Reasoning skills in post-16 mathematics students

该博士项目将调查16岁以上数学学生的推理能力，旨在提供基于研究的信息，以支持这个年龄段学习数学的学生人数的增加。该项目将特别关注核心数学，这是2014年为在GCSE中取得高分但选择不学习AS/ a水平数学的学生推出的16岁以上资格认证。核心数学课程提供了将数学应用于其他领域的机会，并有三个主要目标：深化选择方法和技术的能力；培养运用数学表达和分析真实情况的信心；培养数学思维、推理和沟通能力。一篇关于16-18岁数学教育的综述论文（Smith, 2017）的研究结果表明，提高16岁后的数学水平是有充分理由的。该报告强调，在发达国家中，英国仍然是不寻常的，因为数学并没有被16岁以上的学生普遍学习：大约四分之三在普通中等教育证书数学考试中获得高分的学生没有选择学习超过这个水平的数学。此外，该报告的调查结果显示，在英国大学学习STEM科目的19岁学生中，约有40%没有GCSE以外的数学资格证书。此外，该报告还为教育部提出了建议，特别强调了考虑如何加强核心数学品牌的重要性，旨在提高对该资格的认识和接受。这一点，再加上行业对高水平定量技能的持续需求，凸显了从推理技能角度研究核心数学的重要性。一般的推理能力在许多职业和学位中都很重要，引入核心数学的一个原因是学习数学被认为可以提高这些技能。这一论点被称为“形式纪律理论”，并被用于政策辩论，以优先考虑学校课程中的数学。阿特里奇和英格利斯（2013）在一项比较义务教育后数学和英语文学学生条件推理行为发展的研究中验证了这一理论。研究结果支持形式纪律理论，因为数学学生的条件推理比文学学生发展得更大。这显示了A级数学如何提高这些技能，但我们还不知道核心数学是否如此。因此，这个项目将问：在核心数学和AS/A水平数学中，一般推理和定量推理在多大程度上得到了发展？什么机制将数学学习与一般推理和定量推理联系起来？我们如何提高一般推理和定量推理能力？这些主要的研究问题将通过与致力于改善数学教育的独立慈善机构“数学教育与工业”（MEI）合作来回答。MEI为成千上万的学生/教师创造创新资源，并提供一系列专业发展。它开发了两个核心数学和数学AS/A级规范，通过OCR进行检查。研究成果将有助于理论发展，并使MEI能够更好地支持学生和教师，表明该项目在教育部门和行业都具有很大的影响潜力。

This PhD project will investigate reasoning skills in post-16 mathematics students, aiming to provide research-based information to support an increase in the numbers of students studying mathematics in this age group. The project will place specific focus on Core Maths, a post-16 qualification introduced in 2014 for students who scored highly in GCSE but chose not to study mathematics at AS/A level. Core Maths provides opportunities to apply mathematics to other fields, and has three key objectives: deepening competence in selecting methods and techniques; developing confidence in applying mathematics to represent and analyse authentic situations; and building skills in mathematical thinking, reasoning and communication.There is a strong case for improving post-16 mathematics, demonstrated by the findings in a review paper on 16-18 mathematics education (Smith, 2017). The review highlights that England remains unusual among advanced countries, as mathematics is not universally studied by students beyond the age of 16: around three quarters of students with high grades in GCSE mathematics do not choose to study mathematics beyond this level. Further, findings from this report show that around 40 per cent of 19-year-old students studying STEM subjects in UK universities do not have a mathematics qualification beyond GCSE. Furthermore, this report sets forth recommendations for the Department of Education, specifically highlighting the importance of considering ways in which the Core Maths brand could be strengthened, aiming to improve awareness and take-up of the qualification. This, in combination with the continuing demand for high level quantitative skills in industry, highlights the importance of researching Core Maths from a reasoning skills perspective.General reasoning skills are valued in many careers and degrees, and one reason for the introduction of Core Maths is that studying mathematics is thought to improve these skills. This argument is known as the 'Theory of Formal Discipline' and is utilised in policy debates to prioritise mathematics in the school curriculum. This theory was tested by Attridge and Inglis (2013), in a study comparing the development of conditional reasoning behaviour in post-compulsory mathematics and English literature students. Findings support the Theory of Formal Discipline as conditional reasoning was developed to a greater extent in mathematics students compared with the literature students. This shows how A level mathematics improves these skills, but we do not yet know whether this is the case for Core Maths. Therefore, this project will ask:To what extent are general and quantitative reasoning developed in Core Maths and AS/A level mathematics?What mechanisms link mathematical learning to general and quantitative reasoning? How can we improve general and quantitative reasoning skills? These main research questions will be answered by working in collaboration with Mathematics in Education and Industry (MEI), an independent charity committed to improving mathematics education. MEI creates innovative resources for thousands of students/teachers and offers a range of professional development. It has developed two Core Maths and mathematics AS/A level specifications that are examined through OCR. The research findings will both contribute to theoretical development and enable MEI to better support students and teachers, demonstrating that this project has high potential for impact in both the education sector and industry.