Promoting Mathematical Conflict: Eight Tasks That Produce Mathematical Discourse(now with a bonus 9th task!)Geoff Krall | New Tech Math CoachEmergentmath.wordpress.com

The Problem Based Learning process

Guided Instruction vs. Conflict and Discussion (Malcolm Swan)

• How does the speed of the ball vary?

• Sketch a speed v. time graph

(Swan, 2006 continued)

Expository Approach• Short Introduction• Students work in

groups at their own pace.

• Teacher intervenes when they get answers wrong

• Short final discussion

Conflict and Discussion Approach• Think about the problem

alone.• Discuss the problem with your

group.• Write about the problem.• Sketch the graph.• Interpret the graph back into

words.• Long discussion, error

guessing.

Results

• Conflict and discussion approach yielded better post assessment scores.

• Students felt • the task was more interesting, • that they worked harder, • that they learned more.

• Students need to swim in conflict and discuss mathematics in order to understand and retain mathematics.

TASKS THAT PROMOTE CONFLICT AND DISCUSSION

Look!Listen!Be present, but be aware of your surroundings!

Odd one out

Forcing or Creating the DefinitionWhich of the following triangles is more

equilateral:  the 10-10-11 triangle, or the 10-11-11 triangle?

Classifying or Sorting Things

Evaluating “Truthiness”

Dominoes

Uber-Perplexing Entry Events or #anyqs

Matching

Evaluating Student Work

Mathematical Conflict-Producing Tasks

• Matching• Odd One Out• Forcing/Creating the Definition• “Uber-Perplexing” Entry Events• Dominoes• Analyzing Student Work• Truthiness – Always, Sometimes, Never• Classifying• Ordering

Two ways to a “conflict-centric” approach

TasksTasks

END OF CLASS DEBRIEF

Which task was your favorite?

Which task could you incorporate tomorrow into a PBL Unit?

Templates for Conflict & Discussion Producing Tasks: emergentmath.wordpress.com

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