Tag Archives: meta-representation

Learning problem-solving skills

Inukshuk: meaning ‘in the likeness of a human’ in the Inuit language. A traditional symbol meaning ‘someone was here’ or ‘you are on the right path’.

One definition of engineering given in the Oxford English Dictionary is ‘the action of working artfully to bring something about’.  This action usually requires creative problem-solving which is a common skill possessed by all engineers regardless of their field of specialisation.  In many universities, students acquire this skill though solving example problems set by their instructors and supported by example classes and, or tutorials.

In my lectures, I solve example problems in class using a pen and paper combined with a visualiser and then give the students a set of problems to solve themselves.  The answers but not the solutions are provided; so that students know when they have arrived at the correct answer but not how to get there.  Students find this difficult and complain because I am putting the emphasis on their learning of problem-solving skills which requires considerable effort by them.  There are no short-cuts – it’s a process of deep-learning [see ‘Deep long-term learning’ on April 18th, 2018].

Research shows that students tend to jump into algebraic manipulation of equations whereas experts experiment to find the best approach to solving a problem.  The transition from student to skilled problem-solver requires students to become comfortable with the slow and uncertain process of creating representations of the problem and exploring the possible approaches to the solution [Martin & Schwartz, 2014].  And, it takes extensive practice to develop these problem-solving skills [Martin & Schwartz, 2009].  For instance, it is challenging to persuade students to sketch a representation of the problem that they are trying to solve [see ‘Meta-representational competence’ on May 13th, 2015].  Working in small groups with a tutor or a peer-mentor is an effective way of supporting students in acquiring these skills.  However, it is important to ensure that the students are engaged in the problem-solving so that the tutor acts as consultant or a guide who is not directly involved in solving the problem but can give students confidence that they are on the right path.

[Footnote: a visualiser is the modern equivalent of an OverHead Projector (OHP) which instead of projecting optically uses a digital camera and projector.  It’s probably deserves to be on the Mindset List since it is one of those differences between a professor’s experience as a student and our students’ experience [see ‘Engineering idiom’ on September 12th, 2018]].

References:

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.

 

CALE #9 [Creating A Learning Environment: a series of posts based on a workshop given periodically by Pat Campbell and Eann Patterson in the USA supported by NSF and the UK supported by HEA] – although this post is based on an introduction to tutorials given to new students and staff at the University of Liverpool in 2015 & 2016.

Photo: ILANAAQ_Whistler by NordicLondon (CC BY-NC 2.0) https://www.flickr.com/photos/25408600@N00/189300958/

Meta-representation competence

toasterdrawingOk, 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…

Dynamics Example:

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.

Sources:

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.