A Comparative Study of M-APOS, Knisley, and Discovery Learning on Students' Advanced Mathematical Thinking Skills - Ilmadi Ilmadi; Elda Herlina (Ta'dib, 2026)
Advanced Mathematical Thinking (AMT), which includes representation, abstraction, creative thinking, and mathematical proof, is crucial for studying abstract algebra. However, there is limited research specifically investigating how the M-APOS, Knisley, and Discovery Learning models influence students' AMT abilities, especially in the context of self-regulated learning. This study aims to analyze the impact of these three learning models and self-regulated learning on students' AMT abilities, as well as to examine their interactions. This quantitative study utilized a 3×2 quasi-experimental factorial design. The participants were 66 students from the Mathematics Study Program at Universitas Pamulang, selected via purposive sampling. Twenty-two students were assigned to each learning model group. AMT proficiency was evaluated using a four-item essay test validated by experts. Self-regulated learning was assessed using questionnaires and classified as high or low based on the total score. Data were analyzed using two-way ANOVA. The results indicated that the learning model significantly affects AMT ability (F=9.66; p=0.001<0.05), whereas self-regulated learning does not have a significant effect (F=1.47; p=0.235>0.05). Furthermore, a significant interaction was found between the learning models and self-regulated learning on AMT ability (F=3.66; p=0.018<0.05). These findings suggest that the M-APOS model is more effective in enhancing students' AMT and that the learning model's effectiveness is influenced by levels of self-regulated learning.