Co-construction of collective algebraic thinking in Digital Mathematical Discussion and beyond

Join this CDE Seminar by Sara Gagliani Caputo.

The integration of digital technologies into educational contexts offers significant opportunities to transform the teaching and learning of mathematics, particularly by enabling collaboration and communication beyond the traditional boundaries of the classroom (Ball & Barzel, 2018). Situated within this research area, my work contributes to the study of the role of digital technologies in extending mathematical discussion beyond the temporal and spatial boundaries of the classroom.

Research in mathematics education has focused primarily on the support that digital technologies can provide for the design and implementation of mathematical discussions conducted synchronously (e.g., Cusi et al., 2017; Giberti et al., 2024); my work extends the investigation to asynchronous mathematical discussions. Asynchronous interaction allows participants to reflect, process information, and contribute at their own pace. Moreover, its predominantly written nature encourages participants to make their reasoning more explicit and generates a trace of the discussion (Wang, 2023). To investigate the challenges and potential of asynchronous mathematical discussion, during my doctoral research I introduced and analysed the didactic methodology of Digital Mathematical Discussion (DMD). DMD builds on balance discussion (Bartolini Bussi, 1996) and consists of three phases: group problem solving in instant-messaging chats, a whole-class discussion on Padlet, and a concluding whole-class discussion in the classroom. So far, my work has focused on the first two phases of DMD, which are conducted asynchronously.

My doctoral research focused both on students’ collaboration and on the development of mathematical thinking processes during the asynchronous phases of DMD. Participants included university students enrolled in a primary education degree programme and grade 9 students attending scientific high schools. The data collected consisted of chat transcripts and Padlet posts generated during the asynchronous phases of DMD. To analyse collaborative processes, I drew on the social modes of co-construction dimension from the framework proposed by Weinberger and Fischer (2006) for analysing argumentative knowledge construction in computer-supported collaborative learning contexts. About the mathematical content of the discussions, I used activities previously implemented in face-to-face mathematical discussion contexts, focusing on the use of algebra as a tool for thinking. These activities form part of a didactic path introducing students to proof in arithmetic through the use of algebraic language (Cusi, 2008). In analysing the development of algebraic thinking, I focused on conceptual frames (Arzarello et al., 2001) and anticipation (Boero, 2001).

The analysis of the data collected during the experiments provided insights into the interplay between social modes of co-construction and the development of students’ algebraic thinking processes. The results revealed different patterns of this interplay across the asynchronous phases of DMD. In the group work conducted through chat, heterogeneous collaborative processes emerged, which varied in their effectiveness in actively considering and building on others’ contributions, as well as in promoting the development of collective algebraic thinking. In the whole-class discussions on Padlet the social modes of co-construction became less differentiated, while individual algebraic thinking prevailed.

These findings highlighted the importance of further exploring the relationship between the individual and collective dimensions of mathematical thinking processes in DMD. This relationship has become central to my postdoctoral research, in which I focused on the emergence of collective algebraic thinking through epistemic activities in group work within asynchronous mathematical discussions, connecting this investigation with the concept of group cognition and further refining the methodological approach used to study it.

In the next stages of my research, I plan to extend this work to algorithmic thinking in problem-solving activities at the intersection of mathematics and computer science. I also aim to integrate the neurodiversity paradigm into the design and evaluation of these activities, exploring how different neurotype constellations may shape participation, collaboration, and the development of mathematical and computational thinking in digitally mediated learning environments.

References

Arzarello, F., Bazzini, L., & Chiappini, G. (2001). A model for analyzing algebraic thinking. In R. Sutherland, T. Roiano, & A. Bell (Eds.), Perspectives on School Algebra (pp. 61–81).

Ball, L., & Barzel, B. (2018). Communication When Learning and Teaching Mathematics with Technology. In L. Ball, P. Drijvers, S. Ladel, H. Siller, M. Tabach, & C. Vale (Eds.), Uses of Technology in Primary and Secondary Mathematics Education: Tools, Topics and Trends (pp. 227243). Springer. http://dx.doi.org/10.1007/978-3-319-76575-4_12

Bartolini Bussi, M. G. (1996). Mathematical Discussion and Perspective Drawing in Primary School. Educational Studies in Mathematics, 31(1-2), 11–41. https://doi.org/10.1007/BF00143925

Boero, P. (2001). Transformations and anticipation as key processes in algebraic problem solving. In Sutherland R., Roiano T., Bell.A. (Eds.), Perspectives on School Algebra (pp. 99–119).

Cusi, A. (2008). An approach to proof in elementary number theory focused on representation and interpretation aspects: the teacher’s role. In B. Czarnocha (Ed.), Handbook of Mathematics Teaching Research (pp. 107–122). Rzeszów University Press.

Cusi, A., Morselli, F., & Sabena, C. (2017). Promoting formative assessment in a connected classroom environment: design and implementation of digital resources. ZDM Mathematics Education, 49(5), 755–767. https://doi.org/10.1007/s11858-017-0878-0

Giberti, C., Arzarello, F., Beltramino, S., & Bolondi, G. (2024). Mathematical discussion in classrooms as a technologically-supported activity fostering participation and inclusion. Educational Studies in Mathematics, 118, 201–228. https://doi.org/10.1007/s10649-024-10356-y

Wang, Y. (2023). Online discussion in secondary and higher education. A complete guide to building a dynamic online discourse community. Springer.

Weinberger, A., & Fischer, F. (2006). A framework to analyze argumentative knowledge construction in computer-supported collaborative learning. Computers & Education, 46, 71–95. https://doi.org/10.1016/j.compedu.2005.04.003