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

This study investigates mathematics teaching in Hong Kong and Shanghai by considering the ways of handling Pythagoras' Theorem at eighth grade from the perspective of variation. It has three aims. Firstly, it attempts to identify the characteristics of the ways of handling the same topic in the two cities. Secondly, it tries to identify patterns of handling the topic in Hong Kong and Shanghai through making a comparison between different ways of handling the same topic. Thirdly, it seeks to interpret the findings from a cultural perspective and contribute to solving the paradox of Chinese mathematics teaching.
The Hong Kong data includes the following: eight videotaped lessons with the same topic of Pythagoras' Theorem and supplementary documents such as teachers' questionnaires, samples of text pages, worksheets, and other materials used in the lessons. All of the Hong Kong data were taken from the Third International Mathematics and Science Study Repeat Video Study. The Shanghai data consists of eleven videotaped lessons from different schools in which Pythagoras' Theorem was taught, with supplementary documents, matching those used in Hong Kong. Mainly based on the videotaped lessons and supplementary documents, the inter-and intra-city comparisons were made from the perspective of variation in order to identify the characteristics of the different ways of handling the same topic.
The following similarities have been observed: (1) the focuses and structures of the lessons are quite similar; (2) The teachers tend to emphasize exploration of the theorem; (3) the teachers seein to emphasize exercises with variation; and (4) the teachers control the classrooin activities but they still encourage students to engage well in the process of learning. However, some differences have also been identified. Firstly, the approaches to encouraging discovery of the theorem vary in that, the Hong Kong teachers prefer to employ physical manipulation while their Shanghai counterparts

背景：為了配合教育改革，教師必須有能力分析試題，以及從中反省改進自己的教學，達到通過評核促進學生學習，改進教師教學，朝向教學與評核結合，提升師生的教與學的質素之目的。
目的或討論焦點：本文把如何應用學生問題分析表及相關係數技術，對試題進行分析及反思某小學三年級數學的教學及評核設計求取「促進學習的評核」的真實經驗，和同工分享學者和前線教師的合作成果。
論點/評論/建議：在應用學生問題分析方面，我們提出在發展評核過程中，要注視三種層次：1. 教師於編寫評核材料前，應要有明確的評核目的；2. 編寫評核材料時，必要留意題意的清晰度、深淺度，以及是否能區別生的能力和如實地反映個別學生的能力；3. 施測後，教師應從評核材料中反思自己的教學程式和方法，從而作出適當的調整，以迎合學生的學習方法和進度。
總結：要做到教學相長，教師就要有能力分析評核學生的工具是否合乎教學目的和需要，以及理解評核結果和教學的關係。因此，教師於整個教學流程中，要結合評核和教學，對編製的評核材料要先進行分析，並依據結果進行修訂，用以達到真正評核學生的能力，同時要在編製之評核材料嚴謹性和有效性加以關注。
Background: Education reform in Hong Kong stresses the learning function of assessment. It is important for teachers to know how to do item analysis of a test. By analyzing the items of the test, teachers will understand how their students have learnt. This will help teachers plan their teaching and eventually help students learn.
Aims or focus of discussion: The author shares an "Assessment For Learning" experience of using Student-Problem Chart Analysis techniques and Correction Coefficient to a grade III Mathematical class in a Hong Kong primary school.
Arguments / comments / suggestions: The experience informed that, when using SPCA, three levels of focus should be considered during the formulating process of assessment tools in class. They included: 1) clear assessment objectives for assessment materials; 2) items clarification, appropriation, discriminative power should be considered; 3) deep reflection of teaching procedures and methods from the assessment materials after the measurement. Teachers should adjust their actions in order to suit the needs of students learning and progress.
Conclusion: It is essential for teachers to know how to analyze assessment tests. Good analysis entails being able to match learning objectives to the needs of their students. Deliberation should start well before the test is developed and after the results have been collected. Teachers should look into relevant materials when considering the test content, analyze

促進學習的評估是近年香港教育界熱門的專業術語之一。評估能促進學生學習，過程中教師要善用評估學生表現的資料，設計出相應的桝與學的措施。為了瞭解這理念在香港小學施行的情況，本文採用個案研究法，與一所小學數學科科主任作深入訪談，透過解構和整理這些質性資料，勾劃出這所學校近年來在數學科實踐評估促進學習的經驗，並指出其成功原因及需考慮的發展方向。
"Assessment for learning" is a professional term and familiar with the educators in Hong Kong recently. Assessment improve students' learning. Teachers analyse the results of students' performance to design relevant teaching activities and materials. This paper aims to illustrate the practice of this concept in the mathematics subject of a primary school in Hong Kong. The case research method is used and the subject panel of this school has been interviewed deeply. By synthesis the qualitative data of the case, the implementation of the assessment for learning of the mathematics subject in this school is outlined. Meanwhile the main reason of the success of this assessment reform is pointed out and suggestion for further development is enclosed.
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