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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.

Fig. 2.8. (A) The Keeling curve, which shows measured levels of atmospheric carbon dioxide measured at Mauna Loa, Hawai‘i.

Image courtesy of Semhur from Wikipedia

Fig. 2.8. (C) A scientist uses a digital probe to measure temperature, pH, and salinity in the Gulf of Mexico.

Image courtesy of United States Environmental Protection Agency (USEPA)


Fig. 2.8. (B) Vector representation of the Coriolis effect.

Image courtesy of SiriusA from Wikipedia


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. 2.8 A). 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. 2.8 B). Scientists across disciplines use computers and probes to collect and analyze data (Fig. 2.8 C).


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.


  1. Physical > World Ocean > Map Distortion > Activity: How Much Water?
  2. Physical > World Ocean > Locating Points on a Globe > Weird Science: The Prime Meridian and Time Zones
  3. Physical > Density Effects > Density, Temperature, and Salinity > Compare-Contrast-Connect: Human Density
  4. Physical > Waves > Wave and Wave Properties > Compare-Contrast-Connect: Estimating Wave Height
  5. Physical > Waves > Wave and Wave Properties > Question Set: Waves and Wave Properties
  6. Physical > Waves > Wave and Wave Properties > Activity: Make Your Own Wave
  7. Physical > Waves > Wave and Wave Properties > Activity: Standing Waves
  8. Physical > Waves > Sea States > Question Set: Sea States
  9. Physical > Coastal Interactions > Wave-Coast Interactions > Activity: Beach Profile Mapping
  10. Physical > Ocean Floor > Change Over Time > Question Set: Change Over Time
  11. Physical > Navigation and Transportation > Wayfinding and Navigation > Traditional Ways of Knowing: Estimating Latitude
  12. Physical > Navigation and Transportation > Wayfinding and Navigation > Activity: Navigating with Nautical Charts
  13. Chemical > Matter > Properties of Matter > Practices of Science: False Positives and False Negatives
  14. Chemical > Chemistry and Seawater > Elemental Abundance > Question Set: Concentration
  15. Chemical > Chemistry and Seawater > Elemental Abundance > Practices of Science: “Parts per” notation
  16. Chemical > Chemistry and Seawater > Elemental Abundance > Activity: Parts Per Thousand
  17. Chemical > Chemistry and Seawater > Elemental Abundance > Weird Science: Compare Your Sense of Smell to a Shark’s Sense of Smell
  18. Biological > Mammals > Structure and Function > Activity: Measuring Whale Dimensions

Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawaii, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.