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Mathematical reasoning

Posted on April 27th, 2021 in STEM gems

The beauty of an inquiry-based approach is that you don’t have to do much! The best advice we can give to educators looking to increase the development of mathematical reasoning skills in their school, service or setting is to encourage your students to ask the question ‘Why?’, creating an environment that welcomes questioning, discussion, creative problem-solving and sharing of ideas. In a fun, hands-on, playful way, look for those everyday STEM opportunities with the children. Encourage meta-cognition among yourself and the children and their peer group.

If you are new to inquiry-based learning, all our workshops will assist you in developing inquiry-based learning techniques and help you spot these everyday STEM opportunities. Our Mathematics workshop explores shape and space, focusing on hands-on, fun mathematical opportunities and talks about mathematical reasoning in depth. Our Air workshop looks into questioning techniques and meta-cognition. We love helping you get started and hope you enjoy your STEM journey!

What is mathematical reasoning?

Mathematical reasoning is essentially the answer to ‘Why maths?’ Why do we need to learn mathematics past the ability to calculate basic change and balance our budgets? What use is maths?

Essentially, mathematical reasoning is the answer. Maths helps us makes sense of certain aspects of our day-to-day lives. Mathematic reasoning is the process of organising thoughts, gathering data, solving problems and making decisions. It is planning, organisation and communication. This is essential to our students and needs to be encouraged by us as their educators and teachers.

Communication is the key: Talk about mathematics techniques, talk about the ‘Why?’ This is what inquiry-based learning encourages, which is why it is the perfect learning environment for teaching mathematical reasoning.

How can we encourage mathematical reasoning?


Instead of telling children that the shape on the left is a square, you could ask why it is a square. This is a great example of mathematical reasoning. By the age of five, most children can spot a square; but can they say why it is a square? Can you?


Perhaps we can talk about length of the sides. All four sides of a square are the same length. But then, so are the sides of the shape on the left.


What about the corners then? We could check the corners with the corner of a piece of paper and make sure they are right-angled.


Is the shape on the left still a square?

Ask the children to explain what makes a square. The ability to argue what attributes make a square is far more important than being able to name all the shapes from flashcards without knowing the reasons why.

Why not a quadrilateral?

Please excuse my Latin but I’m just going to mention that quad means ‘four’ and lateral means side. Therefore, a quadrilateral is a shape that has four sides.


Most children know what a triangle is. Show them a picture of the shape on the left.
No arguments. It’s a triangle.


But what about the shape on the left?


And what about this shape?

How many?

These are both four-sided shapes, i.e. quadrilaterals. It always made me wonder why we often refer to triangles with their general, rather than their specific names, like right-angled, scalene or equilateral triangle, while we rarely use the term ‘quadrilateral’, but rather their specific names like square, rectangle or rhombus. There’s that ‘why?’ question again…

I have three blocks. If I add another two, how many are there?

3 + 2

So, if I have two blocks and I add another three, how many do I have?

2 + 3

So ‘three add two’ is the same as ‘two add three’ – why?

It’s not easy to put an answer to this question into words. Try it. This sort of question is crucial for the development of mathematical reasoning and even thinking about the question or attempting an answer increases a child’s ability for mathematical reasoning beyond the basic question (‘How many blocks do I have?’) Just by asking a slightly different question, you’ve given the child the opportunity to take a step towards understanding commutative and associative laws of mathematics.

About the author:
HAYLEY BATES, National Certifications Coordinator

Hayley Bates

Hayley has an insatiable thirst for learning – about everything! Her sheer joy of discovery and passion for professional development makes her the perfect person to run the Little Scientist’s House Certification program.

Never happier than seeing what happens to balloons in the freezer or exploring the projects submitted by services for certification, her enthusiasm is complemented by her background in science and maths making her the ideal coordinator for our Little Scientists Houses.

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