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
Using mathematical language
Developing an argument, justification or proof
Problems with Intentional learning
Applying procedural skills in context
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.
Deep Learning Through Reasoning
Would You Rather?
What’s the Same? What’s Different?