Factors Influencing Students' Understanding of Mathematical Equivalence

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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.