As previously discussed identifying and understanding boundary objects helps a group communicate and collaborate but what does an individual experience when redefining their understanding of a boundary object? Educational literature discusses the idea of threshold concepts, an understanding of which may help an individual to handle new and alien concepts. An understanding of threshold concepts can help because individuals can start to understand what is happening in their heads when they come across a new or complex concept. This understanding makes the adoption of the new concept easier.

Savin-Baden (2016) defines threshold concepts as being "concepts which transcend disciplines and subject boundaries but which are challenging and complex to understand, but once understood, the student experiences a transformed way of understanding, without which the they would struggle".

More generally Meyer and Land, (2003, 2006) describe a threshold concept as being like a portal which opens new and previously inaccessible ways of thinking about something. It is a transformed way of understanding without which the learner cannot move forward. They give the following example: the objective is to pour two identical cups of tea and cool one down as quickly as possible, milk is added to the first cup right away and a few minutes later milk is added to the second cup. Most people intuitively think that the first cup will cool quicker but by introducing an idea from thermodynamics that heat loss is proportional to temperature difference then it becomes apparent that the second cup cools quicker (its temperature was higher in the first few moments so it must have lost more heat). The threshold concept here is that heat loss is greater when the temperature difference is greater.

Other examples include:

• Gravity: the idea that all bodies attract each other because of their mass

• The equals sign in equations: any operation can be performed on one side of an equation as long as the same operation is performed on the other side

• An atom: solid matter is made up of tiny invisible "balls"

• Opportunity cost: in economics doing anything has a cost because it means that you are not doing something else

• Evolution

• Randomness: if a tossed coin turns up heads 100 times in a row the likelihood of it turning up heads on the next toss is still 50:50

• Limit: in mathematics an infinite series (e.g. 1+1/2+1/4+1/8....) can still have a finite limit (i.e. 2)

Moving from a superficial understanding to a deeper understanding might well be uncomfortable and this discomfort may interfere with understanding the threshold concept.

A threshold concept can transform an individual's philosophical and conceptual standpoint; when an individual grasps a new understanding of something it becomes part of of them and alters how they see, feel and think (Savin-Baden, 2016). It is usually irreversible and unlikely to be forgotten becoming part of who the individual is. It is integrative allowing an individual to see previously hidden connections between things. A threshold concept may well be bounded as it will have frontiers which border with thresholds into other areas. It will usually involve "troublesome knowledge". (Carmichael, 2012; Cousin, 2006; Meyer and Land, 2006; Savin-Baden, 2016).

Perkins (1999) defines 'troublesome knowledge' as knowledge that appears counter-intuitive either because it comes from another culture or it appears to be incoherent. He typifies 'troublesome knowledge' as being ritual, inert, conceptually difficult, or alien. These are not necessarily troublesome but may be if ritual knowledge is not understood by the observer because they lack context e.g. the routine that we might perform to execute a particular task. Inert knowledge is knowledge that is stored somewhere in an individual's brain but not actively used, this can be troublesome if another person is not aware of this knowledge. Conceptually difficult knowledge may be troublesome because we need to think deeply to understand it. Alien knowledge might be the value systems of a foreign culture which may not be understood. Meyer and Land (2006) add to this list tacit knowledge, which is mainly personal and implicit.

Practice

• Can you think of any other threshold concepts that you personally might have encountered in your life?

• If you have ever observed someone experiencing a threshold concept how would you describe their reaction?