Introduction

The students’ activities during independent mathematics may include:• communicating, developing, and demonstrating their learning;• making personal decisions about which tools and strategies to use;• deciding on approaches for completing a task;• working on their own but with the opportunity to ask a peer or teacher forclarification.The teacher’s activities during independent mathematics may include:• interacting with students throughout the classroom;• monitoring students’ activity (academic work and/or behaviour) in order tointervene where appropriate;• interviewing or conferencing with individual students;• posing questions and prompts to help students who are stuck;• providing supports to English language learners that allow them to work independently(e.g., sentence prompts, word walls, personal word-study notebooks,math posters);• making modifications or providing extensions for individuals.The sample lesson in Appendix 4-2 involves mainly guided mathematics, but it alsoincludes an opportunity for independent work. This lesson component is an exampleof independent mathematics because it has the following characteristics:• Students work independently and are responsible for completing the investigationon their own.• The teacher poses questions to individual students.• The teacher makes modifications and provides extensions for individuals.For more examples of how to use the three instructional approaches described in thischapter, see the learning activities provided in the companion documents to thisguide that focus on the individual strands.72 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One