Examples of such subfields are geometry, topology, algebra, differential equations, combinatorics, graph theory, etc. Sometimes mathematics is developed when a problem which arises outside of mathematics is "attacked" mathematically and leads to results of interest to one or more subfields within mathematics itself. Mathematics generates new mathematics in many ways, but in overly simple terms, I wish to call attention to two. Practice 4 sets forth the notion that students should be able to "model with mathematics." My purpose here is to try to clarify what this means, and more broadly to deal with related phrases involving "modeling," " mathematical model" and "mathematical modeling," which not everyone is familiar with. (NCTM refers to the National Council of Teachers of Mathematics which is the largest mathematics professional society concerned with K-12 mathematics education.) One section of the document deals with Mathematical Practices, and one of the mathematical practices, the fourth, uses language that is somewhat different from prior standards documents like the NCTM Standards. This document deals with a variety of content and pedagogical aspects of mathematics education for grades K-12. Recently, 45 states adopted what have come to be called the Common Core State Standards in Mathematics ( CCSS-M). Mathematical Modeling My purpose here is to try to clarify what it means to "model with mathematics," and more broadly to deal with related phrases.
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