We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…

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…

We propose a data driven method for decomposing population level learning curve models into mutually exclusive distinctive groups each consisting of similar learning trajectories. We validate this method on six knowledge components from the log data from an online tutoring system ASSISTment. Preliminary analysis reveals interpretable patterns of…

In adaptive learning systems, various models are employed to obtain the optimal learning schedule and review for a specific learner. Models of learning are used to estimate the learner's current recall probability by incorporating features or predictors proposed by psychological theory or empirically relevant to learners' performance. Logistic…

This report contains reliability and validity evidence for the North Carolina Kindergarten Entry Assessment system (KEA) using a statewide sample of kindergarten children. The KEA was designed as a formative, developmental, authentic, and criterion referenced classroom resource for teachers. As a formative assessment, the KEA focuses on the…

In February 2020, the Ministry of Education asked the New Zealand Council for Educational Research (NZCER) to examine the curriculum-levelling construct that sits at the heart of The New Zealand Curriculum (Ministry of Education, 2007). A key goal of the research was to investigate, whether-- and if so, how--the construct helps (or hinders)…