Factors Influencing Students' Understanding of Mathematical Equivalence
Lead Research Organisation:
Loughborough University
Department Name: Mathematics Education Centre
Abstract
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.
(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.
People |
ORCID iD |
| Emine Simsek (Principal Investigator / Fellow) |
Publications
Simsek E
(2021)
Mathematical equivalence assessment: Measurement invariance across six countries
in Studies in Educational Evaluation
Simsek E
(2022)
Factors associated with children's understanding of mathematical equivalence: An investigation across six countries
in Journal of Educational Psychology
| Description | Research papers, research collaborations, professional development as an early career researcher. Most of the objectives were met. I could not do any international visit because of the pandemic. And I could not finish my data collection for the research (taken up to20% of time) because of opting for online data collection due to covid-19. - Teachers can improve their mathematics teaching based on the suggestions shared in relevant documents. - Other researchers can explore further factors relating to understanding of equivalence based on the suggestions in relevant research papers. - Governments can value research more before investing on something to improve educations. And particularly they can invest to improve teacher education and knowledge. |
| Exploitation Route | The research papers and blogpost as a result of the work funded through this award highlight the importance of teacher knowledge to support students' understanding of mathematical equivalence Teacher educators can create professional development materials to improve teachers' knowledge of students' understanding of mathematical equivalence. Practitioners who read about the research result from the blogpost published might gain awareness about the importance of students' use of correct relational strategies in the classroom when solving equivalence problems and support them using such strategies. |
| Sectors | Education |
| Description | After publishing the blogpost and few primary school teachers contacted me about how they can access research results, from where they can get more information about how to improve their knowledge for teaching mathematical equivalence better and how they can improve their classroom practice when teaching equivalence. |
| Sector | Education |
| Title | Dataset from Factors Influencing Students' Understanding of Mathematical Equivalence: A Cross-cultural Investigation across Six Countries Project |
| Description | This dataset focuses on investigation of factors (teacher knowledge and arithmetic practice as presented in textbooks) influencing students' understanding of equivalence, across samples from China, England, New Zealand, South Korea, Turkey, and the US. This dataset includes data from students, teachers, and textbooks. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2022 |
| Provided To Others? | Yes |
| Impact | Research paper |
| URL | https://osf.io/hf4ad/ |
| Description | Factors influencing mathematics anxiety in men and women. |
| Organisation | Eberhard Karls University of Tübingen |
| Country | Germany |
| Sector | Academic/University |
| PI Contribution | I contributed to the data analyses. Particularly, I played an active and important role on how to analyse data in this project and help data analyses. Also, I revised the manuscript a few times before submission period. |
| Collaborator Contribution | Data collection, Design of the Study, Writing up particular sections. |
| Impact | We have written up a journal article from this collaboration and submitted it to Annals of the New York Academy of Sciences. It has been accepted for publication on 10.03.2022. The title of this paper is "Mathematics-gender stereotype endorsement influences mathematics anxiety, self-concept, and performance differently in men and women". |
| Start Year | 2021 |
| Description | Factors influencing mathematics anxiety in men and women. |
| Organisation | Loughborough University |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | I contributed to the data analyses. Particularly, I played an active and important role on how to analyse data in this project and help data analyses. Also, I revised the manuscript a few times before submission period. |
| Collaborator Contribution | Data collection, Design of the Study, Writing up particular sections. |
| Impact | We have written up a journal article from this collaboration and submitted it to Annals of the New York Academy of Sciences. It has been accepted for publication on 10.03.2022. The title of this paper is "Mathematics-gender stereotype endorsement influences mathematics anxiety, self-concept, and performance differently in men and women". |
| Start Year | 2021 |
| Description | Project: The role of problem format in word problem-solving performance |
| Organisation | Free University of Amsterdam |
| Country | Netherlands |
| Sector | Academic/University |
| PI Contribution | * We conducted a study, a secondary data-analysis study of an existing dataset (see preregistration https://aspredicted.org/blind.php?x=qn7yx9) to explore the following research questions: 1. How does problem format influence second grade children's arithmetic problem-solving performance? 