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…

The Association of Mathematics Teacher Educators recommends that well-prepared beginning mathematics teachers apply their understanding of mathematics, curriculum, pedagogy, student learners, and social constructions to facilitate mathematics learning for all students. Using the context of a secondary methods course, where prospective mathematics…

"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

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…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

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…

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…

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…

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…

Incorporating immersive technologies in education has become increasingly popular due to their ability to facilitate active learning and engage students in the acquisition of concepts and skills. One form of immersive technology includes educational games that incorporate movement interaction, allowing children to engage with in-game elements by…

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,…

The study material on circle areas is contextually oriented and aids students in comprehending their surrounding environment. Higher-order thinking skills are imperative for the success of circular learning, as they help students grasp concepts holistically and solve concept problems. "What-if" questions can enhance students'…

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…