Reasoning is fundamental to knowing and doing of mathematics. Some would call it systematic thinking. Reasoning is the deep learning that occurs when–through the solving of rich, highly cognitive tasks, rigorous discussion and reflection–students make connections among conceptual ideas.

Students develop the ability to reason through opportunities that encourage them to follow a line of inquiry, conjecture relationships, develop arguments, justify or prove, and make generalizations using mathematical language.

Reasoning enables students to make use of all their other mathematical skills and so reasoning is the ‘glue’ which helps numeracy make sense.


Following a line of inquiry

Open questions

Using mathematical language

Developing an argument, justification or proof

Problems with Intentional learning

Applying procedural skills in context

Rich tasks

Making connections


Professional Resources

A Teacher’s Guide to Reasoning and Sense Making

The NCTM outlines how reasoning should be in every class, everyday.

Reasoning: Identifying Opportunities

Francis Fennell (2017) offers 5 highly effective and practical formative assessment tools for math and shows how teachers can make them a part of their regular planning and instruction.

Nrich on Reasoning

A selection of articles about the importance of reasoning and example reasoning tasks.

More Talk in Math Class Please

Talking about math helps elementary students deepen their understanding. Use these three tips to get the conversation started.

Reasoning Strategies

Reasoning Strategies

Deep Learning Through Reasoning

Would You Rather?

What’s the Same? What’s Different?