Since the emergence of the fourth industrial revolution which calls for a new model of learning for the twenty-first century learners, it has been argued that the nature of problems that learners must solve in science, technology, engineering and mathematics (STEM) must also be transformed to enable new forms of learning skills that are needed to tackle complex global challenges. However, the question of how best to teach these skills purposefully and explicitly is largely overlooked. STEM education reformers recognize that the lecture method or traditional method of teaching is highly ineffective for teaching twenty-first century competencies and skills that learners need to develop, yet widespread use of this approach continues. In today’s world, we need STEM graduates who are more sophisticated in understanding the uncertainty of knowledge through quasi-reflective thinking when there is uncertainty about a solution to a problem. For this to happen, STEM learners need skills such as critical thinking, decision-making, innovation, the ability to communicate new knowledge effectively, and the ability to solve various kinds of problems through negotiation and collaboration, all of which present a corpus of knowledge to be constructed and mastered in a learner-driven pedagogy. Therefore, rethinking the kind of problem-solving skills we teach twenty-first century learners is as crucial as identifying a suitable instructional model. This paper demonstrates how the domain of ill-structured problems-based learning may contribute to the development and mastery of twenty-first century competencies and skills, and advance the quality of learning through the argumentation model.