Factors Influencing Students' Understanding of Mathematical Equivalence

该奖学金的主要目的是使自己成为数学教育和数学认知领域的独立、领先的研究人员。为了做到这一点，我确定了我将在整个奖学金期间实现的六个子目标：(I)我的博士研究将在数学教育和数学认知领域得到认可，我将开始在这个领域建立自己的领导地位。为了向学术界传播我的博士研究成果，我将从我的博士研究中再发表两篇文章：一篇是关于我在博士工作中开创的多层次结构方程建模（MSEM）的方法进展；另一篇将报告大规模跨文化比较研究的结果。我将把这些文章提交给两个领先的，高影响力的期刊(即。《评估》和《教育心理学评论》)。此外，我将通过BOLD和BERA博客、政策简报和BBC莱斯特电台发布和交流我的研究成果，以接触到更广泛的受众，包括从业者、政策制定者、家长以及来自不同学科的研究人员。（二）博士期间创建国际研究网络。我将通过参加两个主要的数学教育和数学认知国际会议（即CERME 12和PME 45）来扩展这个网络，以发展影响机会并建立合作关系。参加会议也会给我机会传播我的发现，并使我的研究在该领域得到认可。计划中的国际访问（见下文）也将帮助我实现我的第一个和第二个目标。（iii）我将发展我的技能与先进的统计方法（如潜在增长模型，潜在类分析等），创新的实验技术和实验设计使用软件（如PsychoPy）。通过确定的培训机会，我将能够使用先进的统计方法来分析复杂的数据结构。我还将通过为其他研究人员提供培训，并在未来为本科生设计一门高级统计方法课程，促进这些方法在教育和认知研究中的应用。在实验设计中使用软件的培训将使我能够开发复杂的实验。此外，我参观了威斯康星大学麦迪逊分校心理学系的认知发展与交流实验室，这将为我提供创新实验技术的培训，这将有利于我进一步的研究，也有利于我作为一个独立的数学认知研究者的专业发展。（iv）我将发展我的基金写作技巧，并为此确定相关课程。在奖学金结束前，我将申请外部资助（如ESRC新研究员资助）。计划中的国际访问也将帮助我与潜在的海外合作者发展未来的研究思路。（五）与教育业界及政策制定者分享博士研究成果，以促进知识交流。这将通过教育博客、从业者活动以及利用我的导师和政策制定者之间建立的联系来实现。（六）我将进行一项实验研究，探讨问题特征是否会影响中小学生解方程的表现，如果会，调查不同年龄组样本的影响是否存在差异。这项研究将促进我们对为什么学生发现数学等价问题比其他问题更难的理解，并将有助于发展模型的发展，该模型将显示问题特征是否以及如何以不同的方式影响学生解决方程的表现。研究结果有可能影响教育实践和政策。

The main aim of the Fellowship is to establish myself as an independent, leading researcher in the fields of mathematics education and mathematical cognition. To do this, I identify six sub-aims that I will achieve throughout my fellowship: (i) My PhD research will be recognised in the fields of mathematics education and mathematical cognition and I will begin to establish myself as a leading voice in this field. To disseminate the findings of my PhD research to academic audiences, I will produce two more articles from my PhD research: one will be about the methodological advances focusing in multilevel structural equation modelling (MSEM) that I pioneered in my PhD work; the other will report the results from a large-scale cross-cultural comparison study. I will submit these articles to two leading, high-impact journals (i.e. 'Assessment' and 'Educational Psychology Review'). In addition, I will publish and communicate my research findings through BOLD and BERA Blog, policy briefs and BBC Radio Leicester, in order to access wider audiences including practitioners, policy makers, and parents as well as researchers from different disciplines.(ii) I created an international research network during my PhD. I will extend this network to develop impact opportunities and establish collaborations by attending two leading international conferences in mathematics education and mathematical cognition (i.e. CERME 12 and PME 45). Attending conferences will also give me the opportunity to disseminate my findings and for my research to be recognised in the field. The planned international visit (see below) will also help me to achieve my first and second aims.(iii) I will develop my skills in relation to advanced statistical methods (e.g. latent growth modelling, latent class analysis, etc.), innovative experimental techniques and experimental design using software (e.g. PsychoPy). Through the identified training opportunities, I will be able to use advanced statistical methods to analyse complex data structures. I will also promote the use of such methods in education and cognition research by providing training to other researchers and by designing an Advance Statistical Methods course in the future for undergraduate students. Training on use of software in experimental design will allow me to develop sophisticated experiments. In addition, my visit to the Cognitive Development & Communication Lab, in the Department of Psychology, University of Wisconsin - Madison will provide me with training in innovative experimental techniques, which will benefit both the proposed further research and my professional development as an independent researcher in mathematical cognition.(iv) I will develop my grant writing skills and have identified relevant courses for this. Before the end of the Fellowship, I will apply for external funding (e.g. ESRC New Investigator Grant). The planned international visit will also assist me in developing future research ideas with potential overseas collaborators.(v) I will share the results of my PhD research with educational practitioners and policy makers to maximise the impact for knowledge exchange. This will be done through education blogs, practitioner events, and using the established contacts between my mentor and policy makers.(vi) I will carry out an experimental research study to explore whether problem features influence primary and secondary school students' equation-solving performance, and if so, to investigate whether their influence vary across samples from different age groups. This research will advance our understanding of why students find mathematical equivalence problems harder than others, and will contribute to the evolution of a developmental model showing whether and how problem features influence students' equation-solving performance differently. The findings have the potential to influence educational practice and policy.