When it comes to thinking about how people may start to understand new ideas and concepts the best theorist to look at is Skemp. Skemp (1989) believed that there are two types of understanding when it comes to mathematics: Instrumental and Relational. Through this module and professional reading I have attempted to try and understand the two approaches.

Instrumental understanding is when you are able to use the mathematical rule or concept but do not really have the knowledge behind the concept/rule to apply it in other situations, the method is more a “habit” understanding whereas relational understanding is when you are able to use, apply and manipulate the rule or concept and you know why you use the particular method. Relational understanding allows people to have a more reflective attitude to learning and allows for more exploration to occur.

From this, I can see that relational understanding is a deeper, more complex understanding of instrumental understanding.  Although it is important to highlight that a person who lacks confidence in mathematics can benefit from having an instrumental understanding as it allows for immediate satisfaction and can boost self esteem, however it is equally important that as teachers you try to promote a more relational understanding as this will allow for a more concrete understanding of mathematics.