云课堂回顾丨一线解答，哈罗海口的孩子为什么那么喜欢数学课？

国际化学校的数学课教的太浅太简单？

孩子用英语上数学课听不懂怎么办？

(资料图片仅供参考)

如何让学生从小对数学产生兴趣？

如何引导他们产生数学思维？

......

在哈罗海口，数学是孩子们喜爱、家长们认可的学科，它在孩子的升学和未来发展中举足轻重。哈罗海口连续上线两场数学云课堂，分别邀请到哈罗海口小学部和中学部数学主任做客直播间，家长们在直播间踊跃提问，纷纷感叹专业。今天我们特地把直播分享的部分干货做了总结，提供给未能观看直播的家长。

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小学数学直播回顾

✔取中西方数学中的精髓教授给我们的学生；

✔数学学习以兴趣和数学思维培养为主；

✔使用英语进行推理；

✔老师都能细致观察到每个学生。

✔ 取中西方数学中的精髓来教授给我们的学生

在直播开始，低年级学术负责人Mr. Mark Johnson介绍双语数学的教学特点，小学配备双语数学教师，与主班老师合作教学。

「 我们取中国数学的优势，同时结合西方数学的长处，培养学生解决问题能力和在不同背景下运用数学的能力。每周，外教和双语数学老师一起备课，确保主题框架是一致的，他们互相学习中西方数学法和运用。」

双语数学老师尹老师是哈罗海口小学数学的补充，而不是主班教学的替代，他能给主班教学提供更多、更深度的教学内容。

James Yin

双语数学老师

墨尔本大学数学系本科，并获得墨尔本数学研究奖学金；

墨尔本皇家理工教育研究生；

澳大利亚维多利亚州注册老师；

曾在澳大利亚Thomas Carr当地私校教授数学，带过的3届毕业班，均为全校最高分；

回国后在耀华国际学校担任毕业班老师。

在尹老师的课堂中，重点在于确保学生用母语完全理解所授数学知识。当学生用母语学习数学知识点时，学生首先能用母语来说明自己的解题思路，再用英语来说明他们的解题思路。尹老师能带来的是专业度，特别是中文教学法领域，我们已经见证了很多学生的进步。

作为一所重视双语双文化的国际化学校，引进双语数学老师，能够帮助我们建立真正完整、成熟的双语课程体系。

在备课阶段，中外教团队通过取长补短的合作方式，将中国数学课程的严谨性与高难度，与注重培养发散思维和问题解决能力的国外数学课程相融合。最终形成一套超越中西方标准的成熟的数学课程体系，这样就能够利用学生在一语认知能力的发展来带动二语授课的学科技能知识的掌握，真正地实现双语双文化的授课模式。

——Ken Du

全校双语教学总监

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✔ 生活中需要数学思维

我们如何教授数学的？

在直播中老师以一个个教学中具体的例子来帮助家长理解老师的教学逻辑，并举例说明具象——形象——抽象的数学教学法。

首先第一步是具象的有形的任务，接着再从具象发展到图像化的表达，最后升华到抽象的概念。通过这个连贯的学习过程，学生更能理解所学的数学知识，学生也因此能在不同的情境下使用数学，以此来巩固学习。

直播当天也是世界数学日，小学数学组准备了很多有趣的数学活动，数学寻宝游戏，解谜游戏、时间表竞赛等，激发孩子们组成不同的队伍，一起去寻找答案。通过这些方式与我们学习的数学概念联系起来，让哈罗海口的小小数学家发光发热。

在这种比较生动的主题课过程中，孩子们不仅对所学知识的理解更加深刻了，而且全身心投入之下，他们自己就会生发出创造力，会感受到数学是一门有生命力的学科，自然地，也会对数学产生浓厚的兴趣。

