Competency-oriented mathematics education requires an increased emphasis on learning activities that help students develop mathematical thinking and reasoning competence, particularly in the process of forming mathematical concepts. This study combines theoretical analysis with consultation involving three experts and 32 high school mathematics teachers through a Likert-scale questionnaire. The results initially identify manifestations of mathematical thinking and reasoning competence in mathematical concept teaching, categorized into three groups associated with students’ learning processes. Based on these findings, a four-stage process for teaching mathematical concepts is proposed and illustrated through the teaching of the concept of a geometric sequence. The consultation results indicate that the proposed process is generally appropriate and applicable to mathematics teaching in schools. However, the study has not yet included a pedagogical experiment; therefore, further research is needed to examine the effectiveness of the proposed process in actual teaching contexts.