Acquisition of relational concepts: Pathway to proficient thinking in mathematics and science

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The proposed project is located in the second quadrant of the ROLE description with links to the third and fourth quadrants. It focuses on acquisition, representation, processing, learning and transfer of relational concepts. The study of relational concepts is important because relational concepts are ubiquitous in mathematics and science: ratio, proportion, and function, velocity, acceleration, and density, mutation, evolution and growth rate, probability and statistical interaction, and correlation and contingency are just a few examples. The study will be guided by our hypotheses about representation, processing, learning, and transfer of relational concepts across ages and knowledge domains. The proposed project aims to answer several fundamental questions. What are the basic cognitive mechanisms underlying acquisition of relational concepts, and how are relational concepts represented in the cognitive system? How do these mechanisms and representations change in the course of development? Do these mechanisms differ across knowledge domains? And how can we facilitate learning and transfer of relational concepts within and across domains of mathematics and science? To pursue these questions, we propose a three-year-long research project that will be conducted by a team of researchers collaborating through the Ohio State University Learning Research Initiative and interested in cognition, cognitive development, and the learning of biology, physics, and mathematics. The project would be a systematic empirical study of conceptual development across several knowledge domains. The team will use a wide variety of methods and tasks, ranging from simple tasks allowing participation of young children to relatively complex tasks requiring sophisticated knowledge. The project will generate new basic knowledge increasing our understanding of acquisition and processing of relations, as well as our understanding of learning and transfer of relational concepts in mathematics and science. The proposed project will be an important step towards better understanding of conceptual development and of learning of important concepts in mathematics, physics, and biology, and it will inform practice of teaching of mathematics and science.