## 第十一屆歐洲數學教育會議

由Freudenthal Group與烏得勒支大學的Freudenthal Institute 合作主辦的《第11屆歐洲數學教育會議》於2019年2月6日至2月10日在荷蘭烏德勒支大學舉行，作為「數學化」的追隨者，我們很高興藉着是次會議近距離接觸祖師爺Freudenthal留下來的知識與智慧。

經過連月籌備，最終數學化教學團隊一行九人出發參與是次會議。我們除了參與歐洲數學研究人員主持的講座、分享會及小組討論外，我們還參與了《Freudenthal Event》。《Freudenthal Event》是一個充滿溫情與溫度的活動，包括由Freudenthal的女兒、女婿、孫子、徒弟Marja憶述有關Freudenthal的往事，細說Freudenthal對他們的影響及展覽Freudenthal的手稿、相片等。我們除了參與學術活動外，也有舉辦數學化團隊的聯誼活動，例如與Freudenthal的徒弟Wittmann共進午餐。是次旅程在一片歡樂聲中完滿結束，各人都帶著既珍貴又難忘的回憶歸家去。

## 數學化教學二十週年聚餐

數學化教學團隊於2018年6月9日舉行二十週年聚餐，歷屆數學化團隊成員、隊長、隊目和及一眾嘉賓相聚慶祝，展望數學化教學團隊繼續推動數學教學專業化。以下是聚餐的精彩剪影。

## 數學化教學專用課本面世

十四載數學化教學，在許多熱心的前線教師積極參與之下，取得豐碩的成果。經__馮振業__、__陳麗萍__、__周惠英__、__劉心怡__和__馮仲頤__的努力，這些成果已於2013年初，成功轉化為學校、教師、家長可自由選用和購買的《校本單元數學學習套》（http://www.oupchina.com.hk/pmathskit/），是目前唯一的數學化教學專用教材。此項壯舉，得牛津大學出版社鼎力支持，一方面製成配合教材使用的精美學具，另一方面開發實用性高的電子教件，令數學化教學可以在過去的輝煌成就之上，再闖高峰。

軒尼詩道官立小學

塘尾道官立小學

德信學校

郭怡雅神父紀念學校

寶血會培靈學校

聖嘉祿學校

上水惠州公立學校

五旬節靳茂生小學

五旬節于良發小學

基督教粉嶺神召會小學

北角官立小學

港大同學會小學

漢華中學（小學部）

保良局莊啟程第二小學

樂善堂梁銶琚學校

屯門官立小學

中華基督教會何福堂小學

聖公會天水圍靈愛小學

博愛醫院歷屆總理聯誼會鄭任安夫人學校

光明學校

港澳信義會黃陳淑英紀念學校

聖公會靈愛小學

荃灣天主教小學

元朗商會小學

基督教宣道會徐澤林小學

基督教宣道會宣基小學（坪石）

寶血會嘉靈學校

深水埔街坊福利會小學

深水埗官立小學

## 珠海市香洲區第十六小學第二次來訪

2011年4月13日，珠海市香洲區第十六小學第二次來港考察數學化教學的實踐情況，以下是當天訪問英華小學的剪影。

## 珠海市考察團到訪聖公會蒙恩小學

## 德國專家維特曼教授到訪

德國數學教育家Wittmann教授於2009年5月專程到訪香港，與數學化教學團隊會面交流。在極緊密的行程下，參觀了來自三所小學的四節數學化教學課。以下是他於觀課後的評語：

Over the past weeks the lessons that you gave on May 8 have been present in my mind all the time. Dr. Fung can tell you how disappointing the subsequent conference in Taipei was for me. Your four lessons were the real highlights of my journey to Asia. I am happy to give some comments.

As far as nets of a cube are concerned I have never seen such a clear derivation of all 11 nets. The lesson was a very good exercise for students both in spatial and logical thinking. The idea of classifying these nets according to the length of the longest strip of squares is very powerful. It can also be used for deriving the nets of an open cube (with five squares). This might be a good introduction to the nets of a (closed) cube (in case one has enough time). Of course one can also derive all 12 pentominoes and 30 hexominoes this way. This is very fine.

The lesson on the chords of a circle was also very interesting for me. I think it pays off to let the students measure the length of various chords and compare the results. The diameters as the biggest chords are well recognized and internalized that way. The investigation can be re-visited in various ways. For example, the triangle inequality can be employed, and in later years the length of the chords can be expressed by means of trigonometry. I wish that German teachers could have seen this lesson, as in Germany geometry is receiving less and less attention. Trigonometry has more or less disappeared from the curriculum. Also I was struck by the change of the length of a chord which is rotated around one vertex. The change is rapid when the chords are short and becomes slower and slower when the length reaches its maximum. Thank you, Ms. Yiu, for presenting such a stimulating topic.

The third lesson on measurement was interesting for me not so much for mathematical reasons as in Germany teachers would proceed roughly the same way. However, how you, Ms. Cheung, have succeeded in managing a whole class of small kids for 40 minutes. This is considered as a “mission impossible” in Germany. In our country it is the standard view that first and second graders are simply not able to listen to a teacher for more than 5 minutes. For this reason a method is widespread in this country in which the students are given a plan of tasks at the beginning of the school day and are free to work on these tasks according to their own choice. Students working on the same problem over one lesson with clear directions from the teacher as well as discussions in the whole class are very rare in German primary classrooms. Educators tend to denounce such kind of teaching as „teacher-centered“ what I think a big mistake.

Finally, fractions: Again the comparison with Germany has been striking for me. In our country fractions are considered as a difficult subject that therefore has to be postponed to grade 6. In the years before most curricula allow only for „halves“, „quarters“ and „fifths“. In our project we try to follow the advice given by Alfred N.Whitehead: Difficult subjects should be introduced as early as possible in order to give students more time to get familiar with them. However, we are offered resistance when we try this with fractions. You in Hong Kong can be happy that your curriculum is very advanced in this respect. In talking to Dr. Fung I have learned that the Chinese language has some definite advantages. We will see how we can cope with the German situation in future. In this respect the lesson I have seen has been very enlightening for me.

I would like to thank you all very much for giving me a chance to participate in your teaching. I have been greatly impressed and I cannot but congratulate you for what you are doing. The collaboration with Dr. Fung in the TFM project is obviously very successful. It is a model of how teachers as reflective practitioners and researchers should cooperate.

以下是Wittmann教授於英華小學觀課後接受訪問的節錄：

五月八日觀課之後，數學化教學團隊與Wittmann教授到流浮山共進晚餐，渡過了一個既專業，亦難忘的晚上。

翌日Wittmann教授與馮振業於浸會大學主持一場講座，開啟了互相學習的空間，讓是次訪問以高潮終結。