求同学们对问题进行梳理,注重事物的前后关联。比如在学习负数这个概念时,Mandy老师会要求学生们根据负数进行逻辑拓展,从而进行项目式教学。同学们从负数的历史出发,查找资料,并思考负数在实际生活中的应用,如温度、海平面等,最后再进行反思。整个教学过程形成逻辑闭环,培养锻炼他们的逻辑思维。

 

同学们做的有关负数学习的小组海报

在小学,谷谷老师也会对孩子的逻辑思维能力展开针对性训练。比如在读一道文字叙述的应用题时,谷谷老师用“空雨伞”的方法帮孩子们整理思路。“空雨伞的方法是我在学习方格笔记术的时候学到的一种方法,我把它转化了一下应用到数学教学上。简单理解,就是假如我们看天空有很多云阴天(我们看到题目中的重要信息),说明即将要下雨了(我们基于所学知识对信息产生判断),所以我们出门要带伞以免被淋湿(我们采取的行动)。最后得出结论。这个步骤虽然看起来麻烦,但对于孩子们锻炼逻辑思维能力是必不可少的环节”,谷谷老师说。

 

“空余伞”的解题步骤

同时,谷谷老师在每学完一个单元,还会带着孩子们运用思维导图的方式进行知识的复盘。同学们在复盘中,学习将知识归纳、分类,也自然而然培养了他们的逻辑能力。

四年级同学做的单元思维导图复盘 

解决生活中的问题

数学思维主要是将数学知识体系中较为复杂的问题进行具体化处理。而建立学生们的数学思维,终极目的是教他们运用数学中学到的知识解决生活中的实际问题。

比如在学习周长和面积时,五年级的Luna老师带领孩子们分成小组去探究,几个学生躺在操场上围成一个长方形或正方形,通过小组合作真正让学生体会了长方形周长和面积公式的计算过程。

 

孩子们摆成四边形的样子学习周长和面积

在中学,为了让同学们感知“变量”这个重要的概念,老师在课堂中会要求学生去结合实际生活进行理解。以百分数为例,老师将中国个人所得税率表设计成百分数的实践运用。个人所得税率在不同区间的纳税比例是固定的,每个成人的工资是不固定的,所以同学们通过自己带入数据,来感知“变量”这个概念。与此同时,老师也会要求同学们去查询国外一些国家的个人个税税率,再进行中外计算方法的对比,深化“变量”概念,帮助孩子们解决生活中的问题。

 

从全方位的学习培养逻辑思维,再用习得的逻辑思维去解决生活中的实际问题,朝阳凯文的数学教学打造了一个完整的教学生态与学习闭环,这便是凯文数学教学的秘密。

In this year’s USAP, Evan from Grade 8 won the fifth place in the total score ranking of the North China region by competing in five different subjects.           

At the same time, in September this year, 15 students from Grade 3-9 of Chaoyang Kaiwen Academy participated in the American major league summer mathematics challenge. After intense individual competition and speed competition, four students, including Lin Yutong, Long Junze, Han Muzi and Ren Jiazhen, were ranked 30% and won the bronze medal. Five students got into the top 50% of the results.

If Evan’s steady personal achievement as a founding student is only an individual case, then the achievements of his classmates in the MLS mathematics challenge represent the overall mathematics level of Chaoyang Kaiwen Academy.

 

As a school with only four years of history, does Chaoyang Kaiwen Academy have any secrets in mathematics teaching to support the students to achieve good results in many international mathematics competitions?

 

All Round Mathematics Study

The integration of national curriculum and Cambridge curriculum, the combination of in-class and after-class activities, the interdisciplinary education are the first secret weapon to build all-round mathematics teaching.

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The integration of national curriculum and Cambridge curriculum

In Grades 1-9, Chaoyang Kaiwen Academy provides students with mathematics courses in accordance with national curriculum standards and Cambridge framework. Under the premise of meeting the national curriculum standards, we should carry out skills and development to prepare for the students to enter IGCSE in G9-10 and IBDP in G11-12. The content of mathematics in national curriculum is solid and in-depth, and Cambridge’s mathematics curriculum focuses on problem-solving ideas. The integration of the two curriculum settings cannot only cultivate children’s ability in multiple dimensions, but also be suitable for children to find their own methods.

The combination of in-class and after-class activities

Teaching is not only in the classroom; education happens all the time.

 

At CKWA, we help students build and develop their mathematical thinking skills through a three-in-one approach: classroom, after-school and competition. The Secondary Department has been providing ASA classes for students to strengthen their foundation in mathematics. For example, ASA classes targeting Grade 6-7 students participating in the University of Waterloo’s Gauss Mathematics Contests and ASA classes specifically targeting maths homework.

 

Interdisciplinary integration

 

When it comes to the biggest challenge of learning math in international schools, the number one on the list is the need to read and solve problems in English. In other words, the children need to do a lot of memorization and understanding of mathematical terms in order to complete the first step of solving the problem.

 

To address this challenge, the maths team in the secondary school and the English team are working across the curriculum to help the students strengthen the reading and grammar aspects of reading and understanding maths topics in English.

In order to help the students understand the concepts better, Mrs. Gugu in Grade 4 also communicates interdisciplinarily and takes the children to read mathematical picture books to improve their mathematical skills through out the process.

 

Develop logical thinking

 

The essence of mathematical competence is the ability to think mathematically. Mathematical thinking skills are based on people’s perceptual understanding and are therefore the most important aspect of learning at CKWA.

 

In the Secondary, students are usually asked to comb through problems and focus on how things relate to each other.

 

In the Primary, Ms. Gugu also works on logical thinking skills. For example, when reading an application problem with a narrative, Ms. Gugu teaches the students how to extract important information from the problem and how to disassemble the information into formulas to reach a conclusion. Although this may seem like a lot of work, it is essential for students to practice their logical thinking skills.

Solving real-life problems 

Mathematical thinking is primarily about specifying the more complex problems in the mathematical system of knowledge. The ultimate goal of building students’ mathematical thinking, however, is to teach them to apply what they have learned in math to solve real-life problems.

 

For example, when learning about perimeter and area, Grade 5 teacher Ms. Luna led the children into small groups to investigate, with several students lying on the playground to form a rectangle or square, and through group work the students really got to experience the process of calculating the rectangle perimeter and area formula.

 

From all-round learning to cultivate logical thinking, and then using the acquired logical thinking to solve practical problems in life, CKWA mathematics teaching has created a complete teaching ecology and learning closed loop, which is the secret of CKWA mathematics teaching.

 

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