This study uses the Taiwan Programme for International Student Assessment (PISA) 2006 Main Survey and Taiwan PISA 2015 Field Trial survey datasets to investigate how self-evaluated values (i.e. personal and general) and cognitive factors (i.e. self-efficacy and self-concept) of two groups of Taiwanese 15-year-old students separated by 8 years of classroom-presented science instruction experience impact leisure engagement in science learning activities. To compare differences between these two groups, we verified the statistical fitness of a newly created five-factor model called the self-evaluated values and cognition, and engagement, which revealed a good model fit to both PISA datasets. Results from critical ratio for differences analyses showed a significant increase in pathway parameter strength for students' personal value of science, and a significant decrease in pathway parameter strength for students' science self-efficacy between the two PISA survey cycles. Examination of results and their importance for science educators, investigators, and policy-makers is also offered.