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…

Learning progressions (LPs) are considered to have great potential to improve pedagogical practices. However, even with LPs, teachers may still be unaware of the barriers that keep students from progressing; many are struggling with essential pedagogical strategies to support students' progression. This study thus proposed an educative LP (ELP), a…

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…

Although studies in higher education have paid attention to the complexities of learning disciplinary language and discourse, little attention has been given to learning professional discourse in a second language (L2). Recent studies on language socialization have addressed this gap by focusing on L2 students' emerging communicative competence in…