comparative inquiry into UK and Chinese mathematics teachers' beliefs and instructional practices

国际学生评估方案(PISA)是在近80个国家开展的一项国际评估，旨在调查15岁学生在现实世界情景中解决阅读、科学和数学问题的能力(Skipp&Dommett，2021)。在2018年PISA评估中，英国的数学水平一落千丈，跌至第18位，远远落后于其他12个远远超过英国的国家(Skipp&Dommett，2021年)，特别是在调查中排名第一的中国。博伊德和阿什(2018年，第215页)在一项关于英国小学数学教师在实施新加坡掌握数学方法时改变观念的研究中指出，在西方文化的学校里，数学教学的一个关键问题是，他们往往包括教师示范和讲授，然后是个人实践“，而不是更积极的数学学习方法。”在最近题为《英国数学教学的支持》的一章中，Blausten、Gyngell、Aichmayr和Spengler(2020，第33-34页)强调了英国和东南亚国家(如新加坡、上海)数学教育的主要区别。他们指出，在英国，数学教学有多种途径(例如，学校主导、大学主导)，而在新加坡等国家，只有一条途径通过国家教育学院。与英国形成鲜明对比的是，新加坡和上海的教师是数学专家，甚至在小学阶段也是如此。另一个不同之处在于，在英国，按能力分组与东南亚地区的全班教学形成鲜明对比。最后但并非最不重要的是，Blausten等人指出，由于与学生接触的时间较少，新加坡教师有更多的时间进行计划和反思，上海教师有100个小时的专业发展时间，而英国教师只有10%的时间用于计划、评估和反思。在教师信念方面，其他研究表明，在英国，“教师根据对学生能力的认知来思考学生，并对他们做出不同的反应”(Francis等人，2017年，Blausten等人，2020年第5页，第33页)。在Boaler，William and Brown(2000)的基础上，Blausten等人(2020)补充说，教授高能力集合的教师比教授低能力学习者群体的教师对学习者的期望更高。最后一条特别指出了教师信念相对于数学教学和学生成绩的重要性。已有的比较英国数学教师和中国数学教师信念的实证研究主要集中在他们对“数学教育；数学教育：数学教学，数学的本质”(Yu，2008，p.121)和关于数学课堂提问的信念(张，2019)的信念上。Yu(2008，p.121)对来自10所中学的44名英国教师和96名中国教师进行的一项调查分析后发现，英语教师在数学教学中体现了对理论的务实理解，而中国教师则证明了他们对理论的科学理解。12/19的中国老师也比英国老师更强调逻辑和严谨的推理。张学良(2019，第11页)对数学教师的信念以及课堂提问的实践进行了一项基于访谈的对比研究，结果显示，英语教师更喜欢“通过修改问题来适应不同学习能力的学生的探究式提问”，相比之下，中国教师“对提问不那么积极”，而是优先考虑“深厚的数学内容知识，并展示了一种相对基于内容的提问方式”。研究结果表明，教师信念对数学课堂教学有显著的影响

Introduction The Programme for International Student Assessment (PISA) is an international assessment carried out across almost 80 countries which surveys the competence of 15-year-old learners in solving problems in reading, science and mathematics within real-world scenarios (Skipp & Dommett, 2021). In the 2018 PISA assessment, UK found itself plummeting to the 18th place in mathematics proficiency, behind 12 other countries which outperformed UK by far and wide (Skipp & Dommett, 2021), particularly learners in China which attained the top ranking in the survey. In a study on UK primary school mathematics teachers' changing beliefs while implementing Singapore mastery math approach, Boyd and Ash (2018, p.215), point out that a key issue in 'maths teaching in schools in Western cultures [is that they tend] to consist of teacher demonstration and telling, followed by individual practice' rather than a more 'active learning approach in mathematics'. In a recent chapter titled 'Supporting mathematics teaching for mastery in England', Blausten, Gyngell, Aichmayr and Spengler (2020, p.33-34) highlight key differences between mathematics education in the UK and in Southeast Asian nations (e.g., Singapore, Shanghai). They note that within the UK, there are multiple routes into mathematics teaching (e.g., school-led, university-led), whereas in countries like Singapore, there is only a single pathway through the National Institute of Education. In contrast to the UK, Singapore and Shanghai teachers are mathematics specialists, even in primary schooling. Another difference pertains to the prevalence of grouping by ability in the UK in contrast to whole class instruction in Southeast Asian contexts. Last but not least, Blausten et al, 2020) note that while teachers in Singapore have more time to plan and reflect due to less contact time with pupils and Shanghai teachers have access to 100 hours of professional development, teachers in the UK are only allowed to have 10 percent of their time for planning, evaluating and reflecting. In terms of teacher beliefs, other research has showed that within the UK "teachers think about, and respond differently towards, pupils according to perceptions of their ability" (Francis et al., 2017, p. 5 in Blausten et al, 2020, p.33). Drawing on Boaler, William and Brown (2000), Blausten et al (2020) add that teachers instructing high-ability sets expect more from their learners than their counterparts who teach low-ability learner groups. The last in particular points to the importance of teacher beliefs vis-à-vis instruction and learner outcomes in mathematics. Existing empirical studies comparing the beliefs of mathematics teachers in the UK and China have focused on what they believe about 'mathematics education; mathematics education: mathematics teaching, the nature of mathematics' (Yu, 2008, p.121) and beliefs about questioning in the mathematics classroom (Zhang, 2019). Based on analysis of a survey administered to 44 UK and 96 Chinese teachers from 10 secondary schools in each context, Yu (2008, p.121) found that while the English teachers reflected a 'pragmatic understanding of theory' in mathematics instruction, the Chinese teachers evidenced 'scientific understanding'. The Chinese teachers also 12 / 19 emphasized 'logical and rigorous reasoning' more than the English counterparts. A comparative interview-based research on mathematics teachers beliefs as well as practices on questioning in the classroom by Zhang (2019, p.11) showed that the English teachers preferred 'inquiry-based questioning that modified questions to accommodate students with diversity of learning abilities' in contrast to the Chinese teachers who 'were less positive about questioning' and instead prioritized 'profound mathematical content knowledge, and displayed a relatively content-based approach to questioning'. The findings of these studies indicates that the teacher beliefs influence mathematics instruction according