Exploring critical and reflective thinking in mathematical literacy through variable- and person-centered approaches

Critical and reflective thinking are essential 21st-century skills and play a pivotal role in mathematical literacy (ML). Prior research has neither clearly distinguished these skills nor developed tools to assess them as specific sub-skills rather than broad dispositions. This study addressed this gap by examining the relationship between critical thinking in ML (CT-ML) and reflective thinking in ML (RT-ML), identifying students’ performance profiles, and exploring gender differences using a two-dimensional framework for assessing CT-ML and RT-ML. Results indicate that CT-ML and RT-ML are two distinct but interconnected constructs, each comprising three sub-skills. While the overall structure was consistent across genders, boys and girls differed in the patterns of strengths and weaknesses across CT-ML and RT-ML sub-skills, reflected in their performance profiles. Theoretically, the findings clarify the distinction between CT-ML and RT-ML and establish their complementary nature, offering an innovative perspective on CT and RT as dual constructs. Methodologically, the design of sub-skill assessment items and the application of BSEM provide a rigorous approach to modeling cognitive structures of micro-level thinking skills. Practically, the study highlights the need for learning tasks that foster both CT-ML and RT-ML, while tailoring instruction to students’ distinct profiles and addressing gender-based differences in sub-skill development.