Limited research has been conducted on the influence of computational thinking (CT) dispositions on students' mathematics performance and engagement at the secondary or junior high school level. This study aims to bridge this research gap by developing CT-integrated mathematics lessons that incorporate CT-focused problem-solving and modeling in mathematics education. The study was conducted in a secondary school in Singapore, where students engaged in a mathematics modeling task while learning the four pillars of CT. To investigate the impact of integrating CT dispositions on student engagement and mathematics performance, a one-group posttest design together with a survey was administered. Mixed research methods were employed. Structural Equation Modeling analysis revealed that CT dispositions could enhance students' mathematics performance by fostering greater engagement in math, although a direct effect of CT disposition on mathematics performance was not observed. Additionally, interviews with students highlighted their positive dispositions towards CT, including a sense of capability, inclination, and sensitivity in utilizing CT for the modeling task and other contexts.