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中学数学直播回顾

✔中学数学学什么？

✔如何备战IGCSE？

✔A Level 数学如何与大学课程衔接？

✔孩子英语不好，如何跟上数学课进度？

在高年级数学课直播中，中学数学主任Mr. Jason Booth就以下几个家长最为关心的问题，为我们全面解析了中学数学课堂以及IGCSE数学备考等话题！

「✔中学数学以培养学生的独立探究和自主学习的能力为主」

Mr. Booth介绍到：

「 “在中学阶段，我们会把课堂的主动权交给教给学生，通过课堂的构建以及反转课堂等形式，让学生自主研讨分享交流他们学习的成果。” 」

在中学部，我们把数学分为四大主题——数，代数，几何和统计。根据这几个大主题的不同，融入双语教学来帮助学生同时理解两种语言下的教学。

一个明确的重点是帮助学生深入理解数学知识的底层逻辑。不仅仅是强调计算上的流畅，而是如何把数学知识运用到实际生活中，应用到他们未来的事业和生活中。

在Y6/G5和Y8/G7阶段，我们根据学生不同的能力提供不一样的双语支持。双语数学课+课堂上的双语助教的双重辅助模式，来帮助那些英语程度稍弱的同学能够跟上大家学习的节奏。

当学生进入到Y9/G8-Y10/G9的时候，礼德生和国际生会接入两套有着细微不同的课程框架。

礼德生的课程框架以中国课标为指导，课程设计涵盖了中国课标和IGCSE的核心知识点，帮助在更具有包容性的学习环境中进行深度学科探索，一周设有4节英语数学课和2节数学课。国际生的课程则专注于IGCSE的学科要求，一周设6节英语数学课。

✔ 如何备战IGCSE数学？

升入十年级，礼德生会继续回到英语主导的数学课，与国际生一同全力备战IGCSE。

我们是剑桥考试局认证的学校，因此我们会把剑桥课程与中国国家课程深度融合，所以学生能够充分地准备他们的考试，并保证学习内容质量。这样的教学方法，能够帮助我们的学生不仅为IGCSE考试做准备，同时也能同步完成中国国家课程，两者在某些领域既有不同也有相似之处。

中国国家课程，尤其注重代数和几何，IGCSE课程更关注统计等主题。我们的课程设置会完全考虑到这些主题。

当学生进入十年级备战 IGCSE时，考试分为核心考试和扩展考试两类，学生会被分配到最适合他们能力的水平考试进行评估。

✔ A Level 数学如何与大学课程衔接？

我们已经在为IGCSE考试的变化，调整了我们的课程。

当学生完成IGCSE数学考试，他们将会开始进入A Level备考阶段，最终以A Level成绩申请进入大学。这需要学生拥有较强的数学能力和英语能力，尤其是在力学和统计学方面。

A Level需要两年持续学习，第一年是由纯数学和力学组成的，第二年是由纯数学、概率和统计学组成。全球的许多大学都对数学成绩有要求，特别是和理科相关的专业，比如科技，工程还有数学专业等。这些专业，都要求学生的数学是A等级。

因此哈罗A Level课程将为他们未来选择的专业打好数学基础，将对他们大学阶段的学习大有裨益。

✔ 孩子英语不好，如何跟上数学课进度？

在哈罗海口教数学，我的感受是很开心的，我发现中国的学生会在核心数学技能普遍较好。他们很愿意深入学习，他们明白未来的职业规划需要数学，数学将会为他们未来择业打开更多方向。在这两年的教学过程中，我发现我的学生都很勤奋+和专注，在我们的课堂上我经常能看到哈罗学生互助的样子。

特别是在班上学生水平不一的情况下，他们看到同伴遇到困难时，会非常乐意帮助彼此。互助也是他们谦虚的表现，这样的方法不仅仅让他们变成小老师，也进一步加深了他们对知识点的理解。

在课后，22/23学年的沙夫茨伯里全奖获得者Tiger Matsushita也分享了他在哈罗学习数学的感受：

「“我十分享受学习数学知识的过程，我的IGCSE选课是计算机，历史，经济和生物。基本上你能发现我的选课都和数学相关，我未来想学习的专业是科技领域。

哈罗海口的数学课堂，我认为最大的特点就是老师为我们提供的自由又灵活学习环境。我刚开始入学的时候，我在数学上的学习已经比同年级的很多同学要领先了，所以我的数学老师，会给我布置更难的数学任务，这种定制化的教学方法对于我这种想要学习更多数学知识的同学非常友好。未来我想去美国的大学深造，体验不一样的学习生活，我的目标是永远在进步！”」

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从直播分享中我们发现，老师注重在教授孩子知识的同时，教会孩子更多的方法，多角度、多元化地培养孩子的思维能力，让他们学得轻松自如，扎实高效，并在这个过程中我们发现每个孩子的闪光点，做好精准定制化学习。

整场分享干货满满，一篇文章很难涵盖全貌，所以我们也特地把直播设置了回放，感兴趣的家长们可以扫码关注哈罗海口视频号，回听整期分享，切身感受哈罗数学之美。

Are maths lessons provided in international schools too simple?

