The Hong Kong Education Bureau recommends that primary school pupils' mathematical achievement be enhanced via collaborative discussions engendered by group work. This pedagogic change may be hindered by Confucian heritage classroom practices and Western-dominated group work approaches that predominate in Hong Kong. To overcome these obstacles, we introduced a relational approach to group work in a quasi-experimental study. Our sample included 20 teachers randomly allocated to experimental (12) and control (8) conditions and their 504 mathematics pupils (aged 9-10). The relational approach focused on the development of peer relationships in a culturally appropriate manner and was implemented over 7 months. Pupils were pre-/post-tested for mathematical achievement and systematically observed, and the teachers were assessed for subject knowledge and pre-/post-tested for pedagogic efficacy. Analysis of covariance (ANCOVA) and hierarchical linear modeling (HLM) results show enhanced mathematical achievement, supported by improved peer-based communication skills and time-on-task for the experimental pupils. Experimental teachers raised their pedagogic efficacy. Results indicate the potential of the relational approach for boosting academic achievement via enhanced child-peer-teacher interaction and the need to reassess the role of peer-based latent collectivist learning in Confucian heritage classrooms.

The distributive law or distributive property is a fundamental algebraic property in the arithmetic of numbers and algebraic expressions. This paper reports on an investigation of students' understanding of the distributive law through task-based interviews from the perspectives of constructivists. It explores students' lack of appreciation of the algebraic structure underpinning the distributive law, particularly amongst students who were already proficient in arithmetic and the distributive law. A total of 203 students from one secondary school of average standard in Hong Kong participated in this study, which adopted a cross-sectional approach. Thirty-three students were then interviewed. The study showed that although some students made progress in the understanding and application of the distributive law, others could not make sense of the meaning of variables and algebraic rules. Therefore, their algebra remained a routine instrumental application of rules, and their understanding of the algebraic structure was incomplete. This paper concludes with a discussion on how the tasks used in the interviews provided teachers with an innovative alternative to deepening students' understanding of letters as variables and the distributive law.
[Copyright of Pedagogies: An International Journal is the property of Routledge. Full article may be available at the publisher's website:
http://dx.doi.org/10.1080/1554480X.2010.486156 ]

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]