Growing research groves to visualize young students’ learning in small groups

Abstract

This paper stems from calls for methodological advancement in two areas of research: primary mathematics education and dialogical education. We respond to these calls from the commognitive standpoint by introducing the Grove of Realizations as a tool for capturing and visualizing individual students’ learning through collaborative work in small groups. We focus on a group of four students from a New Zealand Year 4 class (aged 8 and 9 years old), as they classified odd and even numbers and reasoned about their sums. This data is used to present the analytical affordances of the tool for (i) visualizing gaps in communication between group members, (ii) mapping their discursive development, and (iii) showing whether and how gaps are bridged within a group. The paper concludes with the discussion of the tool’s affordances and directions for further development.

Mathematics education research on language and on communication including some distinctions: Where are we now?

“…Four of the selected articles in Table 5 suggests commognition is a collective project shared by authors all over the world, although with a geographic centre, with empirical studies covering a range of mathematical topics and research participants, as well as differently focused on parts of the mathematical discourse characterised by this theory. These articles examine: types of routines of the mathematical discourse and how these are transformed from rituals to explorations in processes of learning (Lavie et al, 2019); emerging routines in the mathematical practices of describing and defining geometrical solids by undergraduate students (Fernández-León et al, 2021); discourse development of young children in tasks of classifying odd and even numbers and of reasoning about their sums (Knox & Kontorovich, 2022); teachers' narratives about unknowns and variables and on mathematics as mutable (Moustapha-Corrêa et al, 2021). Sinclair ( 2022) is a 5th article that interestingly comments on the advances of commognitive research, as well as on the challenges of contributing to the quandary of learning disability and to a shift towards pluralising mathematical discourse.…”