本論文是關於滬港兩地小學數學教師的專業知識的比較研究。研究以兩個「受儒家文化影響的地區」的中國城市---上海及香港為基地，探討兩地小學數學教師的專業知識的異同及缺失，豐富數學教育界對東方數學教師專業知識基礎的認識，並為數學教育的發展方向提供反思的資料及建議方向。
本論文的研究問題是：滬港兩地小學數學教師專業知識有何共同、差異之處和缺失？本研究以質的研究取向從「數學內容」及「教師專業知識」兩個維度出發，前者涵蓋「幾何」、「代數」及「資料處理」三個數學知識領域及一個綜「數」與「幾何」的探究問題，後者涵蓋學科內容知識及學科教學知識兩個類別。透過六個假想任務情境，向兩地各12位小學數學教師進行半結構式的訪談及畫圖或文字闡述的資料搜集。三個範疇的六道情境交錯地涉及在不同的教師專業知識，以數學內容知識的正確性分類及以類屬分析的方法，將資料進行分析，得出兩地小學數學教師專業知識的共同、差異之處及缺失的清單。
研究發現，(1) 有關概念的正確性：香港教師缺失的知識普遍存在於各數學內容，在幾何範疇最明顯。與香港教師不同，上海教師缺失的知識很少屬基本概念。(2) 有關概念間的連系性：香港教師概念間的連系性普遍不強，在幾何範疇出現割裂及矛盾情況。上海教師概念間的連系性較強，但在資料處理範疇未能正確地及有意義地應用在具體情境中。(3) 有關基本原則的理解：香港教師分類的原則及探究的策略掌握不及上海教師般有系統，但探究動機較上海教師強。(4) 有關表徵方法的處理:香港教師用語準確性、簡潔度不及上海教師，差異比上海教師大，對學生的表達方法控制較高。(5) 有關回饋的處理:香港教師給予的回饋對積極及正面建立數學概念及概念間連系的作用不強，給予回饋時關注學生能力差異的考慮較多。上海教師給予回饋時關注對學生將來學習的需要較多。
總結兩地小學數學教師的專業知識的比較及特點，本研究亦就兩地數學教育發展提出了一些關注事項及跟進建議。

This study undertakes a new attempt in theory and practice in curriculum design in mathematics, which includes an operational model, its theoretical interpretation and experimentation
The operational model, called Spiral bianshi (literally means variation) Curriculum, is extracted from the use of connecting problem clusters, one of the prominent features in current practice in mathematics instruction in Mainland China, the origin of which can be traced back to the Qingpu experience in Shanghai in the 1980s Such a long history of practice was conceptualized according to the nature of mathematics and mathematics learning The Spiral bianshi Curriculum comprises four components: The inductive bianshi which abstract mathematics notions from realistic situations, the deepening bianshi which lead one to new concepts and rules from already established one, the broadening bianshi which connects various concepts which are already acquired and the applicative bianshi which helps learners applying concepts and rules to more realistic situations
Division of fraction was taken as the topic for experimentation The corresponding bianshi curriculum was designed and experimented in 14 classes in three Primary schools in Hong Kong The other 13 classes in three comparable schools were taken as control group
The students' cognitive learning outcomes and self-efficacy were measured before and after the experimentation by means of a pre-test and a post-test The students' approach to learning and other affective variables were measured too
Significant positive results were obtained by the spiral bianshi curriculum The post-test scores of learning outcomes in the experimental group were significantly higher than those in the control group while all these scores indicated no significant differences in the pre-tests among these two groups The students in the experimental group reflected that they have clearer relevant concepts than their counterparts They also understood

Students need to be endowed with generic skills so as to meet the challenges of an ever changing and knowledge-based information society like Hong Kong. Traditional education systems that focus on memorization and examination cannot satisfy these new demands. So there is a need for the shift of learning and teaching (L&T). This paper shares the experience of launching "Peer Tutoring" in Advanced-Level Pure Mathematics subject in one school. It focuses on how peer tutoring influences students' learning behaviors and attitudes, learning effectiveness and skill promotion. The change of roles for students and teachers, advantages and limitations of peer tutoring will also be discussed.
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