This study explores the worked-example instruction (WEI) and the van Hiele teaching phases (VHTP) pedagogies to advance students' acquisition of procedural and conceptual understanding of solving simultaneous equations. The quasi-experimental study involved two groups of high school students (age=15): 157 students in total with 72 in one group and 85 in the other. The study followed a pre-, post- and delay tests design and adapted two conceptual frameworks: the structure of the observed learning outcomes (SOLO) model and the Rasch model. It employed Rasch analysis and statistical package for social sciences (SPSS) as data analysis tools. The results indicated that both WEI and VHTP improved students' procedural and conceptual understanding of solving simultaneous equations at the post-test; however, the WEI effects (on both procedural and conceptual understanding) were not sustained after the post-test while the VHTP had a lasting effect on only conceptual understanding. Furthermore, the VHTP group significantly outperformed the WEI group at the post-test and delay test in both conceptual and procedural understanding. These results indicated that the WEI is only beneficial at the initial stage of knowledge acquisition and VHTP is better at the initial and long-term. Practical implications of these results were discussed.