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…

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…

This study aims to design case-based learning with lesson study learning trajectory with the help of teaching aids to make students understand Prim's, Cruscal's, and Djiksra's Algorithms. The validation study was selected because it is a suitable method for this research. The research subjects were 41 Mathematics Education Study Program Students…

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…

In winter 2014, I came upon an opportunity to conduct a case study on a team of middle school math teachers who initiated a study group to examine how a set of learning progressions could help them with their planning, instruction, and assessment. Learning progressions are research-based hypotheses about how students develop more sophisticated…