[ILLUSTRATION OMITTED] Computational thinking is a fundamental skill for everyone, not just for computer scientists. To reading, writing, and arithmetic, we should add computational thinking to every child's analytical ability (Wing 2006, p. 33). A Framework for K-12 Science Education identified eight practices as essential elements of the K-12 science and engineering curriculum (NRC 2012, p. 49). These practices are deeply embedded within the Next Generation Science Standards (NGSS Lead States 2013a), where they are wedded closely to core ideas in the science disciplines. Most of the practices, such as Developing and Using Models, Planning and Carrying Out Investigations, and Analyzing and Interpreting Data, are well known among science educators. In contrast, the practice of Using Mathematics and Computational Thinking raises questions in the minds of many educators. As mathematics has long been integral to science teaching, the questions tend to revolve around the meaning of computational thinking. The Framework envisions computational thinking as a powerful intellectual tool: Since the mid-20th century, computational theories, information and computer technologies, and algorithms have revolutionized virtually all scientific and engineering fields. These tools and strategies allow scientists and engineers to collect and analyze large data sets, search for distinctive patterns, and identify relationships and significant features in ways that were previously impossible. They also provide powerful new techniques for employing mathematics to model complex phenomena---for example, the circulation of carbon dioxide in the atmosphere and ocean (NRC 2012, p. 64). and computational thinking We (the authors) asked ourselves how the different forms of computational thinking suggested in this definition differed from mathematical thinking. Mathematics, it's important to note, is not just a skill but also a way of thinking about the world. The Framework distinguishes mathematics from data analysis in the use of symbols to express relationships. So, for example, a student might graph data from an experiment and notice a pattern. Mathematics comes in when the student expresses the pattern as an equation that can predict additional data points. Students develop mathematical thinking when they approach a new situation with a range of mathematical skills in mind. Similarly, they develop computational thinking when they approach a new situation with an awareness of the many ways that computers can help them visualize systems and solve problems. The Venn diagram in Figure 1 shows how we see the relationship between mathematical and computational thinking. The diagram (itself a mathematical tool) shows which capabilities can be considered part of mathematical thinking, which are part of computational thinking, and which are part of both. As the diagram illustrates, analyzing and interpreting data is common to both mathematical and computational thinking, as are problem solving, mathematical modeling, and statistics and probability. Figure 1 also lists capabilities unique to computational thinking. In the remainder of this article we will illustrate how simulation, data mining, and automated data collection are important in today's science classroom. As you read these examples, keep in mind that simply using computers is not enough; students must be encouraged to re-orient and deepen their understanding about science using computational thinking. Your goal should be to help students build learning skills by recognizing the ways they can use computers to carry out investigations and solve practical problems. [FIGURE 1 OMITTED] The NGSS describes the practice of mathematics and computational thinking for high school as follows: Mathematical and computational thinking in 9-12 builds on K-8 experiences and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. …
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