國際化學校的數學課教的太淺太簡單？

孩子用英語上數學課聽不懂怎么辦？

(資料圖片僅供參考)

如何讓學生從小對數學產生興趣？

如何引導他們產生數學思維？

......

在哈羅海口，數學是孩子們喜愛、家長們認可的學科，它在孩子的升學和未來發展中舉足輕重。哈羅海口連續上線兩場數學云課堂，分別邀請到哈羅海口小學部和中學部數學主任做客直播間，家長們在直播間踴躍提問，紛紛感嘆專業。今天我們特地把直播分享的部分干貨做了總結，提供給未能觀看直播的家長。

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小學數學直播回顧

?取中西方數學中的精髓教授給我們的學生；

?數學學習以興趣和數學思維培養為主；

?使用英語進行推理；

?老師都能細致觀察到每個學生。

? 取中西方數學中的精髓來教授給我們的學生

在直播開始，低年級學術負責人Mr. Mark Johnson介紹雙語數學的教學特點，小學配備雙語數學教師，與主班老師合作教學。

「 我們取中國數學的優勢，同時結合西方數學的長處，培養學生解決問題能力和在不同背景下運用數學的能力。每周，外教和雙語數學老師一起備課，確保主題框架是一致的，他們互相學習中西方數學法和運用。」

雙語數學老師尹老師是哈羅海口小學數學的補充，而不是主班教學的替代，他能給主班教學提供更多、更深度的教學內容。

James Yin

雙語數學老師

墨爾本大學數學系本科，并獲得墨爾本數學研究獎學金；

墨爾本皇家理工教育研究生；

澳大利亞維多利亞州注冊老師；

曾在澳大利亞Thomas Carr當地私校教授數學，帶過的3屆畢業班，均為全校最高分；

回國后在耀華國際學校擔任畢業班老師。

在尹老師的課堂中，重點在于確保學生用母語完全理解所授數學知識。當學生用母語學習數學知識點時，學生首先能用母語來說明自己的解題思路，再用英語來說明他們的解題思路。尹老師能帶來的是專業度，特別是中文教學法領域，我們已經見證了很多學生的進步。

作為一所重視雙語雙文化的國際化學校，引進雙語數學老師，能夠幫助我們建立真正完整、成熟的雙語課程體系。

在備課階段，中外教團隊通過取長補短的合作方式，將中國數學課程的嚴謹性與高難度，與注重培養發散思維和問題解決能力的國外數學課程相融合。最終形成一套超越中西方標準的成熟的數學課程體系，這樣就能夠利用學生在一語認知能力的發展來帶動二語授課的學科技能知識的掌握，真正地實現雙語雙文化的授課模式。

——Ken Du

全校雙語教學總監

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? 生活中需要數學思維

我們如何教授數學的？

在直播中老師以一個個教學中具體的例子來幫助家長理解老師的教學邏輯，并舉例說明具象——形象——抽象的數學教學法。

首先第一步是具象的有形的任務，接著再從具象發展到圖像化的表達，最后升華到抽象的概念。通過這個連貫的學習過程，學生更能理解所學的數學知識，學生也因此能在不同的情境下使用數學，以此來鞏固學習。

直播當天也是世界數學日，小學數學組準備了很多有趣的數學活動，數學尋寶游戲，解謎游戲、時間表競賽等，激發孩子們組成不同的隊伍，一起去尋找答案。通過這些方式與我們學習的數學概念聯系起來，讓哈羅海口的小小數學家發光發熱。

在這種比較生動的主題課過程中，孩子們不僅對所學知識的理解更加深刻了，而且全身心投入之下，他們自己就會生發出創造力，會感受到數學是一門有生命力的學科，自然地，也會對數學產生濃厚的興趣。

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中學數學直播回顧

?中學數學學什么？

?如何備戰IGCSE？

?A Level 數學如何與大學課程銜接？

?孩子英語不好，如何跟上數學課進度？

在高年級數學課直播中，中學數學主任Mr. Jason Booth就以下幾個家長最為關心的問題，為我們全面解析了中學數學課堂以及IGCSE數學備考等話題！

「?中學數學以培養學生的獨立探究和自主學習的能力為主」

Mr. Booth介紹到：

「 “在中學階段，我們會把課堂的主動權交給教給學生，通過課堂的構建以及反轉課堂等形式，讓學生自主研討分享交流他們學習的成果。” 」

在中學部，我們把數學分為四大主題——數，代數，幾何和統計。根據這幾個大主題的不同，融入雙語教學來幫助學生同時理解兩種語言下的教學。

一個明確的重點是幫助學生深入理解數學知識的底層邏輯。不僅僅是強調計算上的流暢，而是如何把數學知識運用到實際生活中，應用到他們未來的事業和生活中。

在Y6/G5和Y8/G7階段，我們根據學生不同的能力提供不一樣的雙語支持。雙語數學課+課堂上的雙語助教的雙重輔助模式，來幫助那些英語程度稍弱的同學能夠跟上大家學習的節奏。

