Problem-Based Learning and Its Impact on 21st Century Competencies for the Study of Quadratic Functions

Abstract

One of the most significant challenges in mathematics education stems from the mismatch between the competencies demanded by contemporary society and the conventional teaching approaches still widely employed. This disparity is particularly evident within the Ecuadorian education system. Accordingly, this study examined the influence of Problem-Based Learning (PBL) on the development of 21st century competencies during the teaching of quadratic functions among first-year high school science students. Guided by a positivist paradigm, the research adopted a quasi-experimental design involving 56 participants, equally divided into a control group (N=28), which received traditional instruction, and an experimental group (N=28), which was taught using PBL. A five-stage instructional sequence, designated IDRAC and grounded in constructivist learning theory, was developed to support the intervention. Data were collected using three instruments: a pre-test/post-test achievement assessment validated through a pilot study (Pearson’s r = 0.696), an instructional sequence implementation checklist demonstrating acceptable internal consistency (Cronbach’s α = 0.791), and the TAC (Attitudes) Questionnaire v5.11. Baseline analysis confirmed that the two groups were statistically comparable before the intervention, as indicated by the Mann-Whitney U test (p = 0.238). Following the intervention, the experimental group demonstrated a statistically significant improvement in achievement between the pre-test and post-test (p = 0.018). The greatest gains were observed in problem-solving ability (MO +21.43 percentage points) and conceptual understanding (MO +16.07 percentage points). Furthermore,
82.14% of students in the experimental group reported favourable attitudes towards the PBL approach. Overall, the findings suggest that PBL effectively promotes the acquisition of 21st-century competencies, although variations across competency domains highlight the need for stronger instructional scaffolding to enhance mathematical reasoning, communication, self-assessment, and peer-assessment practices.