Introduction

• explaining their own mathematical thinking in response to ideas presented by theteacher;• asking questions of the teacher and other students.The teacher’s activities during guided mathematics may include:• helping students connect a new concept with prior knowledge;• demonstrating an approach to investigating a concept;• modelling mathematics language, problem solving, and thinking (e.g., using thethink-aloud strategy);• using strategies that help English language learners understand mathematical concepts(e.g., using simple language structures; teaching mathematical vocabularyexplicitly; supporting oral explanations by using manipulatives, pictures, diagrams,and gestures);• modelling a problem or a mathematical idea with appropriate materials and tools;• demonstrating the appropriate use of tools (e.g., manipulatives, calculators,computers);• posing questions that are thought provoking and that capture the essence of themathematics;• referring to visual cues in the classroom (e.g., displays, a math word wall, a strategywall).Appendices 4-1 and 4-2 contain sample guided mathematics lessons for Grade 1 andGrade 5. These lessons are examples of guided mathematics because they have the followingcharacteristics:• The teacher plans questions ahead of time that will help students develop key concepts(e.g., the concept of 5 in the Grade 1 lesson, the concept of perimeter in theGrade 5 lesson);• The teacher activates students’ prior knowledge to prepare them for the learningtask (e.g., by counting fingers and counters in the Grade 1 lesson, by reviewing themeaning of perimeter in the Grade 5 lesson);• The teacher provides specific materials for the activity (e.g., counters and fiveframes in the Grade 1 lesson, Cuisenaire rods and centimetre grid paper in theGrade 5 lesson).• The teacher gives explicit instruction on how to use the materials70 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One