ABSTRACT
This chapter explores an important aspect of the way people in the United Kingdom and in some other countries think about how mathematics should be taught and learnt. It calls this ‘ability thinking’ or more properly ‘fixed-ability thinking’. Many people believe that each person has a particular level of mathematical ability that is relatively stable or fixed. Ability thinking also supposes that mathematical ability is a single entity that is generally disconnected from other human capacities. However, mathematics is much more diverse than the content that is included on tests of mathematical ability. Ability thinking entails and is supported by a narrow view of what mathematics is that can exclude these other aspects of thinking mathematically including problem-solving, communicating about mathematics and collaborating with others. Further, ability thinking can get in the way of understanding and appreciating these differences as it can lead to ‘seeing and teaching the label’ rather than the student.
