# Using Mathematics and Computational Thinking

Engineers and scientists across disciplines use mathematics and computation in support of investigations. Mathematics includes the representation of variables and relationships using numbers and symbols. Scientists and engineers use mathematics for data collection and analysis in order to answer questions and solve problems. Math can also be used to communicate results and models. Models can be in the form of statistics and probability, equations, or visual models. Computation using computers and information technology allows scientists and engineers to perform mathematical operations quickly on large data sets. Computers let scientists and engineers create visual representations that are not possible with paper and pencil alone. Mathematics serves as a universal language through which scientists and engineers from around the world can communicate. Although scientists and engineers use math for different purposes in scientific investigations and engineering design, the language of math allows them to share ideas across disciplines. Â

Ocean scientists and engineers use mathematics, including statistics, for a variety of purposes. For example, for the carbon cycle, biogeochemists use math to quantify and model atmospheric carbon dioxide (Fig. 1). Ecologists use mathematics to sample and count organisms and statistics to analyze and report their findings. Physical oceanographers use calculus and models to understand and predict wave and current motion (Fig. 3). Scientists across disciplines use computers and probes to collect and analyze data (Fig. 2).

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The framework states that students should be able to use dimensional quantities and units appropriately, express relationships mathematically, understand that computer simulations are built on mathematical models, and use mathematics and statistics to analyze data. Young students can use numbers to describe patterns in nature. As students progress though the grades, they should be able to use instruments to measure physical quantities and use mathematics and statistics to describe those quantities. Students should be able to use algebraic expressions, tables, and graphs to analyze data. In the laboratory or field, students should experience using digital instruments to collect data and computer programs to analyze data.

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