2. Which domain-general and mathematics-specific skills uniquely predict performance on these different formats? We analysed data from two hundred and ninety-four 7- to 9-year-old (second grade) children who completed booklets with arithmetic problems presented in five different formats with increasing levels of element interactivity: 1) symbolic, 2) bare word problems, 3) word problems accompanied by an unhelpful illustration, 4) word problems accompanied by a helpful illustration and lastly 5) word problems accompanied by an illustration with essential information. We also explored which cognitive skills, domaingeneral (e.g., working memory) and mathematics-specific skills (e.g. nonsymbolic and symbolic processing and estimation skills) uniquely predict children's performance on these five different arithmetic problem formats. Our results verify and extend past research. Overall, we found that the format of an arithmetic problem influences children's problemsolving performance and the type of information included in illustrations is crucial. Symbolic, bare word problems and word problems with illustrations that include helpful information were the easiest for children. But word problems with unhelpful and especially essential information in their illustrations lead to decreased performance. Further, we found that different constellations of domain general and mathematics-specific skills predicted performance across the different types of arithmetic problem formats. I preregistered the study, analysed the data and wrote a conference paper. This paper was presented at EARLI 2021 Conference. * Currently, in August 2021, we designed a new study to explore the following question: "How does problem format influence Year 3 and Year 4 children's arithmetic problem-solving performance?" with a sample of primary school pupils. We submitted an ethics application to Loughborough University Ethics Committee and our application was successful. We are planning to collect data for this project online in primary schools in England between November 2021 and February 2022. * I am working on writing up a paper from the first study which was a secondary data analysis of a previous project and we will submit this paper to Learning and Instruction journal. |
| Collaborator Contribution | Our partners have contributes to writing up literature review and reviewed the analyses plan. They contributed to the design of the new study which we plan to collect data for the project in November 2021. |
| Impact | Xenidou-Dervou, I., Simsek, E., van Luit, J. E. H., Kroesbergen, E. H., Friso-van den Bos., I., van der School, M., & van Lieshout, E. C. D. M. (2021, August). The Effect of Problem Format on Second Grade Children's Arithmetic Problem-Solving Performance [Single Paper]. EARLI 2021 Conference, Online. A new study is designed and this study will be undertaken between November 2021 and February 2022. |
| Start Year | 2021 |
| Description | Project: The role of problem format in word problem-solving performance |
| Organisation | University of Twente |
| Country | Netherlands |
| Sector | Academic/University |
| PI Contribution | * We conducted a study, a secondary data-analysis study of an existing dataset (see preregistration https://aspredicted.org/blind.php?x=qn7yx9) to explore the following research questions: 1. How does problem format influence second grade children's arithmetic problem-solving performance? 2. Which domain-general and mathematics-specific skills uniquely predict performance on these different formats? We analysed data from two hundred and ninety-four 7- to 9-year-old (second grade) children who completed booklets with arithmetic problems presented in five different formats with increasing levels of element interactivity: 1) symbolic, 2) bare word problems, 3) word problems accompanied by an unhelpful illustration, 4) word problems accompanied by a helpful illustration and lastly 5) word problems accompanied by an illustration with essential information. We also explored which cognitive skills, domaingeneral (e.g., working memory) and mathematics-specific skills (e.g. nonsymbolic and symbolic processing and estimation skills) uniquely predict children's performance on these five different arithmetic problem formats. Our results verify and extend past research. Overall, we found that the format of an arithmetic problem influences children's problemsolving performance and the type of information included in illustrations is crucial. Symbolic, bare word problems and word problems with illustrations that include helpful information were the easiest for children. But word problems with unhelpful and especially essential information in their illustrations lead to decreased performance. Further, we found that different constellations of domain general and mathematics-specific skills predicted performance across the different types of arithmetic problem formats. I preregistered the study, analysed the data and wrote a conference paper. This paper was presented at EARLI 2021 Conference. * Currently, in August 2021, we designed a new study to explore the following question: "How does problem format influence Year 3 and Year 4 children's arithmetic problem-solving performance?" with a sample of primary school pupils. We submitted an ethics application to Loughborough University Ethics Committee and our application was successful. We are planning to collect data for this project online in primary schools in England between November 2021 and February 2022. * I am working on writing up a paper from the first study which was a secondary data analysis of a previous project and we will submit this paper to Learning and Instruction journal. |
| Collaborator Contribution | Our partners have contributes to writing up literature review and reviewed the analyses plan. They contributed to the design of the new study which we plan to collect data for the project in November 2021. |
| Impact | Xenidou-Dervou, I., Simsek, E., van Luit, J. E. H., Kroesbergen, E. H., Friso-van den Bos., I., van der School, M., & van Lieshout, E. C. D. M. (2021, August). The Effect of Problem Format on Second Grade Children's Arithmetic Problem-Solving Performance [Single Paper]. EARLI 2021 Conference, Online. A new study is designed and this study will be undertaken between November 2021 and February 2022. |
| Start Year | 2021 |
| Description | The role of cognitive and behavioural executive function skills in learning new mathematics material |
| Organisation | University of Nottingham |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | I analysed the data and wrote the analysis and results section in a conference paper and a journal article. The journal article is still in preparation phase and we submitted the conference paper to "Developing and stimulating competencies: Methodological challenges and opportunities for research"International Scientific Network in Leuven from October 13 till October 15, 2021. |
