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


Reasoning Strategies


Robert Kaplinsky demonstrates that math is about sense making with middle school students

Dor Abrahamson explains why it is important for students to have opportunities to reason mathematically

Douglas Fisher explains Deep Learning from the Visible Learning for Mathematics series

A Grade 3 classroom example in a classroom that promotes reasoning using the find 3 ways routine

Visible Learning for Mathematics video on why collaborations supports deep learning

Mike Flynn explains the importance of mathematical reasoning

Flexible grouping strategies explored and explained by Visible Learning For Mathematics


Reasoning Strategies

Deep Learning Through Reasoning