This paper focuses on the structure and substance of the Core Content Framework (CCF), a controversial document which stipulates content that providers of teacher education in England must incorporate in their programmes. We identify both a concept of instrumental trainability and a lack of coherence in the CCF which suggests it is unsuitable as a…

In this article, the authors explore how the 3C Model can be used to integrate other curriculum areas with mathematics, namely digital technologies. To illustrate the model, they provide a practical example of a teaching sequence. T he 3C Model is designed to create opportunities for applying reasoning and problem-solving skills and learning…

Presenting a pictorial representation followed by a textual representation supports learners to build a coherent mental model. Providing an elaboration prompt stimulates learners to process the learning content semantically. Hence, combining both approaches might result in synergetic effects as both foster mental model development, which could be…

Music curriculum programmes are designed by English Music teachers in schools as the primary means of musical engagement for young people aged 11-14. Such Music curricula are often structured in learning topics. However, Music teacher rationales for the sequencing of the topics they have chosen to include in their curriculum is an under-developed…

Transition metrics, which quantify the propensity for one event to follow another, are often utilized to study sequential patterns of behaviors, emotions, actions, and other states. However, little is known about the conditions in which application of transition metrics is appropriate. We report on two experiments in which we simulated sequences…

In this paper I explain how I usually introduce the Schrödinger equation during the quantum mechanics course. My preferred method is the chronological one. Since the Schrödinger equation belongs to a special case of wave equations I start the course with introducing the wave equation. The Schrödinger equation is derived with the help of the two…

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…