Ok, it’s a challenging title and a strange thumb-nail diagram but stick with it! Last week I was giving revision lectures for my first year class in thermodynamics which is why my post was about problem-solving. I mentioned the difficulty in persuading students to represent problems pictorially. It is called meta-representational competence. It is a knowledge of when visual representations are likely to be appropriate, how to create them and how to interprete them, according to Disessa and Sherin (2000).
It is hard because you need to become comfortable with the slow and uncertain process of creating representations and exploring the space of possibilities, to quote Martin and Schwartz (2014). This is achieved through practice. Oh, and now we are back to students testing their skills against problems set by their tutors. It is what engineers learn to do as part of their formation. They might not realise it but their meta-representation competence is one of the attributes that make them so attractive to employers.
Now, what about that thumb-nail. Well, it is my picture drawn as part of the staff answer to the Everyday Engineering Example below, which was given to our new engineering students in their first week at university and subsequently discussed with their personal tutor. Can you solve it with my sketch? Answers via the comments…
A two-slice toaster is switched on by depressing a slider which causes the slices of bread to fall downwards into the toaster between heating elements and also extends a pair of springs at each end of the toaster. When the toast is ready a pair of triggers releases both springs simultaneously, which in turn cause the toast to ‘pop’ up. If the toast is to just not jump completely out of the toaster when it is ready and in the ‘off’ position rests with two-thirds in the toaster, calculate the force that must be applied to the slider when switching on the toaster. Neglect the weight of the mechanism and assume that there are no losses.
Disessa AA & Sherin BL, Meta-representation: an introduction, J. Mathematical Behaviour, 19(4):385-398, 2000
Martin L & Schwartz DL, A pragmatic perspective on visual representation and creative thinking, Visual Studies, 29(1):80-93, 2014.
Martin L & Schwartz DL, Prospective adaptation in the use of external representations, Cognition and Instruction, 27(4):370-400, 2009.