Argumentation is a scientific literacy practice focused on developing scientific thinking skills associated with problem-solving. As computing has become an integral part of our world, computational thinking skills are requisite for successful problem-solving. The significant effect of computational thinking applications on the efficacy of scientific literacy practices is increasingly acknowledged. In this article, we propose a framework that conceptualizes the constructivist argumentation as a context for problem-solving by applying five computational thinking dimensions, viz. algorithmic design, decomposition, abstraction, evaluation, and generalization. The framework emphasizes two aspects, students’ problem-solving capability and quality of argumentation. Drawing from the literature on scientific argumentation and problem-solving, we argue that the application of computational thinking dimensions in science learning is currently overlooked in the instructional environment. To nurture higher order thinking skills and to engage effective problem-solvers, our framework incorporates four Computational Thinking-Argumentation design principles to support instructional innovation in the teaching and learning of science at the secondary school level, viz. 1) developing problem-solving competencies and building capability in solving uncertainties throughout scientific inquiry; 2) developing creative thinking and cooperativity through negotiation and evaluation; 3) developing algorithmic thinking in talking and writing; 4) developing critical thinking in the processes of abstraction and generalization.