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 book introduces the main concepts of pragmatics as they relate to the young English language learner classroom and research with young second language learners (YLLs). It considers the speech acts which are particularly relevant to YLLs and presents research findings on learners' development of speech act perception and production. It…

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…

Pearson's Learning Foundations describe the optimal conditions for learning and reflect the learner experience Pearson hopes their products will create. Pearson does this by incorporating the Learning Design Principles. Each of the Learning Design Principles goes into detail about a key principle, supporting product design and marketing by…

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,…

The international bestseller "How Do We Learn?" decodes years of cognitive science research into actionable strategies for K-12 teachers, curricula designers, and administrators. You'll discover how classic and emerging findings can transform pedagogy by pointing at practices that take advantage of the innate structures of the human…

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…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

Abstract concepts, such as gravity, may provide the perfect opportunity to bring phenomena into the classroom. As a knowledge generation strategy, summarizing can foster that opportunity. Using phenomena and summary writing together might help student learning since it requires making connections between their ideas and words to explain the…

This book offers a new perspective on the professional world of higher education. Using social practice theory, it presents a practice sensibility rooted in concepts which illuminate teaching and learning contexts. The book takes the reader through the social processes occurring within higher education institutions which shape contexts and…

Many K-16 educators agree that active learning is a key component for student success in life sciences. At the same time, some instructors are frustrated by inconsistent student participation in these activities and may revert to traditional teaching strategies. Horse caregivers face a similar frustration when they lead a horse to water and it…