當學生進入到Y9/G8-Y10/G9的時候，禮德生和國際生會接入兩套有著細微不同的課程框架。

禮德生的課程框架以中國課標為指導，課程設計涵蓋了中國課標和IGCSE的核心知識點，幫助在更具有包容性的學習環境中進行深度學科探索，一周設有4節英語數學課和2節數學課。國際生的課程則專注于IGCSE的學科要求，一周設6節英語數學課。

? 如何備戰IGCSE數學？

升入十年級，禮德生會繼續回到英語主導的數學課，與國際生一同全力備戰IGCSE。

我們是劍橋考試局認證的學校，因此我們會把劍橋課程與中國國家課程深度融合，所以學生能夠充分地準備他們的考試，并保證學習內容質量。這樣的教學方法，能夠幫助我們的學生不僅為IGCSE考試做準備，同時也能同步完成中國國家課程，兩者在某些領域既有不同也有相似之處。

中國國家課程，尤其注重代數和幾何，IGCSE課程更關注統計等主題。我們的課程設置會完全考慮到這些主題。

當學生進入十年級備戰 IGCSE時，考試分為核心考試和擴展考試兩類，學生會被分配到最適合他們能力的水平考試進行評估。

? A Level 數學如何與大學課程銜接？

我們已經在為IGCSE考試的變化，調整了我們的課程。

當學生完成IGCSE數學考試，他們將會開始進入A Level備考階段，最終以A Level成績申請進入大學。這需要學生擁有較強的數學能力和英語能力，尤其是在力學和統計學方面。

A Level需要兩年持續學習，第一年是由純數學和力學組成的，第二年是由純數學、概率和統計學組成。全球的許多大學都對數學成績有要求，特別是和理科相關的專業，比如科技，工程還有數學專業等。這些專業，都要求學生的數學是A等級。

因此哈羅A Level課程將為他們未來選擇的專業打好數學基礎，將對他們大學階段的學習大有裨益。

? 孩子英語不好，如何跟上數學課進度？

在哈羅海口教數學，我的感受是很開心的，我發現中國的學生會在核心數學技能普遍較好。他們很愿意深入學習，他們明白未來的職業規劃需要數學，數學將會為他們未來擇業打開更多方向。在這兩年的教學過程中，我發現我的學生都很勤奮+和專注，在我們的課堂上我經常能看到哈羅學生互助的樣子。

特別是在班上學生水平不一的情況下，他們看到同伴遇到困難時，會非常樂意幫助彼此。互助也是他們謙虛的表現，這樣的方法不僅僅讓他們變成小老師，也進一步加深了他們對知識點的理解。

在課后，22/23學年的沙夫茨伯里全獎獲得者Tiger Matsushita也分享了他在哈羅學習數學的感受：

「“我十分享受學習數學知識的過程，我的IGCSE選課是計算機，歷史，經濟和生物。基本上你能發現我的選課都和數學相關，我未來想學習的專業是科技領域。

哈羅海口的數學課堂，我認為最大的特點就是老師為我們提供的自由又靈活學習環境。我剛開始入學的時候，我在數學上的學習已經比同年級的很多同學要領先了，所以我的數學老師，會給我布置更難的數學任務，這種定制化的教學方法對于我這種想要學習更多數學知識的同學非常友好。未來我想去美國的大學深造，體驗不一樣的學習生活，我的目標是永遠在進步！”」

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從直播分享中我們發現，老師注重在教授孩子知識的同時，教會孩子更多的方法，多角度、多元化地培養孩子的思維能力，讓他們學得輕松自如，扎實高效，并在這個過程中我們發現每個孩子的閃光點，做好精準定制化學習。

整場分享干貨滿滿，一篇文章很難涵蓋全貌，所以我們也特地把直播設置了回放，感興趣的家長們可以掃碼關注哈羅海口視頻號，回聽整期分享，切身感受哈羅數學之美。

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?

......

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.