On Composing Meaning

In the journal article, Constructing Meaning: Standards for Mathematical Practice, the writers discuss the differences between modeling with mathematics versus modeling mathematics.

Modeling mathematics "is using concrete materials or other visual representations to clarify or give meaning to mathematics" and modeling with mathematics is using mathematics to describe and/or explain a real-world context.

The teachers that were involved in the summer institute that the research was based on did certain standards for mathematical practice and reflected on their day's experience.

This distinction makes sense, because one term discusses using manipulatives to explain a mathematical problem and the other is to use math to describe a situation.

The teachers worked through a problem and then reflected on what they did. It is important to provide teachers with this distinctions because it provides insight in the language of teaching.