This paper characterizes early mathematics instruction in Hong Kong. The teaching of addition in three pre-primary and three lower primary schools was observed and nine teachers were interviewed about their beliefs about early mathematics teaching. A child-centered, play-based approach was evident but teachers emphasized discipline, diligence and academic success. Observations also revealed practices reflective of both constructivist and instructivist pedagogies. Results from interviews suggest that teachers' traditional cultural beliefs about instruction were challenged by western ideologies introduced in continuing professional development courses and by notions promulgated by the educational reforms. Both consistencies and inconsistencies between teachers' beliefs and practices were identified. Implications of the findings are discussed.
[Copyright of Early Years: An International Journal of Research and Development is the property of Routledge. Full article may be available at the publisher's website:
http://dx.doi.org/10.1080/09575140802020917]

A review of recent studies in Hong Kong suggests that possible problems in secondary school algebra may be due to the procedural paradigm orientation in the curriculum and the conventional style of teaching in the classroom which do not provide sufficient opportunities for students to develop conceptual understanding. Based on the works of a number of projects in the West, it is hypothesized that the introduction of technology in lessons which embody a cognitive model in their design and delivery will provide a viable alternative for enhancing algebraic thinking. The key features of the cognitive model are concrete preparation, cognitive conflict, construction, metacognition and bridging, imbedded in a 'mediation' style of teaching. These features are exemplified by detailed accounts of classroom episodes from a Hong Kong lesson supported by the use of graphics calculators. Results indicate that while the approach places particular demands on teachers (a tension between a transmission style of teaching and mediating) there is real potential for supporting more dynamic student constructions.
[Copyright of International Journal of Mathematical Education in Science and Technology is the property of Taylor & Francis. Full article may be available at the publisher's website:
http://dx.doi.org/10.1080/002073900412660]

作者認為數學教學的目的不是數學知識的掌握而是培養學生透過學習數學知識來發展高層次的思維能力。作者引用Resnick（1987）的觀點，列出高層次思維能力的特色。作者指出，香港的數學教師對高層次思維的評估，如何結合評估和教學，以至建立完整的評估理論，至今仍未有清晰的路向。

作者指出香港數學教育在眾多的包袱之上，近來也出現了一些契機。作者並論述在文化、社會和政治幾方面，已隨著1997年主權回歸所衍生的新挑戰：在文化方面，隨著民族主義泛起，香港新一代客觀地吸收西方文化；在社會上，土生土長的香港人比較容易接受新生事物；在政治方面，由於政府趨於開放和問責，教師聲音亦開始有發表的渠道。作者指出，重要的是數學教育研究的群體已經步入成熟期，故作者預期整個數學教育圈子的專業醒覺將日漸冒起。

作者詳細分述設計香港小學數學課程的考慮的因素，並引入英國，美國及台灣在數學課改革的理念，強調數學課程的設計的重點應在於引起學生的學習興趣，及培養正確的態度。最後還比較中港台三地小學數學課程的目的和取向。