Using MATHEMATICS and Computational Thinking
"Increasing students’ familiarity with the role of mathematics in science is central to developing a deeper understanding of how science works."
Introduction to Using Mathematics and Computational Thinking
Mathematics and computational tools are central to science and engineering. Mathematics enables the numerical representation of variables, the symbolic representation of relationships between physical entities, and the prediction of outcomes. Mathematics provides powerful models for describing and predicting such phenomena as atomic structure, gravitational forces, and quantum mechanics.
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.
Mathematics and computation can be powerful tools when brought to bear in a scientific investigation. Mathematics serves pragmatic functions as a tool—both a communicative function, as one of the languages of science, and a structural function, which allows for logical deduction. Mathematics enables ideas to be expressed in a precise form and enables the identification of new ideas about the physical world. In much of modern science, predictions and inferences have a probabilistic nature, so understanding the mathematics of probability and of statistically derived inferences is an important part of understanding science.
Mathematics (including statistics) and computational tools are essential for data analysis, especially for large data sets. The abilities to view data from different perspectives and with different graphical representations, to test relationships between variables, and to explore the interplay of diverse external conditions all require mathematical skills that are enhanced and extended with computational skills.
Key Features
Finding ways to theorize, test, and refine their understanding of patterns, relationships, and processes they notice in the world
Learning how both to apply formulas and tools that already exist and create new ones
Having access to a toolkit of resources that help students make sense of data.
What it is NOT
Using simulations or data visualizations to illustrate a phenomenon, without allowing students to pursue their own question or explore the phenomenon
Using spreadsheets to input data and perform calculations, without having students reason about what those calculations mean scientifically.
Having students complete simple word problems or fill out predefined data tables to reinforce a given formula
Using computer based flashcards, quizzes, wikis, or videos to introduce science concepts.
K-12 Progressions for Using Mathematics and Computational Thinking
SEP_UMCT.pdfInstructional Strategies for Using Mathematics and Computational Thinking
Source: Instructional Science Leadership
Provide opportunities for students to perform calculations on their gathered data, such as finding the mean (average) of several trials of data.
Engage older students in using computer programs such as excel to analyze large data sets from scientific organization (e.g. NASA, NOAA).
Create activities in which students are given a scientific question and must decide how to use mathematical or computational thinking to address the question.
Use various tools to gather data such as graduated cylinders, thermometers, balances, etc.
Have older students decide whether to represent their data in different ways such as using ratios, percents, etc.
Engage students in investigations that require them to use mathematical operations (e.g. subtract quantities to determine the volume of an object).
Learn more about Using Mathematics and Computational Thinking
Bozeman Science Video - Practice 5 - Using Mathematics and Computational Thinking
Wonder of Science Organizer: Using Mathematics & Computational Thinking - Google Draw or PDF
STEM Teaching Tools - Practice Brief 56: Engaging Students in Computational Thinking During Science Investigations
Articles:
Science Practices Continuum - Tool for guiding and evaluating science-practice based instruction
Instructional Resources:
PhET - Fun, interactive, research-based simulations of physical phenomena from the PhET™ project at the University of Colorado.
NetLogo - A multi-agent programable modeling environment
Next Generation Molecular Workbench - Visual simulations for teaching and learning
SageModeler - a systems modeling tool to facilitate the building of dynamic models.
Loopy - a tool for thinking in systems.
InsightMaker - a powerful simulation tool that runs in your browser.