Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We…

This study is a case study within a three-year-long design research study. The purposes of this study are twofold. The first purpose includes investigating whether there is a significant difference in seventh-grade students' proportional reasoning skills before and after a teaching experiment conducted in line with the perspectives of Hypothetical…

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…

Amid climate change, digital transformation, global warming, economic recessions, and rising geopolitical tensions, K-12 and higher education are undergoing a profound transformation. All these remarkable and unsettling changes, along with groundbreaking advancements over the past decade, will undoubtedly impact students' learning trajectories and…

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…

Writing is the highest form of thinking, as evidenced by neuroimaging that shows how more neural networks are activated simultaneously during writing than during any other cognitive activity. This book will help teachers understand how the brain learns to write by unveiling 15 stages of thinking that underpin the writing process, along with…

This research report describes a Learning Trajectory-based Curricular Design project that engaged teachers and coaches in the design and implementation process. As the project team, we focused on deepening teacher designers' understanding of the learning trajectory (LT) while situating student learning along a continuum to advance student…

Education systems around the world have moved to develop literacy progressions that describe a sequence of development in oral language (talking and listening), reading/viewing and writing. In Australia, the National Literacy Learning Progression (ACARA, 2021) is designed to support students' literacy development across the years of primary and…

Designers of critical mathematics instruction have documented difficulties in simultaneously fostering the development of critical consciousness while supporting students in developing understandings of new mathematics. However, confining justice-oriented tasks to applications of previously learned mathematics limits the degree to which these…

When the need of transforming and remixing music education is illuminated, fields of tensions in relation to the traditional master-apprentice model of teaching often appear. Binaries have been constructed and critiqued in research to describe tensions at various music educational levels. Some studies have also asked for a holistic,…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

This study explores a spatial reasoning learning trajectory of a student with difficulty in mathematics. Using a teaching experiment methodology across 15 instructional sessions, we observed how the student responded to instruction based on an established 2D shape composition learning trajectory (Sarama & Clements, 2009). A narrative…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

Instruction in many STEM domains heavily relies on visual representations, such as graphs, figures, and diagrams. However, students who lack representational competencies do not benefit from these visual representations. Therefore, students must learn not only content knowledge but also representational competencies. Further, as learning…

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…