Illustrative Mathematics organized a special session at the Joint Mathematics Meeting on January 7, 2016 in Seattle, WA called Essential Mathematical Structures and Practices in K-12 Mathematics. Here is a description of the session:

The mathematics curriculum in the US has been shaped by myriad forces over the years, including the competition for market share among publishing companies, economic realities of school districts’ purchasing power, the ease with which teachers can deliver the material, traditional expectations of what mathematics classroom work should look like, and so on. Surprisingly absent from these forces is the nature of the discipline of mathematics itself. The focus of this special session was on identifying and describing the essential mathematical structures of the K-12 curriculum, as well as the key mathematical practices in the work of mathematicians that should be mirrored in the work of students in K-12 classrooms.

• Up first was Susan Addington, who spoke about Essential Mathematical and Cognitive Structures in K-5 Mathematics: Where They Come From and Where They Go. (Link to slides.)
• Next, Jim Madden spoke about An Historical Perspective of Proportion, Ratio and Measurement. (Link to slides.)
• Then Kristin Umland asked, What Do We Mean by Proportionality?  (Link to slides.)
• Maggie Cummings and Hugo Rossi spoke about The Emergence of Essentiality from Educator-Mathematician interactions in context. (Link to slides.)
• Then Cody Patterson spoke about Functions, Rates, and Quantitative Reasoning: From Proportionality to Exponential Growth. (Link to slides.)
• Bill McCallum wrapped up with a talk entitled, From the ark of history to the arc of reasoning. (Link to slides.)