Cognitive Aspects of Students’ Mathematical Reasoning Habits: A Study on Utilizing Lesson Study and Open Approach

Abstract

This study aimed to investigate the cognitive aspects of the mathematical reasoning habits of 3rd Grade students by utilizing Lesson Study (LS) and Open Approach (OA) in teaching mathematics. The cognitive aspects of mathematical reasoning habits are a powerful complement to teaching mathematics because they are particularly focused on skills and procedures. However, the major problem with teaching mathematical reasoning is that teachers cannot teach mathematical reasoning habits directly but can set up tasks that encourage reasoning. A total of eight students were purposively selected as they have been taught using OA treatment in the LS process for two years, from 2016 to 2018. Four study instruments were used: lesson plans, activity worksheets, field notes, and an interview protocol. In addition, the National Council of Teachers of Mathematics (NCTM) (2009) framework, consisting of four cognitive aspects of mathematical reasoning habits, namely (i) analyzing a problem; (ii) implementing a strategy; (iii) using connections, and (iv) reflecting on a solution, was employed to determine the cognitive aspects of mathematical reasoning habits. Qualitative results revealed three pieces of evidence to support all four cognitive aspects of mathematical reasoning habits. In conclusion, the results of this study contribute significantly to our recognition of the importance of OA treatment in the LS process while teaching mathematics in improving students’ mathematical reasoning habits.