This study compares the effects of student-centred teaching methods, teacher-centred methods, and teacher-student interactive methods on students' mathematics academic achievement. For this purpose, calculus, compound interest, annuities, and depreciation topics were taught to first-year college students in three different groups: traditional lecture (TL), group discussion (GD), and modified lecture (ML). In the TL group, the lecturer taught mathematical concepts through lectures. In the GD group, students worked in small groups to solve mathematics problems with the lecturer's assistance. Whereas in the ML group, the lecturer used both lecture and questioning to teach mathematics concepts to students. Both groups were taught by the same lecturer and took the same post-test at the end of these lessons. In both contexts, the analysis is based on the same cohort of students (N = 250) using one-way ANOVA. The results of the test showed that there was a significant difference between the performances of the three groups. The results of this test showed that the ML group had a better performance compared to the GD and TL groups, and low-ability students in the ML group had higher gain scores compared to other students. These findings suggest that an interactive approach (a modified lecture) could improve academic achievement in mathematics.