Introduction

Teachers need a sound understanding of the key mathematical concepts in everystrand of the curriculum, as well as an understanding of what students are to learnin connection with each concept at every grade level and how that learning connectswith previous learning (in the grade before) and future learning (in the next grade).Liping Ma’s research (1999) indicates that teachers of elementary mathematics musthave a profound understanding of fundamental mathematics. Such knowledge includesan understanding of the “conceptual structure and basic attitudes of mathematicsinherent in the elementary curriculum” (Ma, 1999, p. xxiv) as well as a knowledgeof how to teach the concepts to students.Focusing on the big ideas provides teachers with a global view of the conceptsrepresented in the strand. The big ideas also act as a lens for:• making instructional decisions (e.g., deciding on an emphasis for a lesson ora set of lessons);• identifying prior learning;• looking at students’ thinking and understanding in relation to the mathematicalconcepts addressed in the curriculum (e.g., making note of the strategies astudent uses to count a set or to organize all possible combinations to solve aproblem);• collecting observations and making anecdotal records;• providing feedback to students;• determining next steps;• communicating concepts and providing feedback on students’ achievementto parents (e.g., in report card comments).Diversity and Effective InstructionA VISION FOR EQUITY IN ONTARIO CLASSROOMSSchool classrooms represent the world in miniature; they mirror our larger society.The diversity that exists in our classrooms has helped to shape our vision for educationin Ontario today. All children, regardless of their background and/or ability,deserve opportunities to learn and to grow, both cognitively and socially. The challengeis to reach more children more effectively. To do this, we need to create avision for learning that makes every child feel included.To develop the right learning conditions for each individual child, we must allow fora variety of cultural experiences and multiple perspectives, so that all children feelvalued in the classroom.34 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One