Utilizing Annotated Digital Timelining in Mathematics Education Research: Exploring Elementary School Teachers’ Culturally Relevant Competencies and Finch Robot Orchestrations

• In Event: Innovative Mixed Methods Research Practices in Mathematics Education Contexts

Abstract

Annotated digital timelining is an innovative visual research method that enhances mixed methods research (MMR) by integrating qualitative and quantitative data in a unified visual format, facilitating in-depth analysis of constructs of interest over time (Lyublinskaya, 2022). This paper illustrates how this method merges results of qualitative and quantitative data analysis to reveal patterns, and provide insights into elementary teachers' development of culturally relevant competencies (Coward et al., 2025) and their instrumental orchestrations (Cheung & Lyublinskaya, 2025) using the Finch robot in mathematics classrooms. The two illustrative case studies were grounded in culturally relevant mathematics pedagogy (CRMP; Matthews et al., 2022) and instrumental orchestration theories respectively (Trouche, 2004). CRMP emphasizes academic success through conceptual understanding, relationship building, cultural responsiveness, and social justice engagement in mathematics education. Instrumental orchestration framework (Drijvers, 2009) provides a framework to analyze how teachers utilize digital tools in instruction.
The annotated digital timelining was utilized within a convergent MMR design (Figure 1).
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Data sources comprised videos from six mathematics lessons per study, conducted over one academic year within elementary classrooms in two urban Title I schools, teacher reflections, and co-designed mathematics tasks incorporating the Finch robot. Participants included a team of first-grade teachers in the first study and a team of third-grade teachers in the second study.
In the first study, videos were scored using a validated CRMP rubric (Lyublinskaya et al., 2024) and teacher competencies and reflections were coded thematically. In the second study, videos were analyzed to identify orchestration types and sequences and to calculate orchestration frequencies. In both studies, results of quantitative analysis were plotted on a timeline, while qualitative results were added as annotations (Figures 2 and 3).
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In both studies, the use of annotated timelining allowed for the integration of quantitative and qualitative results, surpassing traditional joint displays by aligning data on a unified timeline for in-depth temporal analysis. This method provided clear insights into the convergence of data and highlighted non-linear patterns in teachers' development that would be challenging to discern using conventional MMR. Annotated timelining emerged as a robust analytical methodology to reveal the nuanced interplay among constructs of interest in each study. This alignment illuminated critical moments of pedagogical transition, emphasizing that the teacher’s growth is a complex and non-linear process, whether it is development of cultural competencies or integration of robots into mathematics instruction, thus providing a comprehensive perspective on the fluid nature of teaching practices.
These studies illustrate the transformative potential of annotated timelining in advancing the analysis and understanding of complex educational research contexts, particularly within MMR. Annotated digital timelining not only enriches the methodological toolkit of MMR but also bridges the gap between quantitative precision and qualitative depth. By capturing the intricate interplay of temporal, cultural, and instructional dynamics, it holds promise for advancing the scholarship of teaching and learning and fostering more equitable and inclusive educational practices.

Authors

• Marcus Yuen-Yiu Cheung, Teachers College, Columbia University

• Chamarra Alicia Ophelia Coward, Teachers College, Columbia University

• Irina Lyublinskaya, Teachers College, Columbia University