What if my child doesn"t understand maths lessons taught in English? How can the school get students interested in maths from an early age?

How can we guide them to develop mathematical thinking?

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At Harrow Haikou, maths is a subject that children love, and as parents recognise. It is crucial to their children"s further education. Harrow Haikou has launched two consecutive Maths Cloud Classes, featuring the Head of Maths Department of Harrow Haikou Lower and Upper Schools respectively. Parents were keen to ask questions during the live sessions and were impressed by the professionalism of Harrow"s maths teaching. Today we have summarised some of the key points shared in the live stream for those parents who couldn’t attend the event.

Review of Cloud Maths Class at Pre-Prep

✔ Taking the best of Chinese and Western teaching.

✔ Focusing on developing interest and mathematical thinking development.

✔ Using English for reasoning.

✔ Teachers can observe each student carefully.

✔Taking the best of Chinese and Western maths teaching

Mr Mark Johnson, the Deputy Head of Lower School (Academic), introduced the features of bilingual maths teaching, the Pre-Prep school has bilingual teachers who work with the homeroom teachers.

「We combine the strengths of Chinese mathematics teaching methods with those of Western teaching to develop students" problem-solving skills and the ability to use mathematics in different contexts. Each week, the foreign teacher and the bilingual maths teacher prepare lessons together to ensure that the subject framework is consistent and that they learn from each other about Chinese and Western mathematical methods and applications.」

Mr. James Yin, the Bilingual Maths Teacher, is a supplement to maths teaching at Pre-Prep, rather than a replacement for homeroom teaching.

James Yin

Bilingual Maths Teacher

-Bachelor of the School of Mathematics and Statistics at the University of Melbourne

-Master of Education at Royal Melbourne Institute of Technology

-Registered teacher in the State of Victoria, Australia

-Former teacher at Thomas Carr - a local private school in Australia and the classes he taught have achieved the highest scores in the school

-Former Sixth Form teacher at Yew Wah International Education School in China

In Mr Yin"s classroom, the focus is on ensuring that students fully understand the maths taught in their mother tongue. When students learn maths in their mother tongue, they are able to illustrate their solutions first in their mother tongue and then in English. Mr. Yin is highly professional in Chinese pedagogy. We have witnessed the progress of many students.

As an international school that values bilingualism and biculturalism, the introduction of bilingual maths teachers can help us to build a truly complete and mature bilingual curriculum.

In the lesson preparation stage, the Chinese and foreign teaching teams work together to blend the academic rigor and difficulty of the Chinese maths curriculum with the foreign maths curriculum that focuses on developing divergent thinking and problem-solving skills. Ultimately this could lead to a mature mathematics curriculum, which would use students" cognitive development in the first language to facilitate the acquisition of subject skills in the second language.

——Ken Du

Director of Bilingual Education (Whole School)

✔Mathematical thinking is needed in daily life

How do we teach maths?

In the live stream, the teacher uses a concrete example from teaching to help parents understand the teaching logic and gives examples of the Concrete-Representational-Abstract approach to teaching maths.

Students are introduced to a new mathematical concept through the use of concrete resources (e.g. fruit, base ten blocks, fraction bars, etc). When they are comfortable solving problems with physical aids, they are given problems with pictures – usually visual representations of the concrete objects they were using.

The day of online session was also World Maths Day; our Pre-Prep maths team prepared lots of fun activities, scavenger hunts, puzzle-solving games and more to inspire the children to work together to find the answers.

In lively themed lessons, children not only gain a deeper understanding of what they are learning, but they also gain more creativity and realise that mathematics is a living subject and, naturally, develop a strong interest in it.

Review of Cloud Maths Class at Upper School

✔ What to study in maths at Upper School?

✔ How to prepare for IGCSE tests?

✔ How does A Level Maths link to university courses?

✔ How do students who are not proficient enough in English keep up with their maths lessons?

In the live maths lesson, Mr. Jason Booth, the Head of the Maths Department at Upper School, gave us a comprehensive overview of the following topics on the maths classes for Upper School students and IGCSE maths preparation that parents are most concerned about.

✔ Teaching maths at the Upper School focuses on developing students" independent inquiry and self-directed learning skills.

