Bilateral (Hong Kong) The effects of social pedagogical contexts in the teaching of primary mathematics: facilitating learning in two cultures

这项双边研究正在英国和香港进行，目的是培养教师在小学数学中有效使用协作小组作业的理解和能力。这项研究解决了两个地区政府目前关注的互补领域：香港在国际数学竞赛中取得了突出的成功，但目前的政策是鼓励更多的学生活动和课堂上的小组合作，放弃课本和教师主导的方法。另一方面，在英国，小学教师非常熟悉使用互动方法和小组合作，但历届政府都急于在国际比赛中提高数学成绩。沃德曼(2011)最新发表的数学评论呼吁“采取紧急措施，改善小学教师的数学背景”(第35页)，因为“许多人缺乏数学学科知识，以及与之相关的信心”(第3页)。然而，仅有数学学科知识是不够的，正如彼得·威廉姆斯爵士为上届政府对小学数学教学进行的审查所得出的结论：“促进学习需要深厚的学科知识和教学技能的结合”(第7页)，因为“只有通过建设性的对话……在课堂上才能充分发展逻辑和推理”(第3页)。然而，他指出，关于小学数学中分组作业的影响的研究很少，而且模棱两可。此外，尽管人们普遍熟悉小组作业，但英国的小学教师很少以最好的方式实施小组作业以达到他们的目标，也最不可能在数学中使用小组作业(Kutnick，Blatchford&Baines，2002)。因此，这个项目旨在培训英格兰和香港的小学教师，让他们了解如何最好地利用小组合作，并使他们能够交流他们的专业知识，以改善儿童的数学思维和课堂讨论的质量。虽然英国对小学数学小组工作的研究很少，但美国有大量研究表明，小组工作可以改善儿童在数学方面的学习和态度(Webb，2009)。在英格兰，这个项目是由ESRC资助的“春天”项目(小组工作的社会教学研究)的后续行动，该项目由布拉奇福德、高尔顿和库特尼克从2001年到2004年指导。春季的研究发现，在5-7岁到11-14岁的学生中，小组合作对英语、数学和科学的成就、态度和动机都有积极的影响，前提是它是按照社会教育学原则实施的。这意味着要仔细计划小组的规模、小组成员、任务类型、教师角色等，以最大限度地发挥小组工作对特定任务的好处。然而，在21世纪初，国家算术策略禁止8-11岁的学生学习数学小组活动。这个项目将填补我们在小组活动是否以及如何改善10岁儿童的数学思维和成就方面的知识空白。该项目将通过互联网交流和教师之间的视频交流，在10名10岁的英语教师和10名香港教师之间建立一个实践社区。在每个国家的面对面会议上，研究小组将发展教师对社会教学原则的理解，以及如何将这些原则应用于他们的教学中的小组工作。通过在教室里交换小组活动的视频，他们可以从对方的教学中学习。将使用课堂观察、录像和对学生成绩以及教师对数学和小组活动的信心的测试来衡量项目从头到尾的进展情况，并将培训小组的结果与每个地区的对照组教师进行比较。其目的是在教师之间建立专业关系，以便在项目结束后大学专业发展进程将是可持续的。

This bilateral research is being conducted in England and Hong Kong to develop teachers' understanding and ability to use collaborative groupwork effectively in primary mathematics. The research addresses current and complementary areas of government concern in both regions: Hong Kong is outstandingly successful in international mathematics competitions but current policy is to encourage more pupil activity and groupwork in classrooms and move away from text-book and teacher-led methods. In England, on the other hand, primary teachers are very familiar with using interactive methods and groupwork but successive governments have been anxious to improve mathematics performance in international competitions. The newly published Vorderman (2011) review of mathematics calls for 'urgent steps to be taken to improve the mathematics background of teachers in primary schools' (p.35), since 'many lack subject knowledge in mathematics, and the confidence that goes with it' (p.3). Mathematical subject knowledge is not enough however, as Sir Peter Williams' review of primary mathematics teaching for the previous government concluded: 'it is a combination of deep subject knowledge and pedagogical skills that is required to promote learning' (p.7) since 'only by constructive dialogue ... in the classroom can logic and reasoning be fully developed' (p.3). He pointed out, however, that research on the effects of groupwork in primary mathematics is scarce and equivocal. Furthermore, despite general familiarity with groupwork, England's primary teachers rarely implement it in the best ways to meet their objectives, and are least likely to use groupwork in mathematics (Kutnick, Blatchford & Baines, 2002). This project therefore aims to train primary teachers in England and Hong Kong to understand how best to use collaborative small groupwork and enable them to exchange their professional expertise to improve children's mathematical thinking and the quality of classroom discussion.While research on groupwork in primary mathematics is scarce in England, there is ample research from the US showing that groupwork can improve children's learning and attitudes in mathematics (Webb, 2009). In England, this project follows up the ESRC-funded 'SPRinG' Project (Social Pedagogical Research into Groupwork) directed by Blatchford, Galton and Kutnick from 2001 to 2004. The SPRinG research found positive effects of groupwork on achievement, attitudes and motivation in English, Mathematics and Science between ages 5 - 7 and 11-14, provided that it was implemented according to social pedagogical principles. This means careful planning of group sizes, group membership, type of task, teacher's role and so on to maximise the benefits of groupwork for the particular task. In the early 2000s, however, the national numeracy strategy prevented study of groupwork in mathematics at ages 8 - 11. This project will fill that gap in our knowledge of whether and how groupwork can improve 10 year olds' mathematical thinking and achievement.The project will set up a 'community of practice' between 10 English and 10 Hong Kong teachers of 10 year olds using internet communication and video exchange between teachers. In face to face meetings in each country, the research teams will develop teachers' understanding of social pedagogic principles and how to apply them to groupwork in their teaching. By exchanging videos of groupwork in their classrooms they can learn from each other's teaching. Classroom observation, video and tests of pupil achievement and teachers' confidence in mathematics and groupwork will be used to measure progress from start to end of the project, and to compare the trained groups' results with a control group of teachers in each region. The aim is to establish professional relationships between the teachers such that the process of collegial professional development will be sustainable after the project ends.