Introduction

Teachers use the shared-mathematics approach to promote the development of students’understanding of mathematical concepts and skills, and to encourage studentsto solve problems, reason mathematically, and communicate their thinking in thecontext of students’ interactions with their peers. Although play, exploration, andinvestigation in shared group settings do not guarantee mathematical development,they offer rich possibilities when teachers follow up by engaging students in reflectingon and representing the mathematical ideas that have emerged.The use of cooperative group structures is a highly effective means of facilitatingstudent learning of mathematics. In establishing cooperative group structures in theclassroom, the teacher does not assume that students will automatically know how tocooperate in a group. Hence, the teacher works with the students to establish groupnorms, or standards for behaviour in the group – for example, “Listen to others” or“Give reasons for your ideas” – and emphasizes both individual and group accountability.Problem solving remains the focus of cooperative activities. There are manyresources available to help teachers understand the key characteristics of cooperativelearning structures and establish effective guidelines for cooperative group work inthe classroom.FORMS OF SHARED MATHEMATICSThe focus in shared mathematics is on the sharing, discussing, and exploring of students’mathematical ideas, strategies, and solutions. Shared mathematics can occurbetween pairs of students, in small groups, or within the entire class.The students’ activities during shared mathematics may include:• working collaboratively with their peers to investigate a mathematical conceptand/or solve a mathematical problem;• working at centres in small groups;• engaging in decision making with their peers (e.g., deciding which tools to use toexplore a concept, deciding ways to record a solution to a problem);• demonstrating a mathematical idea or strategy to their peers;• learning a concept, skill, or strategy from other students;• explaining and justifying their thinking;• providing feedback on the ideas of other students.The teacher’s activities during shared mathematics may include:• observing students to ensure that pairs or small groups of students understand thetask at hand, and clarifying the activity if necessary;Instructional Approaches 67