In 2008–2009 Dick Stanley and Phil Daro, with the help of Vinci Daro and Carmen Petrick, convened a group of mathematicians and educators to write essays clarifying the mathematical underpinnings of secondary school mathematics in the United States. At the urging of Dick Stanley I am publishing these essays here.

There are many resources available to both pre-service and in-service teachers to help them increase their content knowledge in a way directly related to how they teach. Still, there are areas of mathematical content, relevant to the core of the mathematics curriculum, that somehow fail to receive systematic treatment in any of these resources. For many teachers, this means that there are always nagging questions that go unanswered. These teachers experience mathematics as a subject that somehow never fully makes sense.

The purpose of the Noyce-Dana project was to address this issue by building a community of scholars and practitioners focused on clarifying the mathematical underpinnings of middle and high school mathematics. It was hoped is that the work of this community would be a valuable resource for all those concerned with the teaching and learning of mathematics. The project was not continued after the first year, but I hope that publishing the essays that came out of that year will serve to continue the original vision of the project.

The members of the group were Dan Chazan, Scott Farrand, Sol Friedberg, Emiliano Gomez, Roger Howe, Eric Hsu, Jim Madden, myself, Mike Oehrtman, and Harris Shultz. The essays are linked below

## Algebra

Extraneous and Lost Roots (Chazan-Gomez-Farrand)

Letters & Types of Representations in Algebra (Oehrtman-Shultz)

What Is a Variable (Epp)

## Arithmetic

Minus Times Minus (Gomez-Hsu)

Rule of Signs (Howe-Friedberg)

## Functions and Equations

AXplusB (Howe)

Equations & Functions (Friedberg)

Equations & Functions-3 Views (Stanley)

Equations from Functions (Stanley)

Expressions-Functions-Equations (McCallum)

Functions (Howe)

Graphs-Equations-Functions (Stanley)

## Inverses

## Order of Operations

Order of Operations (Hsu-Madden)

## Proportionality

Proportion (Madden)

Proportion-Euclid (Madden)

Proportionality (Madden-Oehrtman)

Two Meanings of Proportional (Stanley)

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