| NSES Content Standard A
Science as Inquiry: Understanding about scientific inquiry Grades 9-12, page 175 Mathematics is essential in scientific inquiry. Mathematical tools and
models guide and improve the posing of questions, gathering data, constructing
explanations and communicating results.
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Benchmark 2B The Nature of Mathematics:
Mathematics, Science, and Technology
Grades 9-12, page 33
Developments in mathematics often stimulate innovations in science
and technology.
Benchmark 2C The Nature of Mathematics:
Mathematical Inquiry
Grades 9-12, page 38
Much of the work of mathematicians involves a modeling cycle, which
consists of three steps: (1) using abstractions to represent things or
ideas, (2) manipulating the abstractions according to some logical rules,
and (3) checking how well the results match the original things or ideas.
If the match is not considered good enough, a new round of abstraction
and manipulation may begin. The actual thinking need not go through these
processes in logical order but may shift from one to another in any order.
Benchmark 4A The Physical Setting: The
Universe
Grades 9-12, page 65
Mathematical models and computer simulations are used in studying evidence
from many sources in order to form a scientific account of the universe.
Benchmark 11B Common Themes: Models
Grades 9-12, page 270
The basic idea of mathematical modeling is to find a mathematical relationship
that behaves in the same ways as the objects or processes under investigation.
A mathematical model may give insight about how something really works
or may fit observations very well without any intuitive meaning.
See also Chapter 9 The Mathematical World.