Learning trajectories (LTs) can inform teaching by contributing a variety of pedagogical and content-related insights and strategies. They support sequencing topic introduction and development. Because ideas evolve gradually and often rely on a careful introduction of new representations, operations, cases of numbers, structures, and definitions,…

In the context of a professional learning research project we investigated the nature of support offered to classroom teachers and school mathematics leaders to facilitate teachers' implementation of sequences of challenging tasks. End of year questionnaire data were collected from 70 Foundation to Year 2 teachers and ten numeracy leaders who…

Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives -- base-ten blocks -- to support children's place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in…

Both sequencing content and fading instructional support are scaffolding techniques designed to make it easier for learners to process information. While sequencing content separates problems into manageable parts before problem-solving, fading of instruction gradually reduces instructional support before problem-solving. Although cognitive load…

The purpose of the study was to examine the effects of an instructional sequence involving simple tact, category tact, and match-to-sample instructions on the emergence of metaphorical extensions about emotions for children with autism spectrum disorder. Three Chinese children (1 girl, 2 boys, 7-8 years old) with autism spectrum disorder…

This learning activity outlines the transitioning of a Hotel and Lodging Management undergraduate course from face-to-face to asynchronous format. It describes how topics were converted into sequential learning modules that included short pre-recorded lectures (from the instructor and guest lecturers), discussion questions, activity tasks, quiz…

In course design, topic outline organization encompasses the structuring and sequencing of topics to be delivered in a learning environment. Recent studies in topic outline optimization revolve around massive open online courses (MOOCs) due to their abundance but not much has been studied on the traditional courses. This study investigates the…

This article provides an example of the implementation of school-wide professional learning as part of an Australian Research Council grant and the Catholic Schools Parramatta Diocese (CSPD) called Exploring Mathematical Sequences of Connected, Cumulative and Challenging Tasks (EMC[superscript 3] ) (Sullivan et al., 2021). By using sequences of…

It is easy to dismiss the work of "teaching students to apply formula" as a low-order priority and thus trivialises the professional knowledge associated with this practice. Our encounter with an experienced teacher--through the examination of her practices and elaborations--challenges this simplistic assumption. There are layers of…

Finding the optimal topic sequence of online courses requires experts with lots of knowledge about taught topics. Having a good order is necessary for a good learning experience. By using educational recommender systems across different platforms we have the problem that the connection to an ontology sometimes does not exist. Thus, the state of…

Purpose: Estimating the sequential associations between educators' and children's talk during language learning interactions requires careful consideration of factors that may impact measurement stability and resultant inferences. This research note will describe a preliminary study that used generalizability theory to understand the contribution…

Understanding scientific phenomena requires learners to construct mental models of causal systems. Simulation-based discovery learning offers learners the opportunity to construct mental models and test them against the behavior of a simulation. The purpose of this study was to investigate sequential patterns of learner actions and utterances…

This study tested how different implementations of explaining and drawing activities affect learning from a multimedia science lesson. After studying a multimedia slideshow about the human respiratory system, college students (n = 145) were assigned randomly to one of four learning activity conditions: write explanations before drawing pictures…

In learning diagnostic assessments, the attribute hierarchy specifies a sequential network of interrelated attribute mastery processes, which makes a test blueprint consistent with the cognitive theory. One of the most important functions of attribute hierarchy is to guide or limit the developmental direction of students and then form a…

To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with…