This paper is a practical how-to guide to help you start using active learning or to have greater success and more fun with it. We categorize active learning techniques as Think, Pair, Share, Composite, Group, Move, or Lead and discuss how to implement activities in each category, along with advice on creating engaging, effective, and equitable…

Manipulative-based instructional sequences--including both concrete and virtual manipulative instructional sequences--are evidence-based or research-based mathematical interventions for students with disabilities. However, as options for manipulative-based instructional sequences increase, educators need support in deciding the best approach. In…

We define and describe how subitizing activity develops and relates to early quantifiers in mathematics. Subitizing is the direct perceptual apprehension and identification of the numerosity of a small group of items. Although subitizing is too often a neglected quantifier in educational practice, it has been extensively studied as a critical…

This practical guide for teaching numeracy to children with a developmental disability is based on core concepts from the landmark Mathematics Recovery® text Teaching Number (aka 'the green book') that have been adapted for children with developmental disabilities. It sets out key principles of teaching and learning underpinning an evidence-based…

We are pleased to bring you this follow-up to Mairéad Hourigan and Aisling Leavy's article [EJ1289314] that was published in issue 1 this year. In this contribution, they demonstrate that embedding mathematics within a rich context and learning sequence assists with the consolidation of student understanding and makes more effective use of teacher…

Many teachers are using the Five Practices model to guide them in orchestrating whole-class mathematics discussions that focus on understanding: (1) anticipate an array of possible student-generated solution strategies to a mathematical task before implementing the lesson; (2) monitor students' work as they grapple with the task; (3) select a…

This article suggests an activity, called the epsilon-strip activity, as an instructional method for conceptualization of the rigorous definition of the limit of a sequence via visualization. The article also describes the learning objectives of each instructional step of the activity, and then provides detailed instructional methods to guide…

Circle Geometry, a senior mathematics topic, is often regarded as time-consuming and associated relational concepts difficult for students to grasp. Units of work that introduce students to circle geometry theorems are frequently described as a string of tedious constructions. This article explores teacher-designed dynamic geometry software…

To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic…

Using investigations in teaching mathematics has for many years become an established feature of most curricula around the world. Investigations can be a vehicle for enabling children to experience the genuine excitement that comes from mathematical discovery. The true spirit of inquiry and investigation lies in the mind-set that continually asks…

Suitable for secondary school students, the workbook provides flowcharting activities to help students understand the logical steps used in problem solving. Before applying the flowcharting procedures to mathematical problems, students are first introduced to familiar non-mathematical problems such as sharpening a pencil or eating peanuts. Section…

We are researching actions that teachers can take to improve mathematics learning for all students. Structural elements of the lessons being trialled include making aspects of pedagogy explicit to seek to overcome differences in familiarity with schooling processes, and sequencing tasks with the potential to engage students. This article reports…

Discusses the importance of revisiting problems to encourage children to amplify their mathematical thinking and for teachers to note developmental growth and patterns among learners. Describes experiences with a classic problem that was revisited several times. (ASK)

Good early mathematics is broader and deeper than early practice on "school skills." High-quality mathematics should be a joy--not a pressure. It can emerge from children's play, their curiosity, and their natural ability to think. This article describes the areas of mathematics that young children can learn, and encourages elementary teachers to…

A sequence of number pairs can be used to generate many interesting examples in teaching mathematics subjects at various levels. It is often used in elementary or middle school mathematics classes to illustrate the concept of "patterns." In this paper the authors present a few interesting ways of using this sequence to form examples for high…