2015 Volume 21 Issue 2 Pages 123-132
The objective of this research is to make students’ mathematical noticing related to mathematical thinking clear, and then understand mathematical thinking as activities in a classroom. For this objective, this article aims to grasp a dynamics of noticing in mathematics classrooms by referring to the results from investigations in Kageyama et al. (2014).
In this research, we defined mathematical noticing as a series of cognitive actions such as selecting, recognizing particular features and rationally interpreting them. Plus, we propose 4 viewpoints to analyze students’ complex, cognitive actions in a classroom - individual cognitive dispositions, interactions, material resources, and a problematic situation. We implemented mathematical lessons for the first and fourth graders, obserbed and analysed them by making use of the 4 points framework. As a result, we identified that students’ mathematical noticing was sometimes persistent, while changing dramatically depended on the situations. Finally, we suggested that there were 3 possible factors to change noticing as below:
・aims of activities by students in action,
・a renovation of a problematic situation,
・an invention of new objects depended on the above both.
Students in action often say that there is a rule. This might be a key term related to the above, therefore the future task is to grasp students’ mathematical noticing deeply by focusing on a literal objective such as a rule.
