Teachers' Sharing

Teaching at PolyU has always been challenging. For some reasons, the subjects our undergraduate students are taking aren’t necessarily their first choice.  It could be part of a package bundled with their bachelor’s degree programme. For example, students majoring in one science discipline are required to take mandatory mathematics courses. Though learning mathematics and statistics skills is important for their research and academic development, some may not find it as enjoyable r engaging as their preferred subjects. While some students might be enthusiastic, they may feel “haunted” by a few predominating factors that have yet to be resolved. For example:

1. There is a lack of the traditional mathematics ambiance in secondary school (as evidenced by the decreasing percentages of students taking M1 or M2, and the syllabus of HKDSE Maths/M1/M2 has been reduced compared to that of the previous curriculums like HKCEE Maths and A-Maths, as well as HKAL Pure-Math). While it may be possible to teach students at the tertiary level, the mentality of refusing to understand deeper mathematics or lacking the perseverance to learn harder concepts has been harmful.

2. We also have to face the problem that students are indoctrinated with the habit of exam-oriented drilling of maths exercises, which can hinder their ability to appreciate the beauty of mathematics at their younger age. Despite getting high exam score, many lack the interest in exploring the significance of mathematics, and its rich cultural achievements throughout human history.

To tackle this phenomenon, lecturers are trying very hard to make their lectures and tutorials more interesting within the limits of the syllabus. Some adopt modern gadgets with trendy high-tech tools to teach, while some attempt to build an approachable and friendly relationship with students to let them have a positive image towards maths.

As we are all aware, undergraduate curriculum particularly focuses on teaching basic and fundamental concepts and skills, and more advanced research only when getting into research school. To inspire student interest in these subjects at the undergraduate level, lecturers usually recall their first passion that sparkled for the subjects years ago, in an attempt to reignite the passion of students by sharing their personal experience.

Nevertheless, I have a bolder suggestion. On the one hand, with the old school approach, to look back in time, to see how human civilization first became interested in mathematics and other science disciplines, as history gives us a better understanding of the logic behind some practices and the reason they change over time. And knowing all the history gives students a strong foothold to move forward. If STEM is an arrow pointing towards a target future, then knowing where the arrow starts and how history forms its natural direction is far more important than just focusing on the advanced achievements at the target end.

On the other hand, with the new school approach, I strongly encourage the incorporation of cloud computing mathematics software in teaching, such as using of CoCalc, as they can reduce the amount of monotonous work involved in mathematics teaching, and free up more time for students to confirm their graph sketching and the partial fraction expansions, or practice mathematical thinking, with just a click.

溫故至盡、知新以極，探幽窮賾在理工

在大學任教所面對的挑戰素來不少。基於某些原因，選擇修讀我們學科的學生未必視其為他們的首選科目，因為我們都只不過是他們的學位課程裡的其中一個必修科，就好像主修科學學科的學生需要強制修讀數學課程一樣。雖然大家都知道數學和統計技能對學生的研究和學術發展十分重要，但始終有部份學生未必會像他們喜愛主修科目般對此如痴如醉。當然，有部份學生對數學充滿熱誠，但始終有些因素，令部分學生對我們的科目未能產生很大的興趣。例如：

1. 由中學時期已經欠缺學習數學應有的傳統風氣(可見於選修M1或M2的學生比例下降，而HKDSE數學/M1/M2的課程相比以往HKCEE數學、附加數學，以及高考純數科的課程亦有所縮減 )。雖然在高等學院可以彌補當中部份所失，但學生不再熱衷於理解更深奧的數學或學習更深入的概念，這種風氣顯然難以挽救其中。

2. 我們不得不承認，我們的學生已經被灌輸為應付考試而不停操練數學題的觀念，而這種風氣的確會令他們從小開始就對學習數學失去耐性。雖然操練或可達至不錯的考試成績，但很多學生已經對探索數學的意義以及了解數學對整個人類文化發展的貢獻失去了興趣。

有見及此，不少講師都非常努力想辦法令他們的課堂和教學變得有趣。有些講師會利用吸引眼球的高科技玩意來進行教學，有些則嘗試與學生建立平易近人的友好關係，希望學生可以對數學科產生正面的印象。

眾所周知，大學本科的課程只會著重教授基本和基礎概念與技能，只有成為研究生之後才有機會接觸到更高階的研究。為了在大學時期就能激發學生的興趣，講師通常會試圖勾起學生選讀這些學科的初衷，並嘗試透過分享個人經驗來重新燃點學生的熱情。

不過，我的做法則更加大膽。就是一方面用傳統方法回顧歷史，細看縱橫交錯的人類文明起源是如何與數學和一些科學學科交織而成，因為歷史可以讓我們更清楚地理解一些做法背後的邏輯，以及它們為何會發展至此。了解所有歷史淵源可以幫助學生鞏固基礎，往後才能學有所成。如果STEM是通往羅馬的一條大路，那麼知道大路的起點以及歷史如何自然地成為引領大路的明燈，遠比只著重功過成就重要得多。

另一方面，我亦會嘗試新的教學方式，在教學當中引入一些例如CoCalc的雲端數學計算軟件，因為這些軟件可以減少教學過程中出現大量單調沉悶的公式，只需按一下鍵就能製作大大小小不同圖形，變相能騰出時間讓學生訓練更有趣味的數學思維，或了解更多代數部分分式的理論。

_{Received a postcard from a graduate who went on to pursue further studies.
收到一名繼續深造的學生寄來的明信片。}

_{Taking students on a field trip to the Tsim Sha Tsui Clock Tower and using techniques from the Ancient Text “The Sea Island Mathematical Manual” to estimate its height.
帶領學生實地考察尖沙咀鐘樓，並借用古籍《海島算經》裡的算術技巧來推算鐘樓的高度。}