Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

Algebraic thinking is an essential component of the K-12 mathematics curriculum. Early algebra focuses on the overall numeric structure (Kaput, 2008; Kieran,2018; Kieran et al., 2016) which focuses on the noticing of arithmetic patterns leading to generalizations supported by justification, reasoning and justifications (Blanton, 2008; Blanton et…

This study examines whether teachers' content adaptations to middle school math curricula align with mathematical learning progressions and explores their motivations for adaptation. This study originates from a concern that as teachers make adaptations to their lessons, they may make adaptations that move students away from the intended learning…

Learning Trajectories have the potential to be used as a tool to advance equity by explicitly connecting to anti-deficit framing and asset-based instruction. This plenary paper highlights research on three use cases for learning trajectories (LT) with an intentionality around promoting equity: 1) the use of LT based Lesson Study with vertical…

Learning trajectory (LT) research in mathematics education has shaped both instructional materials and assessments. But, the body of LT research has also been critiqued for not adequately considering equity and addressing student diversity. This study begins to fill this gap by characterizing the reasoning of 23 multilingual students who…