Introduction

these terms are not the same in reading and in mathematics. However, in bothmathematics and reading, each instructional approach involves providing a particularbalance of learning opportunities in which students work collaborativelywith peers, receive guidance from teachers, and work autonomously.Because there is no “right”, or formulaic, way of teaching mathematics, teachersshould plan for a mix of these approaches when creating their unit or lesson plansand should take into account, in particular, the type of mathematics being taught.Some types of lessons or tasks lend themselves to shared more than to guidedmathematics, or to shared more than to independent mathematics.Teachers should be flexible and use the approach that best applies to“Teachers should consider anthe situation.appropriate balance ofMoreover, although the three approaches are listed in a specific shared, guided, andorder (shared, guided, and independent mathematics), that order is independent mathematics,not meant to suggest a sequence that must be rigidly adhered to in a which together create anmathematics classroom. For example, in the development of a concept,the teacher might first use a shared-mathematics approach to students have theenvironment where allallow students to explore the problem and discuss possible solutions,and then a guided-mathematics approach to help build a com-and skills.”opportunity to learn conceptsmon understanding of the new concept; the class might then engage (Expert Panel on Literacy andin more shared mathematics; and, finally, students might solidifyNumeracy Instruction for StudentsWith Special Educationtheir understanding of the concept with an independent mathematicalactivity, such as using a manipulative to demonstrate theirNeeds, 2005, p. 80)understanding.The information in this section of the guide has been adapted from the discussionof shared, guided, and independent mathematics that appears on pages 33–37 ofthe report of the Expert Panel on Early Math in Ontario (2003). See also page 7 ofthe report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario (2004).Shared MathematicsShared mathematics is an instructional approach in which students participatecollaboratively in learning activities. With guidance from the teacher,students learn from one another as they share, discuss, and explore mathematicalconcepts together. Shared mathematics can occur between pairs orsmall groups of students working together on a mathematical investigation orproblem, or it can involve large-group discussions in which students sharetheir understanding of mathematical ideas, strategies, and solutions.Shared mathematics:• provides opportunitiesfor students to learnfrom one another;• encourages discussionand sharing of ideas;• involves students inworking collaborativelyto solve a problemor investigate amathematical idea.66 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One