Abstract: Several decades in the past saw the change of focuses in mathematics education research community from cognitive approaches to affective aspects (the second wave), and then the recent trend (the third wave) on the discursive approach. This project uses qualitative tools to investigate effectiveness in mathematics lessons from both the standpoints of the learners and the teachers. The findings have identified what learners value in effective mathematics learning, and how these findings can help teachers and mathematics educators to develop students’ mathematical autonomy in classroom learning.

Key words: Third wave; Effective mathematics lessons; Beliefs; Values; Mathematical autonomy