One of the most vital mathematical structures that a child develops early on is that of a number sequence. In math education, research aims often at effectiveness of curriculum, but is then left in need of an underlying language to interpret the skills and structures that the students either already harbored, or are improving upon. In our work, we analyzed student learning sessions to develop an algorithm of iterative unit coordination, and then used it to code session transcripts. We will discuss influential authors in the field of unit coordination at the developmental level, as well as the activity of coding for units coordination that took place as a result of our research.

Using factorial design and group structures to reduce the amount of testing needed for experimental designs.

Horn's Conjecture is a statement about the existence of matrices with certain eigenvalues. This statement has troubled mathematicians since it was conjectured by Horn in 1962. Mathematicians were able to prove this statement using puzzles called "hives" and "tableaux" which come up in many areas of mathematics. In this talk, we will explore these puzzles and dive into their fun and beauty. We will discuss open problems about these puzzles that still intrigue many.