「Mr. Booth explains, "At the secondary level, we give the initiative of the classroom to the students to teach them and allow them to share and communicate their learning through independent workshops."」

At the Upper School, we divide maths into four main topics - number, algebra, geometry, and statistics.

Depending on these broad topics, bilingualism is incorporated to help students understand the teaching in both languages.

A clear emphasis is placed on helping students to gain a deeper understanding of the underlying logic of the knowledge. It is not just about faster calculations, but about how to apply mathematical knowledge to real-life situations and to their future careers and lives.

At Y6/G5 and Y8/G7, we provide different bilingual support depending on the ability of the students.

Bilingual maths lessons are combined with a bilingual teaching assistant in the classroom to help those students who are less able to speak English to keep up with the pace of learning for everyone.

As students move into Y9/G8-Y10/G9, students at Harrow Innovation and Leadership Academy (HILA) and Harrow International School (HIS) are provided with two slightly different curriculum frameworks.

The curriculum framework for HILA students is guided by the Chinese Curriculum and is designed to cover the core knowledge of both the Chinese Curriculum and IGCSE to aid in-depth subject exploration in a more inclusive learning environment. Four English Maths lessons and two Maths lessons are provided for HILA students a week. For international students, the curriculum focuses on the subject requirements of IGCSE, with 6 English Maths lessons a week.

✔How students can prepare for their IGCSE tests?

As they move into Year 10, HILA students will continue to return to English-led maths classes and prepare fully for their IGCSEs alongside international students.

Harrow Haikou is a Cambridge Assessment International Education (CAIE) accredited school, so we integrate the Cambridge curriculum deeply with the Chinese National Curriculum (CNC) so that students are fully prepared for their exams and are assured of the quality of the content they are studying. This approach helps our students not only prepare for their IGCSE tests, but also complete the Chinese National Curriculum at the same time.

CNC focuses particularly on algebra and geometry, with the IGCSE course focusing more on topics such as statistics. Our curriculum takes these topics fully into account.

When students enter Year 10 in preparation for IGCSE, the tests are divided into two categories, Core and Extended, and students are allocated to the level test that best suits their ability.

✔How does A Level Maths link to university courses?

We are already adapting our curriculum to the changes in IGCSE tests.

Once students have completed their IGCSE maths test, they will begin their A Level preparation and eventually apply for entry to university with A Level results. This requires students to have strong mathematical skills and English language skills, particularly in mechanics and statistics.

A Level requires two years of continuous study, with the first year consisting of pure mathematics and mechanics and the second year consisting of pure mathematics, probability, and statistics. Many universities around the world require a grade in mathematics, especially in science-related subjects such as technology, engineering, and mathematics. For these subjects, students are required to achieve a grade of A in Mathematics.

The Harrow A Level course will therefore provide them with a good foundation in mathematics for their chosen future studies.

✔ How do students who are not proficient enough in English keep up with their maths lessons?

I find it very enjoyable to teach maths at Harrow Haikou and I find that Chinese students will generally be better at core maths skills.

They are very willing to study in depth and they understand that Maths will provide them with more opportunities for their future career choices. During these two years of teaching, I have found my students to be hardworking and dedicated, and I can often see Harrow students helping each other in our classrooms.

They are very willing to help each other when they see their peers struggling, especially when the class is of varying levels. Helping each other is not only a sign of their good qualities, but it can also further their understanding of knowledge.

After the class, Tiger Matsushita, the Shaftesbury scholarship winner for the 22/23 Academic Year, shared his feelings about studying maths at Harrow:

“I really enjoyed learning about maths and my IGCSE options are computing, history, economics and biology. You can find that my course selection is basically related to maths, and the field I want to study in the future is technology.

I think the main feature of the maths classes at Harrow Haikou is the free yet flexible learning environment that the teachers provide for us. When I first joined the school, I was already ahead of many of my classmates in maths. So, my maths teacher would give me higher level maths tasks and this approach was very good for me. In the future, I want to study at a university in the United States to experience a different kind of learning life, and my goal is to always be improving!”

From the sharing, we found that the teachers focus on teaching the children and developing their thinking skills in many ways at the same time. In the process, we discovered the strengths of each child and were able to develop a teaching plan to suit each child"s situation.

The whole sharing session provides a lot of information. To help parents access the full content, we have also prepared a replay of the live stream. Parents can scan the QR code below to follow the account of Harrow Haikou to view the whole session.