Teaching Reasoning in Mathematics • Module 2
Increasing Cognitive Demand
Essential question: How can I increase the thinking without simply making the mathematics harder?
This module focuses on the core design principle: vary the thinking, not just the numbers.
Experience
Harder numbers are not the same as deeper thinking.
Consider the same calculation. The learning demand changes when students must represent, explain, compare, diagnose or decide.
Notice
Cognitive demand is about the thinking required.
A multi-step task can still be low demand if each step is signposted. A small-number task can be high demand if students must decide, justify or generalise.
Not just larger numbers
Increasing numerical difficulty may increase calculation load without increasing reasoning.
Not just more steps
More instructions can sometimes remove thinking rather than create it.
Change the demand
Ask students to represent, compare, justify, reverse, find an error, generalise or transfer.
Understand
One idea, many forms.
Start with one mathematical kernel and systematically change what students need to think about.
Apply
Transform one routine classroom question.
The goal is not to make the task look more complicated. The goal is to create a better opportunity for mathematical thinking.
Reflect
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Module review