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

这项双边研究现正在英国和香港进行，目的是发展教师对在小学数学中有效运用小组合作的理解和能力。研究针对两个地区政府关注的当前和互补领域：香港在国际数学竞赛中取得了杰出的成功，但目前的政策是鼓励更多的学生活动和课堂小组合作，并摆脱教科书和教师主导的方法。另一方面，在英国，小学教师非常熟悉使用互动方法和小组工作，但历届政府都急于提高国际比赛中的数学成绩。新出版的Vorderman（2011）数学评论呼吁“采取紧急措施提高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，以及随之而来的信心”（第3页）。然而，数学学科知识是不够的，正如彼得威廉姆斯爵士对上届政府小学数学教学的审查所得出的结论：“这是一个结合了深厚的学科知识和教学技能，需要促进学习”（第7页），因为“只有通过建设性的对话.在课堂上，逻辑和推理才能得到充分发展。然而，他指出，关于小学数学中小组工作的影响的研究是稀缺和模棱两可的。此外，尽管一般熟悉小组工作，英格兰的小学教师很少实施它的最佳方式，以满足他们的目标，最不可能使用小组工作在数学（Kutnick，Blatchford & Baines，2002）。因此，本计划旨在培训英国及香港的小学教师，让他们了解如何善用小组合作，并让他们互相交流专业知识，以改善儿童的数学思维及课堂讨论的质素。美国有大量的研究表明，小组活动可以改善儿童在数学方面的学习和态度（Webb，2009）。在英国，该项目是2001年至2004年由Blatchford，Galton和Kutnick指导的ESRC资助的“SPRIG”项目（小组工作的社会教育研究）的后续项目。SPRinG研究发现，小组工作对5 - 7岁和11-14岁之间的英语、数学和科学成绩、态度和动机有积极影响，前提是小组工作是根据社会教育原则实施的。这意味着要仔细规划小组的规模、成员、任务类型、教师的角色等，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，国家算术战略阻止了8 - 11岁儿童的数学小组学习。这项计划将填补我们对小组活动能否及如何提高10岁奥尔兹数学思维和成绩的认识上的空白。该计划将建立一个由10名10岁英语教师和10名10岁香港教师组成的“实践社区”，通过互联网交流和教师之间的视频交流。在每个国家的面对面会议中，研究小组将提高教师对社会教育学原则的理解，以及如何将其应用于教学中的小组工作。通过交换教室里小组活动的录像，他们可以从彼此的教学中学习。将使用课堂观察、录像和学生成绩测试以及教师对数学和小组工作的信心来衡量项目从开始到结束的进展情况，并将培训组的结果与每个地区的对照组教师的结果进行比较。目的是在教师之间建立专业关系，以便在项目结束后，学院专业发展的过程是可持续的。

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.