The 3 Pillars of Teaching Maths
How do you feel about maths? Do you love it? Are you confident in your abilities? Do you enjoy teaching it?
My mission is to help schools create confident mathematicians through creative and engaging experiences and to change the culture of it being okay to be bad at maths.
Through my work with schools, I have developed 3 pillars that I believe are essential for effective teaching and for learners to love maths.
There are many tricks and formulas that we can be taught that help us to solve mathematical problems quickly and efficiently.
The problem comes when these tricks are taught without conceptual understanding.
Conceptual understanding means knowing more than isolated facts and methods, understanding mathematical ideas, and having the ability to transfer that knowledge into new situations and apply it to new contexts.
It is essential that learners have a good conceptual understanding of the maths that they are doing.
A learner without conceptual understanding, when faced with a calculation such as 5000 - 1999, might immediately write it out as a long subtraction. If a learner has conceptual understanding, they can see that 1999 is almost 2000 and it is far more efficient to do the calculation in your head.
Conceptual understanding is my 1st pillar for teaching maths effectively and it is also one of the 7 effective mathematics teaching practices identified by NCTM in their 2014 report Principles to actions: Ensuring mathematical success for all.
It is also essential that learners are not taught incorrect information in maths as this can greatly impact on their understanding and confidence.
One common example is 2D shapes. Schools up and down the country have drawers labelled 2D-shapes that actually contain 3D shapes.
To a confident mathematician this is obvious and may not be an important matter, but to someone who is struggling with maths, it can cause confusion and further undermine their confidence.
Through my work with schools, I have become more aware of the incorrect mathematical ideas that some teachers have such as using the word sum for all calculations. Part of the problem is that you don’t know it is incorrect until someone tells you. Just ask any secondary maths teacher about bar graphs!
This is my 2nd pillar of teaching maths effectively - good subject knowledge and using accurate terminology.
I believe that it is important to help learners see that maths is more than just numbers and calculations. Maths can be beautiful and creative and is interwoven throughout our lives.
When most people say that they are bad at maths, what they usually mean is that there was one or more areas of maths that they found difficult in school. When you see the maths around you, you begin to see the beauty in maths, what a critical part it plays in our lives and how much maths we all do every day without thinking about it.
What number would the next blue door be?
Llygaid Mathemateg is a strategy to open people’s eyes to the maths in the world around them and the free resources have been accessed thousands of times from all around the world.
Once you see the the maths in the world arouind us, a whole new world is opened up. Maths becomes a subject that can and should be explored. One of the reasons that many people can feel a failure in maths is because they believe that all maths has a correct answer and if they don’t know that answer instantly, it is because they aren’t any good at maths.
Reasoning is an essential part of developing confident mathematicians and it is so important to model that it is okay to be stuck. Providing real-life contexts and examples for learners and using a reasoning and problem-solving approach is my 3rd pillar of teaching maths effectively.
Teaching maths can be creative, exciting and rewarding and one of my proudest moments was when a reluctant participant in one of my Y6 maths workshops declared on their way back to class ‘You can make maths fun!’
What have you discovered on your own journey with mathematics? Did you hit any of these roadblocks? What do you believe are the essentials of effective maths teaching?