What does it mean to have mathematical authority? How does it differ from pedagogical authority? We drew upon Goffman's (1981) ideas of author and animator to exemplify modes of mathematical authority that extend beyond the authorship of ideas. Through a series of excerpts from lessons in middle-grades mathematics classrooms, this paper emphasizes…

Mathematics growth trajectory plays a significant role to predict future outcomes and careers. We examined the existence of different growth trajectories in mathematics during the late elementary-school period (from Grades 4 to 6) and the relationship between the trajectory group classification and later mathematics achievement (Grade 8). Then,…

Background: Mindfulness practices enhance executive function skills and academic achievement, spurring interest in integrating mindfulness interventions into education. Embedding mindfulness practice into a digital math game may provide a low-cost, scalable way to induce mindfulness and boost game-based learning, yet this approach remains…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

This paper presents results of a score interpretation study for a computer adaptive mathematics assessment. The study purpose was to test the efficacy of item developers' alignment of items to Range Achievement-Level Descriptors (RALDs; Egan et al.) against the empirical achievement-level alignment of items to investigate the use of RALDs as the…

Generative AI, particularly Language Models (LMs), has the potential to transform real-world domains with societal impact, particularly where access to experts is limited. For example, in education, training novice educators with expert guidance is important for effectiveness but expensive, creating significant barriers to improving education…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…