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…

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression -- the cognitive core of a learning trajectory -- for length measurement in the early years. A complete learning trajectory includes…

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…