It would appear that maths is permeating my entire life at the moment. This is undoubtedly because of the looming assignment I am due to write and the several books that I am dipping into.  However, I have found myself thinking quite a lot recently about the ways in which maths is seen and used in everyday situations and I am finding that I am enjoying these little eureka moments. I have to admit that this is most likely due to the inputs I have had recently for the mathematics elective at university. It has made me realise that maths is, in fact, embedded everywhere around us and really I had not thought deeply about the way in which maths plays quite a crucial part of everyday life.

Recently, during one of those eureka moments, I realised what was really meant by instrumental understanding and relational understanding.

My definitions are;

Instrumental understanding is the fundamental and basic understanding of principles and concepts of number and number applications like addition , subtraction and the ability to apply these concepts.

Relational understanding means an understanding of how concepts are related and connected to each other and interlinked for example the relationship between adding and subtracting or multiplication and division.

Ma(2010) discusses this and describes the need for teachers to have understanding of  key principles. The first being connectedness. Ma states that a teachers knowledge of mathematics must be fully connected in so much that the teacher must be able to see how maths concepts relate to each other in order to provide relevant next steps for the children. Thus building upon children’s existing knowledge. The next principle is Multiple perspectives which really means having the ability to approach maths in various ways. For example:

Take a very basic sum like  8  +  ? = 11

There are various ways this can be solved  we can start from 8 and count on (adding) up to 11 or we can subtract 8 from 11 either way the answer is the same and we have demonstrated multiple perspectives at a basic level also showing relational understanding.With this profund understanding of fundamental maths we are far better placed to then teach students successfully because we have the confidence and underpinning knowledge that enables us to do so.

Numbers are truly everywhere. books , newspapers, technology and even in our starbucks coffee…Ratio of coffee shots to milk = perfect latte !  🙂