Action Research (AR) focusses on classroom research for improving instructional practices while the Japanese inquiry-model of Lesson Study (LS) emphasises on teachers’ collaborative work on student-engaged lessons. Both approaches are central to professional development as they draw on students’ feedback for designing quality lessons. Through AR design, this paper reports on the effectiveness of LS in enhancing the enquiry approach and student engagement in a mathematics classroom. The main objective is to investigate and demonstrate the value and use of enquiry approach and how teachers can engage students in the development of the concept of perimeter during problem-solving, which was investigated by analysing the type of questions asked and the follow-up instructional activities. Our data focus on questions the teacher posed, classroom observation of 27 Grade Four students’ behaviour while solving a perimeter problem, and teacher’s feedback during the debriefing session. Findings revealed higher use of open-ended questions (88.89%) that elicited higher-order thinking than closed questions (11.11%). We argue that the enquiry approach in this LS probed students’ ability to explore alternative solutions, extend their prior conceptual understandings, developed teacher’s support for activation, and use of higher-order mathematical thinking during the course of searching for solutions. Results suggest that LS constitutes a powerful context to understand the quality of questions that teachers use during their day-to-day practice. Further, we have evidenced that LS conducted within an AR design could be a useful research strategy in better understanding teachers’ support for the development of 21st Century skills among our students