Introduction

Instructional ApproachesThree instructional approaches – shared mathematics, guided mathematics, and independentmathematics – support students in learning mathematics. A balanced mathematicsprogram includes opportunities for all three approaches. Teachers need toconsider an appropriate balance of these three approaches when they are planningunits of instruction and daily lessons. Each of the approaches is described in the followingsections.Integral to the effectiveness of these three approaches is the establishmentof a rich and stimulating learning environment in which students:• solve mathematical problems;• reason mathematically by exploring mathematical ideas, makingconjectures, and justifying results;• reflect on and monitor their own thought processes;• select appropriate electronic tools, manipulatives, and computationalstrategies to perform mathematical tasks, to investigatemathematical ideas, and to solve problems;• make connections between mathematical concepts, and betweenmathematics and real-life situations;• represent mathematical ideas and relationships and model situations,using concrete materials, pictures,diagrams, graphs, tables, numbers, words,and symbols;“[Teachers] . . . need to be thearchitects of the classroomenvironment, ensuring thatchildren’s curiosity isprovoked and their pursuitof learning is well supported.They must investigate withthe children and monitortheir performances. And theymust set the example fororal communication and forthe investigation process.”(Greenes, 1999, p. 47)• communicate mathematical ideas andunderstanding orally, visually, and inwriting.Teachers who are familiar with instructionin reading in the primary and junior gradeswill be aware of the terms shared, guided,and independent. What the teacher does andwhat students do in the context of each ofthe instructional approaches represented by65