Course Objectives

Students will work in groups and give an attempt to solve the following geometry problems:

• Transformations of Planes and Equidcomposition of Areas

• Geometry vs Algebra

• Pythagoras’ Theorem

• Properties of Polyhedron

• Volume of Pyramid, Cone and Sphere

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In addition, students will be able to:  

• have hands-on experiences in some exploration activities, group discussion as well as interactions with the instructor in learning the captioned five topics in an interesting way;

• initially grasp some ideas for the captioned topics;

• apply those geometrical knowledge to the solution of some unfamiliar problems in geometry;

• improve their problem solving and higher ordering skills through the learning activities;

• improve their interpersonal and intrapersonal skills while they would collectively solve some challenging problems together; and

• appreciate the beauty of mathematics and also perceive math learning to more fun and meaningful.

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Course Description

What is mathematics? Calculation? Or loads of working steps? The aim of this course is to let students have an in-depth understanding towards geometry as well as how geometrical methods can be used to solve complicated algebraic problems in an easier way.

Topics that will be covered in the course include: 

• How to find some formulas of areas of planes by using the basic concept of integration;

• How to solve algebraic problems by Platonic solids & Euler’s formula;

• Application of Pythagorean theorem in figures of 2-D figures and 3-D figures; and

• Speculation of the formulae of finding volumes of pyramids and spheres.

 

After the course, students will know more about geometry in a wider and deeper way so that they would be able to appreciate the extraordinary charm of geometry in math.

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Target Participants / Prerequisite​

P4-P6 students  

• High scores obtained in all summative assessments of Math in P. 3, P. 4 or P. 5

• Obtaining any award in local or international math competitions

• Good conduct

 

Course Instructor

Mr. Anderson KWAN

Anderson KWAN (Cert.Ed., B.Sc., M.Sc., M.Ed., MACE), who seconded to Mathematics Education Section of Education Bureau (EDB) for 2 years, is an adjudicator of EDB Math Book Report Competition since 2009, a focus and working group member of EDB Digital Depository (Math) from 2009 to 2013. 

In addition, he was also a founding member of the special interest group for Gifted Education, Creativity and Talent Development at HKU. Besides, he has acted as a course designer and tutor of gifted programmes held by HKU for several times as well as had a sharing to HKU M.Ed. students regarding gifted education. 

He was also a guest speaker invited by the Review and Planning Section of EDB as well as the Faculty of Education at HKU respectively to conduct a sharing to secondary teachers and HKU M.Ed. students how to conduct math lessons for junior form secondary students by English Medium Instruction. 

At last, he also publishes a journal in 2013 jointly written with a HKU associate professor regarding the design of the programmes about gifted education in Math in Gifted and Talented International Journal as well as another paper about the design rationale and implementation of mathematically gifted programs in 2019 School Mathematics Newsletter Vol. 22 published by Mathematics Education Section, Curriculum Institute, Education Bureau, Government of the Hong Kong Special Administrative Region. 

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Medium of Instruction

Cantonese supplemented with English

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課程宗旨

參與本課程的學生以小組的方式就以下的幾何課題，嘗試解決相關問題:

·       平面的變換及面積的等分組成

·       幾何與代數

·       畢氏定理

·       多面體的特性

·       錐體、圓錐體及球體的體積

 

在參與課程內各種學習活動時，參與課程的學員能:

1.      透過參與課程內各項解難活動、分組討論及與導師的交流，使更具趣味來學習以上五個課題;

2.      初步理解以上五個課題的相關知識;

3.      應用相關幾何知識來解決不同情況下的幾何問題;

4.      提高其解難及高階思維能力;

5.      提高個人表達能力及與人溝通能力;

6.      欣賞數學之美及明白學習數學更具意義。

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課程大綱

數學等同算術？學習數學過程只涉及一大堆計算步驟？本課程的目的讓學員認識及研習幾何問題，並教導學員如何使用幾何去解決一些複雜的數學問題。課程內容包括:使用積分概念推測一些平面圖形面積的公式、使用幾何方法處理代數問題、柏拉圖立體與尤位公式、畢氏定理在平面和立體上的應用及推測錐體及球體的體積公式。學員完成本課程後對幾何課題會有更深入和廣泛的認識，更能體會幾何在數學中的超凡魅力。

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目標對象／參加條件

小四至小六的學生：

• 需在需在小三、小四或小五取得優異的數學科成績；

• 曾獲得任何本地或國際的數學比賽獎項；

• 良好品德 

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課程導師

關焯權先生

關先生獲取香港大學教育碩士、理碩士(電腦) 、理學士(工程) 、教育文憑及香港電腦教育學會專業會員。他曾以借調形式在教育局數學教育組工作兩年，並從2009年開始至今擔任教育局數學組數學閱讀報告比賽的籌委及評判之一。在2009年至2013年期間，他曾獲邀擔任教育局「課程為本學與教資源庫(數學) 」焦點及工作小組成員之一。

 

此外，他亦為香港大學教育學院融合及特殊教育研究發展中心轄下資優教育、創意及天才發展工作小組創始成員之一。過往數年，他均擔任本暑假資優課程的課程設計者及導師，並早年獲邀與修讀港大教育學院教育碩士生分享對資優教育的看法。

 

他也曾分別獲教育局檢討及策劃組和港大教育學院邀請擔任講者，向中學數學老師及任讀港大教育學院教育碩士生分享以英語教授數學的經驗。

 

最後，他聯同一位港大教育學院副教授撰寫一篇有關數學資優課程設計的論文，並於2013年《資優及天才國際期刊》內發表。他亦將於港特別行政區教育局課程發展署數學教育組《2019學校數學通訊第二十二期》內發表一文章有關數學資優課程的設計理念及實踐。

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授課語言

廣東話輔以英文筆記

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