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…

Children's informal and formal learning experiences with geometric shapes currently result in misconceptions that persist into adulthood. Here, we combine research from mathematics education as well as cognitive science pertaining to concepts, categories, and learning strategies to propose a more optimal progression that is better specified and…

This study was conducted to investigate the effects of learning trajectories-based coding (LTs) and LTs-based program on preschoolers' length, area, volume, and angle measurement skills. A quasi-experimental research design was utilized with a quantitative approach. The study's participants were 47 children between the ages of 55-71 months who…

This study evaluated recent advances in learning progressions for the concept of matter (LPCM) and explored trends by reviewing the literature on the topic published between 2005 and 2021. A total of 21 studies were reviewed. Fifteen studies were devoted to developing LPCM of varying spans and grain sizes. There were six follow-up studies based on…

In this theoretical paper, I use an empirically based example to illustrate particular design features of the Learning Through Activity (LTA) design framework and examine the impact of particular design principles. The LTA design framework is based on our elaboration of Piaget's construct of reflective abstraction. The example discussed here,…

Field supervisors are central to clinical teaching, but little is known about how their feedback informs preservice teachers' (PSTs) development. This sequential mixed methods study examines over 3,000 supervisor observation evaluations. We qualitatively code supervisor written feedback, which indicates two broad pedagogical categories and nine…

A design experiment where students in Grade 5 (11-12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space…

The aim of this article is to present a pedagogical approach for history education. This approach is called Meaningful History and it outlines the process by which upper-level secondary history students can cultivate historical consciousness. Based on the notion of learning as meaning making and historical consciousness as a disposition to engage…

Although earlier studies have documented the importance of spatial orientation skills in early childhood development, teachers often need more experience and guidance in teaching these skills. This research investigates how two kindergarten teachers, guided by two teacher education researchers, utilized Learning Trajectories (LT) in a Professional…

Recent research suggests the benefits of supporting a progressive understanding of concepts of inference prior to the teaching of procedures and formal calculations through the study of informal statistical inference (ISI). To contribute to the growing knowledge about the early learning and teaching of statistics, particularly regarding the…

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

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.…

In this study, we explore the use of analogies with classical physics in introductory quantum physics (QP) teaching. This work is part of a larger project in which a learning sequence covering three introductory QP topics was designed, tested, and evaluated in collaboration with high school teachers and physics education researchers. Based on the…

Critical thinking is essential in academia and the workforce. Although writing can be used as a pedagogical tool for fostering deeper subject matter understanding, increased retention, and critical thinking, relatively few science courses are writing based. This writing-based introductory science course provided an opportunity for students to…

Field supervisors are central to clinical teaching, but little is known about how their feedback informs preservice teachers (PSTs) development. This sequential mixed methods study examines over 3,000 supervisor observation evaluations. We qualitatively code supervisor written feedback, which indicates 2 broad pedagogical categories and 9 separate…