Monitoring one's learning activities is integral to self-regulated learning (SRL) and contributes significantly to successful learning outcomes. Judgments of learning (JOL), a crucial component of SRL, involve metacognitive assessments where individuals gauge their ability to recall learned material on future tests. While prior research…

The construct of static and emergent shape thinking (Moore & Thompson, 2015) characterizes differences in students' reasoning about graphs. In our previous work with middle school students, we found that this construct may also be useful in characterizing students' reasoning about other representations such as simulations and tables. In this…

Solving mathematical problems is cognitively complex, involving strategy formulation, solution development, and the application of learned concepts. However, gaps in students' knowledge or weakly grasped concepts can lead to errors. Teachers play a crucial role in predicting and addressing these difficulties, which directly influence learning…

Recent research seeks to develop more comprehensive learner models for adaptive learning software. For example, models of reading comprehension built using data from students' use of adaptive instructional software for mathematics have recently been developed. These models aim to deliver experiences that consider factors related to learning beyond…

Units coordination, defined by Steffe (1992) as the mental distribution of one composite unit (i.e., a unit of units) "over the elements of another composite unit" (p. 264) is a powerful tool for modeling students' mathematical thinking in the context of whole number and fractional reasoning. This paper proposes extending the idea of a…

This study addresses the need to better describe instructional strategies used by middle grades mathematics teachers. After coding 177 videos of grades 6-8 mathematics instruction for indications of effective instructional practices, we further analyzed 8 of the highly scored videos with specific attention to teachers' implementation of strategies…

Teacher expectancy (TE) refers to the inferences that teachers make about academic achievement, and future career choice of their students, it is a teacher level variable, and it mediates the teacher-student interaction. I hypothesize that the TE impacts the distribution of learning opportunities in 8th grade mathematics classes. So, I investigate…

Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

In response to the challenge of geometry's abstract and less engaging nature for students, this study explored the potential of connecting geometry to cultural elements, specifically geometric ornaments found in various cultures worldwide. Geometric ornaments, laden with cultural and spiritual significance, serve as a bridge between mathematics…

There are strong motivations to implement integrated STEAM activities that engage with key ideas in mathematics. In integrating mathematics with other STEM disciplines, however, epistemic tensions can emerge. Rather than attempting to suppress, avoid, or adjudicate these tensions, we propose a strategy of "epistemic rekeying," in which…

Units Coordination and Covariational Reasoning are powerful frameworks for modeling students' mathematics in arithmetic reasoning and construction of relationships between changing quantities, respectively. This case study of an advanced stage 2, 8th-grade algebra student, Daniel, investigated connections between his units coordination and…

This study investigated what 12 prospective mathematics teachers (PTs) in a middle school mathematics method course reported during a video-stimulated recall interview about their experiences when they were engaged in a doing math task that yielded an Opportunity for Productive Struggle (OPS). We investigated their reported feelings during the…

It is particularly important to identify and address issues of fairness and equity in educational contexts as academic performance can have large impacts on the types of opportunities that are made available to students. While it is always the hope that educators approach student assessment with these issues in mind, there are a number of factors…

The Edu-social Algorithm research project aims to construct a micro-pedagogical, experimental, digital research action to create a methodological model using the functions and algorithms found in social media used by Generation Alpha (specifically Instagram). The project is the manifestation of an explorative research path seeking to alter the…

Prior studies identified effective, but mainly non-digital, homework aids. This research involved 18 middle school students in a lo-fi prototyping study to integrate traditional homework support tools with intelligent tutoring systems (ITS), leveraging rich log data for personalized learning. Feature investigations in standardized diaries, goal…