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…

The Essential Practices for College and Career Ready Instruction framework identifies research-based instructional strategies for use in early college high school programs, as well as other educational settings where educators seek to build a rigorous and engaging culture of learning grounded in student ownership of the learning process. The early…

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…

"Effective Use of Collective Peer Teaching in Teacher Education" investigates the learning benefits of letting students assume leadership roles in the classroom, emphasizing both theoretical analysis and firsthand empirical research conducted with pre-service teachers. Building on Vygotsky's (1987) sociocultural theory of human learning…

This brief and infographic highlights the importance of explicit vocabulary instruction as part of intensifying reading instruction, with a focus on what to teach and how to teach it. Grounded in the science of reading, this resource offers practical guidance to help educators deliver instruction that is clear, accessible, and effective for all…

What are some of the most common myths about teaching and learning? Renowned educator Thomas R. Rosebrough debunks ten popular beliefs and offers principles that will have a bigger impact in the classroom. The principles center on teaching for learners, not only to meet their academic needs but to transform their lives. The ten myths explore…

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…

"Critical Practice in Higher Education" provides a scholarly and practical entry point for academics into key areas of higher education practice. Each book in the series explores an individual topic in depth, providing an overview in relation to current thinking and practice, informed by recent research. The series will be of interest to…

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…

This comprehensive handbook delves into timely issues in STEAM (science, technology, engineering, arts/architecture, and mathematics) curriculum and praxis. Cutting-edge research will help STEAM educators and researchers recognize and appreciate students' understanding of STEAM concepts, as well as capture contemporary educational, psychological,…

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…

As a genre, science fiction is uniquely suited for highlighting and modeling the basic tenets of critical pedagogy, that branch of educational philosophy and theory devoted equally to 1) exposing the hidden power structures embedded in educational practice and 2) articulating equitable and sustainable alternatives. The science fiction novum --…

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…

United States math achievement has long lagged behind that of other nations and has been relatively stagnant for 8th-graders on national assessments over the past 2 decades. The need to understand how teachers can better support mathematics learning is particularly acute in the wake of pandemic-era learning disruptions, which impacted already low…

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…