Introduction

When planning for instruction, teachers need to consider how to keep students workingin this zone. As students are introduced to new concepts, their thinking is stretched,and they experience a state of discomfort known as cognitive dissonance. This is thepoint at which they need the most support. Teachers give this support through askingquestions, guiding discussion and dialogue, and providing appropriate activities.The following chart provides a summary of the impact on the student of learningbelow, within, or above the zone of proximal development.Vygotsky’s Zone of Proximal Development (as related to mathematics)Below the Zone ofProximal Development• The student can complete thetask independently.• The student does not gain newknowledge, but the task maybuild confidence and fluencyand may help to consolidatepreviously learned concepts.• The student practises thelearning/skill/concept to deeplyentrench understanding.• The student’s learning isproficient and automatic.• Tasks may be too easy if thestudent remains in this zonelonger than is appropriate.In the Zone ofProximal Development• The student’s learning is supportedso that the studentcan move to a higher level ofunderstanding (i.e., teacherassistance is required to ensurethat problems at an appropriatelevel are presented, and thatmodelling, guidance, andquestioning occur duringthe task, as necessary).• The student’s learning is linkedto prior knowledge.• New learning occurs. Theexperience is challengingenough to trigger newunderstandings.• The student contributesmeaningful talk and actionduring the construction ofnew knowledge.• The learning tasks are”just right”.Beyond the Zone ofProximal Development• The student can completethe task only through relianceon procedures at the expenseof conceptual understanding(e.g., performs step-by-steplong division withoutunderstanding).• There is no new learning;understanding is limited;the student cannot generalizeand apply the knowledge tonew situations.• The student may disengagefrom the learning process.• Tasks are too difficult and leadto frustration.30 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One