In this paper we discuss the types of knowledge used by six middle school students as they engaged with a debugging task designed to integrate ideas from computer science, mathematics and science. Our findings show that the computational thinking practice of debugging is a rich source of opportunities to integrate these different disciplines. The…

Analyses highlighting the epistemic dimension of students' participation in science have dominated science education literature for the past several years. While most of this literature has focused on how students learn together, the relational nature of these knowledge-building interactions has been under-examined. In response, this paper…

Concerns about the disconnect between what goes on in teacher preparation programs and school classrooms have led to a greater emphasis on opportunities for preservice teachers to engage in the practice of teaching during their teacher education programs. Pedagogies of enactment have been shown to provide opportunities for preservice teachers to…

Mastery goal structures, which communicate value for developing deeper understanding, are an important classroom support for student motivation and engagement, especially in the context of science learning aligned with the Next Generation Science Standards. Prior research has identified key dimensions of goal structures, but a more nuanced…

Research about modeling emphasizes the importance of heterogeneity in science learning. At the same time, a growing body of scholarship seeks curricular pathways for epistemic and representational convergence. In response to this tension, we propose two constructs: heterogeneity-seeking curricula and commitments. Heterogeneity-seeking curricula…

While issues of (in)justice in K12 STEM learning have garnered increasing attention, limited research has attended to learning as "social-spatial transformation." We draw upon a justice-oriented framework of equitably consequential learning to call attention to how learning and engagement in K12 STEM is rooted in the history and…

In this article, we examine eighth graders' incorrect responses to a specific task on a national standardized assessment of mathematics. The task asked students to write the formula for the perimeter of a given figure as a function of a variable. We focus on incorrect responses to better understand students' difficulties with the algebraic…

Collaborative design (co-design) involving practitioners and researchers is emerging as a productive context for addressing theoretical as well as practical issues of teaching and learning. Co-design affords learning opportunities for "all" participants, although the focus has typically been on teachers. In this study, the Interconnected…

The present study is motivated by a significant body of research documenting teachers' perennial difficulties with a critical swath of topics related to multiplication. In response, we track how Nina, a future middle grades mathematics teacher, made progress constructing explanations across topics by reasoning with measurement-based definitions of…

Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…

Scientific observation is central to classroom inquiry and children's investigations and explanations in science. Young children can struggle with observation, and research has shown that professional scientists who engage in complex observation tasks, observe detailed patterns when they have well-developed disciplinary knowledge. However, fewer…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

This article presents a formative intervention study, called "Learning Lab" that facilitated the collective design of a culturally responsive behavioral support system at an urban middle school in the United States. Learning Lab united parents, teachers, support staff, education leaders, and researchers, specifically those who have been…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

The ability to efficiently compare number symbols, such as digits, is associated with mathematics competence across the lifespan. Performance on symbolic number comparison tasks differ across age groups; young students who are developing fluency with digits improve on symbolic number comparison, and performance is better in adults than children.…