| Collaborator Contribution | My partners have contributed to writing up the conference paper and have been working on writing up the journal article (particularly on literature review and discussion sections). |
| Impact | In this study, we followed a cohort of 8- to 9-year-old children across 20 months from the point they were first introduced to symbolic representations of rational numbers. Prior to this instruction, we administered measures of executive functions including working memory, inhibition (numerical and non-numerical content) and switching. In addition to standard cognitive measures of executive functions we also administered behavioural measures, including a following instructions task, teachers' ratings of executive function and observations of classroom on-task behaviour. Procedural and conceptual measures of rational number knowledge were administered at three time points. Latent growth curve models were conducted to provide estimates of initial performance and growth over time and we investigated how far the cognitive and behavioural executive function measures were predictive of initial performance and growth. We found that initial performance was more strongly predicted by cognitive measures while growth over time was more strongly predicted by behavioural measures. There were only weak to moderate correlations between the cognitive and behavioural measures of executive functions. These findings highlight the complex role of domain-general skills on learning both directly and indirectly via influencing classroom behaviour. Conference paper: Joanne Eaves, Emine Simsek, Lucy Cragg Gilmore, C., Eaves, J., Simsek, E., & Cragg, L. (2021, October). The role of cognitive and behavioural executive function skills in learning new mathematics material. Developing and stimulating competencies: Methodological challenges and opportunities for research, 2021International Scientific Meeting, Online. |
| Start Year | 2020 |
| Description | 9th ERME Topic Conference: New Researchers' Day |
| Form Of Engagement Activity | A formal working group, expert panel or dialogue |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | With eight other postgraduate students and postdoctoral researchers, we came together to share and discuss our research. The topic of this special day was Arithmetic and number systems: Number Sense and Flexibility. |
| Year(s) Of Engagement Activity | 2021 |
| Description | Conference Presentation |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I presented the results from a study called "The Effect of Problem Format on Second Grade Children's Arithmetic Problem-Solving Performance" at EARLI Conference to an audience formed by academics and practitioners and this increased awareness and interest on the role of illustrations when solving word problems. Xenidou-Dervou, I., Simsek, E., Van Luit, J., Kroesbergen, E., Friso-van den Bos, I., van der Schoot Jones, M., & van Lieshout C. D. M. E. (2021, August). The Effect of Problem Format on Second Grade Children's Arithmetic Problem-Solving Performance. [Single Paper]. The European Association for Research on Learning and Instruction (EARLI) 2021 Conference, Online. |
| Year(s) Of Engagement Activity | 2021 |
| Description | Conference Presentation |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I presented the results from a study called "What Features of Equivalence Problems Relate to Adults' Problem-Solving Performance?" at EARLI Conference to an audience formed by academics and practitioners, and increased interest and awareness on problem features relating to problem solving. Simsek, E., Jones, I., & Xenidou-Dervou, I. (2021, August). What Features of Equivalence Problems Relate to Adults' Problem-Solving Performance? [Single Paper]. The European Association for Research on Learning and Instruction (EARLI) 2021 Conference, Online. |
| Year(s) Of Engagement Activity | 2021 |
| Description | Conference Presentation |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I presented the results from my PhD (cross-cultural study) at MCLS Conference. This increased awareness in the area. Simsek, E., Xenidou-Dervou, I., Hunter, J., & Jones, I. (2021, March). Factors influencing students' understanding of mathematical equivalence. Understanding of mathematical equivalence in elementary and middle school: Predictors and implications [Symposium]. Mathematical Cognition and Learning Society (MCLS) 2020 Conference, Online. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://www.youtube.com/watch?reload=9&v=2urrqw5OGrk |
| Description | Fellowship Inaugural Lecture: My ESRC Postdoctoral Fellowship: A 12-month research journey to explore factors relating to students' understanding of mathematical equivalence |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Other audiences |
| Results and Impact | I was invited to give a talk about my ESRC Fellowship, particulary, application process and how my fellowship has helped me develop as a researcher. This talk inspired early career researchers who look for funds to support them stay in academia and how to develop research skills. |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://www.lboro.ac.uk/research/research-staff/fellowship-lectures/ |
| Description | What Relates to Understanding of Equivalence? |
| Form Of Engagement Activity | Engagement focused website, blog or social media channel |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Schools |
| Results and Impact | In this blogpost, I wrote about one of the studies that I undertook during my PhD. This blogpost is one of the only open access resource for teachers to get information about students' understanding of equivalence and the equals sign literature. Also, this blog has potential to influence teachers to improve their classroom practice when teaching mathematical equivalence. I also outlined some take-home points for teachers. After the blogpost gets published, a few teachers contacted me about further information. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://blog.lboro.ac.uk/cmc/2021/07/27/what-relates-to-understanding-of-equivalence/ |