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

国际学生评估计划（比萨）是一项在近80个国家开展的国际评估，旨在调查15岁学生在现实世界中解决阅读，科学和数学问题的能力（Skipp & Dommett，2021）。在2018年的比萨评估中，英国在数学能力方面排名第18位，落后于其他12个远远超过英国的国家（Skipp & Dommett，2021），特别是中国的学习者在调查中排名第一。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信念的研究中，Boyd和Ash（2018年，第215页）指出，“西方文化中学校的数学教学[是他们倾向于]由教师演示和讲述组成，然后是个人实践”，而不是更“积极的学习方法”。在最近一章题为“支持英国数学教学掌握”，Blausten，Gyngell，Aichmayr和Spengler（2020年，第33 -34页）强调了英国和东南亚国家数学教育之间的主要差异（例如，新加坡、上海）。他们指出，在英国，有多种途径进入数学教学（例如，学校主导，大学主导），而在像新加坡这样的国家，只有通过国家教育学院的单一途径。与英国不同的是，新加坡和上海的教师都是数学专家，甚至在小学阶段也是如此。另一个不同之处在于，在英国，按能力分组的流行程度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（2020年）指出，虽然新加坡的教师有更多的时间计划和反思，因为与学生接触的时间较少，上海的教师可以获得100小时的专业发展，但英国的教师只允许有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看法来思考学生，并对学生做出不同的反应”（弗朗西斯等人，2017，第5页，Blausten等人，2020，第33页）。借鉴Boaler，William和Brown（2000年），Blausten等人（2020年）补充说，指导高能力组的教师对学习者的期望高于指导低能力学习者组的教师。最后一个特别指出了教师信念对数学教学和学习者成果的重要性。现有的实证研究比较了英国和中国数学教师的信念，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）和对数学课堂提问的信念（Zhang，2019）。Yu（2008，p.121）根据对来自10所中学的44名英国教师和96名中国教师的调查分析，发现英国教师在数学教学中反映了“对理论的实用理解”，而中国教师则证明了“科学理解”。中国教师也比英国教师更强调“逻辑和严谨的推理”。基于访谈法的张先生关于数学教师课堂提问信念与实践的比较研究（2019年，第11页）显示，英语教师更喜欢“基于探究的提问，修改问题以适应具有不同学习能力的学生”，而中国教师“对提问不太积极”，而是优先考虑“深刻的数学内容知识，并展示了一种相对基于内容的提问方式。这些研究的结果表明，教师信念影响数学教学，

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