Introduction

Involve Students Actively in Their LearningIn an effective program students must be allowed to “do” mathematics.It is an essential fact thatStudents learn to write through the process of writing. They learn to dochildren learn mathematicsscience through the process of designing experiments and rediscoveringthe science ideas of the past. In art, students create their ownprimarily through “. . . doing,talking, reflecting, discussing,“great works”. Only in mathematics has the “passive bystander”observing, investigating,model of learning been accepted.listening, and reasoning”.Students need the opportunity to explore mathematics. Early mathematiciansfirst noticed that ten fingers made a useful tool for organizing(Copley, 2000, p. 29)our base ten number system. Students also need to discover thisrelationship between their fingers and the number system. Once they understandthat relationship, they can come to understand the more complex concept of unitizing(the idea that units of 10 can be represented by a single digit in the tens place andthat tens of tens can be represented also by a single digit in the hundreds place).In doing so, students make a giant conceptual leap similar to the leap mathematiciansmade in arriving at the same concept centuries ago (Fosnot & Dolk, 2001).Students can achieve the “doing” of mathematics by:• actively constructing conceptsFor example, students who experiment with joining and separating quantities canacquire a solid understanding of the effects of operations on numbers.26 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One