Computing with R for Mathematical Modeling

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The depth and complexity of the problems facing the nation and globe increasingly demand complex, computational solutions. Seeking ways to seamlessly build computational thinking in to high school curricula is one way to prepare students for this future. Because computer science courses are unavailable in most schools, integrating computational thinking into existing high school courses may be better suited to provide a solution to this gap in students' preparation. This project will develop a robust infrastructure using the open source statistical program R to support the infusion of computational thinking into high school mathematics courses. Three online curriculum modules will be developed that integrate computational thinking practices: a) interpreting categorical and quantitative data, b) making inferences and justifying conclusions, and c) linear, quadratic, and exponential models. The proposed online learning platform will provide wide access to the computing resources, learning resources, and teacher supports. The project is funded by the STEM+Computing program, which seeks to address emerging challenges in computational STEM areas through the applied integration of computational thinking and computing activities within disciplinary STEM teaching and learning in early childhood education through high school (preK-12).Linking mathematics to everyday problem solving, mathematical modeling is an iterative cyclic process that involves identifying and selecting variables to represent a situation, choosing mathematical representations to describe the variables and their relationships, performing mathematical operations to draw conclusions, interpreting and validating the conclusions against the situation, and iteratively improving the model. In the same spirit, computational thinking is the process of formulating problems and solutions in terms of computational steps and algorithms that can be executed by computers. Both practices aim to connect the real world with the model world, either mathematical or computational, to create solutions to problems. This project focuses on the coupling of these two strategies. For example, one focus of the project is an investigation of how variations of coupling strategies impact learning. This project will systematically manipulate design patterns and compare students' learning outcomes and learning processes across three field tests with Module A. The steps in a computational mathematical modeling cycle can be grouped into subsets for initial task classes to reduce the complexity of dealing with the entire cycle; however, doing so may decrease the level of authenticity and richness of the tasks. Finding a good balance between engagement and cognitive load control will be the focus of this phase of the study.