“Teachers must have a profound understanding of fundamental mathematics.” – Liping Ma, 2010
To teach maths, you must first understand maths. To understand maths you have to be fully engaged and willing to put yourself in your pupils’ shoes and learn. Liping Ma states that this is one of the most important factors in terms of enhancing teachers’ knowledge of, and ability to better teach, primary mathematics.
However, having a concrete profound understanding of the fundamentals of mathematics is much more than being able to understand primary mathematics. You have to make sure you have a sound knowledge of the overall theoretical structure and basic attitudes of mathematics. By having this, you will then be able to use this as a foundation in order to teach your children effectively and inspire them to want to learn maths for themselves and not because they have to. It is very important to have a conceptual and procedural understanding – to know how and why we do something – that is deep, broad and thorough.
In order for yourself and your pupils to meet what Liping Ma states as a profound understanding of the fundamentals of mathematics you have to make sure that you can identify and understand the four principles that are essential in being able to meet this ultimate goal.
The first of these principles are (inter) connectedness. This refers to being able to see connections between concepts and procedures. Meaning that children can see why there is a need to have elements of maths that connect together in order to be able to use at other points of your mathematical education. This could be as simple as letting the children understand that in order to move on to understand and describe two dimensional shapes they first have to know the properties and characteristics of two dimensional shapes. This will then help to ensure learning is not fragmented, but viewed instead as a unified body of knowledge.
The second principle is multiple perspectives. This is having the ability to comprehend and also appreciate the different approaches you can have to one specific mathematical problem. This therefore encourages a more adaptable way of thinking and is therefore not restricting any child as it is not focused on one learning style. Teachers who have the ability to develop multiple perspectives for every topic within mathematics will have a better sound knowledge of the fundamentals of maths overall.
Thirdly, Liping Ma talks about basic concepts and having a full awareness of all the central ideas that surrounds primary mathematics. It is important that the basic ideas that recur throughout maths are constantly revisited until they are fully reinforced and have created a solid foundation in order to move forward onto future concepts. Without basic concepts, we would not be able to move forward and enhance our mathematical ability.
The last feature is longitudinal coherence. This is having a full awareness of the entire mathematical curriculum and how one basic idea or principle can be built upon another. What is taught today becomes the base for future knowledge, just as current mathematics teaching builds upon students’ previous knowledge, however fragmented that knowledge may be. This allows for there to be much more understanding and flexibility in terms of where learning is headed as lessons can be tailored with this in mind.
With this profound understanding of fundamental mathematics, we as teachers will be able to teach students more successfully. I fully agree with everything Liping Ma says and believe that I will definitely work to this model in order to teach mathematics to the best of my ability to my pupils in future.
Ma, L. (2010) ‘Knowing and teaching elementary mathematics’. London: Routledge.
