Concept maps make students' knowledge visible. Creating a mind map gives students an opportunity to organize their knowledge and allows instructors to visualize and assess it. When students create mind maps at multiple time points, instructors can compare the maps and use the themes, patterns, and gaps that emerge to reflect on their teaching and…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

This paper explores the efficacy of ChatGPT, a generative artificial intelligence in educational contexts, particularly concerning its potential to assist students in overcoming academic challenges while highlighting its limitations. ChatGPT is suitable for solving general problems. When a student comes across academic challenges, ChatGPT may…

This article explores situations for improving the collaborative commitments of a group of learner-teachers undertaking action research projects about their own learning processes in a teacher education setting. The encounters are recounted based on the 16-week experience of educators (the first two authors) while facilitating, guiding, and…

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…

Previous studies of affordance have not explored in detail how a special type of affordance -- institutional affordance -- worked in multilingualism. By drawing empirical voices of students, this study investigates how institutional affordance supplied by a collegiate multilingual education policy was perceived and utilised by students. A thematic…

An online authentic learning environment (OnALE) is proposed in this study to facilitate students' learning of inferential statistics in a real-life context. The efficacy of the OnALE, in comparison to the conventional approach relative to the students' performance, was explored. Respondents from the experimental group were purposively selected to…

Previous studies have designed educational methods to cultivate digital citizenship behavior and support the construction of knowledge. However, these methods have not well incorporated personalized feedback mechanisms for enhancing digital citizenship knowledge. Therefore, this study proposed an algorithm that combines concept-effect propagation,…

Playful learning has garnered supporters and research evidence, and also can be seen as nebulous and, therefore, reliant on practitioners' intuitions in early education settings. In this paper, we offer an explicit theoretical account, grounded in developmental psychology of how play might support the acquisition of broad skills and dispositions…

Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Video games have emerged as a medium for learning by creating engaging environments, encouraging creative and deep thinking, and exposing learners to complex problems. Unfortunately, even though there are increasing examples of video games for many basic science and engineering concepts, similar efforts for higher level engineering concepts such…

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,…

Across nearly 20 years working as a secondary mathematics teacher, the author noticed two overarching goals that most teachers of mathematics consider to be important in their practice: (1) students knowing and understanding the content; and (2) students engaging with the learning and enjoying their time in class. However, in practice, attaining…

Visual literacy is essential for engineers. Technological professions have important visual characterization, both in the transmission of information and problem-solving. This means that future engineers must be proficient at communicating, thinking, and learning visually. However, engineering curricula takes partially the need to have visually…

While looking to revamp his department's Year 7 enquiry on the Tudors, Jack Mills turned to historiographical debates regarding the 'mid-Tudor crisis' to inform his curricular decision making. In doing so, Mills noted that the debate hinged on interpretations of substantive concepts such as 'crisis'. He therefore also drew on previous…