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…

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…

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…

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…

An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade…

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.

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.

Assessing student learning traditionally involves determining whether students can solve a certain percentage of problems correctly, under the assumption that this achievement indicates they have the knowledge and understanding they need to progress to new topics. This article explores what teachers can learn from looking closely at student…

"Numeracy for All Learners" is a wide-ranging overview of how Math Recovery® theory, pedagogy, and tools can be applied meaningfully to special education to support learners with a wide range of educational needs. It builds on the first six books in the Math Recovery series and presents knowledge, resources, and examples for teachers…

The inspection of mistakes can play a powerful role in an individual's learning process (Boaler 2015). The purpose of this article is to support the reader in selecting mistakes that can be leveraged to benefit the learning of all students. Specifically, the authors focus on "which" and "why": "which" mistakes to…

"Project-Based Learning in the Math Classroom" explains how to keep inquiry at the heart of mathematics teaching and helps teachers build students' abilities to be true mathematicians. This book outlines basic teaching strategies, such as questioning and exploration of concepts. It also provides advanced strategies for teachers who are…

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

This book uncovers the important issues in language learning and teaching in the intelligent, digital era. "Social connectivity" is a contemporary style of learning and living. By engaging in the connectivity of physical and digital worlds, how essential parts of language learning and teaching can be achieved? How can the advanced…