The more prepared pre-service teachers are, the more fruitful teaching is: a case of complex logarithmic inequalities

Introduction With the understanding of the concept of logarithms, the teaching of logarithmic inequalities becomes one of the important topics in mathematics education. This study focuses on strengthening pre-service teachers’ subject-matter competence through complex (enriched-question-based) logarithmic inequalities, broadening their perspectives, enabling them to approach problems from different angles, and supporting their perceived professional preparedness and pedagogical reflection for future teaching. Methods Using a mixed-methods design, quantitative and qualitative data were collected from 13 pre-service teachers (5 female, 8 male) who are preparing to begin their teaching careers in public schools in Fergana, Uzbekistan. In addition to pre- and post-tests, the findings supported by questionnaires and classroom observations provide an explorative qualitative insight into the didactical richness of complex logarithmic inequalities as tasks to promote content depth, error awareness, metacognitive growth and pedagogical reflection of the participants. Results These results indicate the need to strengthen mathematical content knowledge in teacher education programs to foster professional preparedness among pre-service teachers. Discussion Consequently, the findings indicate the cultivation of professional self-awareness and reflective ability rather than empirically substantiated teaching competence.