Senior high school students’ competence in logical operation and logical reasoning

The research suggests that the framework of logical operations and inference patterns remains unfinished even in adulthood. While various logical models exist beyond the classical true-or-false reasoning model, secondary school students must primarily understand and apply classical reasoning rules. In mathematics, proof, reasoning, and refutation are essential due to the frequent use of logical operations in the subject. This study assessed general logical knowledge and operations within mathematical contexts through classroom tests involving 448 students from 10 public schools and four vocational schools. The students performed best on tasks requiring correct conclusions (69.02%), followed by interpreting “at most”/”at least” (63.41%), with the lowest success rate in negation tasks (29.91%), including negating “at least,” “exists,” and “for every”. The results reveal that accurate interpretation was not dominant across all logical operations for these students. Students performed best on geometric problems (70.05%), followed by algebra, statistics, and calculus problems, with the lowest success rate in calculus-related logical problems (28.04%). Statistical tests showed no significant gender differences in performance; however, according to human capital theory, students with teachers as parents performed significantly better.