The main focus of the study was to identify the the effects of the ACE teaching cycle approach on students' engagement in learning of Elementary Linear Algebra. The Elementary Linear Algebra course was delivered at the Mathematics Education Study Program of State University of Padang, Indonesia. An action research methodology was adopted for the study and the constructivist theory was used as a theoretical framework. This study used mixed methods to collect, describe, and interpret the data. The data were collected through focus group discussion, classroom observations, and questionnaire. The participants in this study consisted of 37 students enrolled in the Elementary Linear Algebra course during the January-June 2011 semester. The ACE teaching cycle approach that was implemented in this study consisted of three steps. The first step in this cycle was the concept maps activity. This activity encouraged students to prepare for the topics that would be discussed in the class. The next step was classroom discussion which provided a social context in which the students could work together to solve mathematics problems. Finally, exercises were assigned as homework. In this part, students practised solving mathematics problems and wrote reflective journal. Students' involvement in the ACE teaching cycle approach in the Elementary Linear Algebra course improved their engagement in mathematics learning in the three domains of cognitive engagement, affective engagement and behavioural engagement.