Students’ Thinking, Reasoning and Learning Proficiency in Problem Solving Rational Functions

The pressing issue of students' poor development of critical thinking and reasoning abilities impedes their skills to understand complex mathematical ideas and restricts their ability for innovation. This situation needs extensive research into successful mathematical instructional strategies. This descriptive correlational study employed simultaneous multiple simple linear regression to assess students' levels of thinking, reasoning, and learning competency. It also looked at how students' thinking and reasoning skills correlated with their ability to solve rational functions. Data from 284 randomly selected students, examined using open-ended math questions and a multiple-choice test, revealed that while students displayed high general thinking and reasoning skills, their proficiency in rational function was average only, with considerable performance variability. A high positive correlation was found between these skills and learning proficiency, with critical and creative thinking, as well as inductive reasoning, having a major influence on mastery of concepts including domain, range, intercepts, zeros, asymptotes, and graphing. Inductive reasoning outperformed deductive reasoning, particularly for overall performance of rational functions. However, both inductive and deductive reasoning skills had a lower influence on acquiring rational inequalities, indicating the necessity for intense direct interactive instruction in this area. These findings highlight the need of including activities that encourage diverse thinking while emphasizing critical and inductive reasoning into modern and interactive direct instructional approaches. Regular assessments of students' thinking and reasoning abilities, together with a variety of interactive and current teaching methodologies on rational inequalities, are critical for improving learning proficiency in rational functions.