Enhancing Students’ Mathematical Noticing in the Classroom: A Case Study of Grade 4 Lessons in a Self-Directed Learning Environment

Keiko Hino* and Chika Oinuma^

*Utsunomiya University
Japan

^Shimotsuga Board of Education Office
Japan

Published in The Mathematician Educator, 2025, Vol 6, No. 1, pp 3-19.

Abstract

The purpose of this study is to examine the characteristics of students’ mathematical noticing during mathematics lessons in a self-directed learning environment. Aiming to foster mathematical noticing in many students, the lessons in this study employed open-ended tasks. Moreover, multiple tasks were prepared, and an environment was provided in which students could choose the order and method of solving them on their own. A detailed analysis of the thinking of three students revealed that, depending on students’ individual preferences, tendencies, and prior learning experiences, the objects they focused on and the nature of the difficulties they faced varied, resulting in differing forms of mathematical noticing. While such spontaneous aspects were observed, a remaining challenge is how to support students in engaging in more deliberate and active reasoning toward noticing productive mathematical ideas. This issue aligns with findings from previous studies. Based on this study, which emphasized self-directed learning, it is suggested that strategies are needed to encourage students’ self-directed noticing, such as designing tasks or difficulties that allow for evaluation and refinement of their own choices.

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