2025 Volume 49 Issue 4 Pages 363-372
The purpose of this study is to clarify the transformation of learners’ routines and to derive implications for mathematics instruction by refining the concept of unitization for grasping the “unit quantity” in learning multiplication tables during arithmetic lessons. To achieve this purpose, a unit lesson on multiplication tables was planned, implemented, and analyzed for second-grade students. Analysis was conducted from the perspective of Sfard’s (2023) commognition theory. One learner was selected, and the formation and transformation of that learner’s routines were observed. The results revealed that learning progressed through multiple overlapping layers of meta-level learning involving metarule changes within the target-level learning of each lesson throughout the entire unit. Furthermore, commognitive conflicts that trigger metarule changes can emerge in any lesson context. Lesson designs that consciously incorporate these conflicts can help gradually develop learners’ proportional reasoning abilities.
