Current environmental problems are the primary focus for environmental science students and researchers. Sustainable environmental solutions require interdisciplinary thought processes, which pose difficulty to both students and the public. Computational thinking is an emerging term emphasized by progressive science curricula. Computational…

Despite substantial research exploring multiplicative thinking and students' difficulty in the domain, the topic of multi-digit multiplication is under-researched. In this paper, I share a learning trajectory for multi-digit multiplication that combined social and cognitive perspectives of learning. Using Design Research methods and involving 45…

Noticing is an essential skill for all teachers of mathematics. Mathematics teacher educators have utilized a variety of tools to practice and develop preservice teachers' (PSTs') ability to notice, which we extend to include photographs and learning trajectories. This article explores PSTs' noticing skills by analyzing work samples from a methods…

Accurate assessment and effective feedback are crucial for cultivating learners' abilities of collaborative problem-solving and critical thinking in online inquiry-based discussions. Based on quantitative content analysis (QCA), there has been a methodological evolvement from descriptive statistics to sequential mining and to network analysis for…

This dissertation reports on three studies about students' conceptions and learning of the idea of instantaneous rate of change. The first study investigated 25 students' conceptions of the idea of instantaneous rate of change. The second study proposes a hypothetical learning trajectory, based on the literature and results from the first study,…

Emergent graphical shape thinking (EGST) entails conceiving a graph as being dynamically generated via the trace of a moving point constrained by two changing quantities. As such, Paoletti et al. (2023) argue that meanings for quantities within a situation and meanings for graphical representations must be connected, or bridged, to engage in EGST.…

Computational thinking (CT) is a set of cognitive skills that every child should acquire. K-12 classrooms are expected to provide students opportunities (tasks) to think computationally. We introduce a CT competency assessment for middle school students. The assessment design process started by establishing a cognitive model of CT domain mastery,…

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about arguments concerning sums of evens and odds. Data are drawn from classroom lessons…

Our complex world requires multivariate reasoning to make sense of reality. Within this paper, we offer a sequence of activities designed to develop multivariate reasoning by explicitly connecting data and visualization. The activities were designed based on a hypothetical learning trajectory we conjectured for students with limited experience…

In 2020, two teachers and seven students participated in an action research project that sought to improve the teaching and learning of fractions in a New Zealand primary school. This research revealed that the collaborative creation of hypothetical learning trajectories was beneficial to the teachers' practice, content knowledge, and confidence,…

There is little empirical research related to how elementary students develop computational thinking (CT) and how they apply CT in problem-solving. To address this gap in knowledge, this study made use of learning trajectories (LTs; hypothesized learning goals, progressions, and activities) in CT concept areas such as sequence, repetition,…

This paper provides a case study account of a preservice secondary mathematics teacher's thinking while engaging in slope tasks using dynagraphs. The data included audio recordings and screen captures of a small group of preservice teachers engaging with these tasks, with our analysis focusing on the case of Robin. Despite familiarity using slope…

Background and Context: Since the surge of grounded cognition (GC) theories in cognitive psychology, many studies have focused on demonstrating the importance of embodiment and sensorimotor activities on students' conceptual development. In computing education, however, there is not yet a conceptual framework for developing age-appropriate.…

Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name…

Background: Data on children's ability to answer assessment questions correctly paints an incomplete portrait of what they know and can do mathematically; yet, it remains a common basis for program evaluation. Indeed, pre-post-assessment correctness is necessary but insufficient evidence for making inferences about learning and program…