Tag Archives: problem-solving

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]].


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/

Getting it wrong

Filming for the MOOC Energy: Thermodynamics in Everyday Life

Last week’s post was stimulated by my realisation that I had made a mistake in a lecture [see ‘Amply sufficiency of solar energy?‘ on October 25th, 2017]. During the lecture, something triggered a doubt about a piece of information that I used in talking about the world as a thermodynamic system. It caused me to do some more research on the topic afterwards which led to the blog post.  The students know this already, because I sent an email to them as the post was published.  It was not an error that impacted on the fundamental understanding of the thermodynamic principles, which is fortunate because we are at a point in the course where students are struggling to understand and apply the principles to problems.  This is a normal process from my perspective but rather challenging and uncomfortable for many students.  They are developing creative problem-solving skills – becoming comfortable with the slow and uncertain process of creating representations and exploring the space of possible solutions [Martin & Schwartz, 2009 & 2014].  This takes extensive practice and most students want a quick fix: usually looking at a worked solution, which might induce the feeling that some thermodynamics has been understood but does nothing for problem-solving skills [see my post on ‘Meta-representational competence‘ on May 13th, 2015].

Engineers don’t like to be wrong [see my post on ‘Engineers are slow, error-prone‘ on April 29th, 2014].  The reliability of our solutions and designs is a critical ingredient in the social trust of engineering [Madhaven, 2016].  So, not getting it wrong is deeply embedded in the psyche of most engineers.  It is difficult to persuade most engineers to appear in front of a camera because we worry, not just about not getting it wrong, but about telling the whole truth.  The whole truth is often inconvenient for those that want to sensationalize issues for their own purposes, such as to sell news or gain votes, and this approach is anathema to many engineers.  The truth is also often complicated and nuanced, which can render an engineer’s explanation cognitively less attractive than a simple myth, or in other words less interesting and boring.  Unfortunately, people mainly pass on information that will cause an emotional response in the recipient, which is perhaps why engineering blogs are not as widely read as many others! [Lewandowsky et al 2012].


This week’s lecture was about energy flows, and heat transfer in particular; so, the following posts from the archive might be interest: ‘On the beach‘ on July 24th, 2013, ‘Noise transfer‘ on April 3rd, 2013, and ‘Stimulating students with caffeine‘ on December 17th, 2014


Martin L & Schwartz DL, Prospective adaptation in the use of external representations, Cognition and Instruction, 27(4):370-400, 2009.

Martin L & Schwartz DL, A pragmatic perspective on visual representation and creative thinking, Visual Studies, 29(1):80-93, 2014.

Madhaven G, Think like an engineer, London: One World Publications, 2016.

Lewandowsky S, Ecker UKH, Seifert CM, Schwarz N & Cook J, Misinformation and its correction: continued influence and successful debiasing, Psychological Science in the Public Interest, 13(3):106-131, 2012.

Red to blue

Some research has a very long incubation time.  Last month, we published a short paper that describes the initial results of research that started just after I arrived in Liverpool in 2011.  There are various reasons for our slow progress, including our caution about the validity of the original idea and the challenges of working across discipline boundaries.  However, we were induced to rush to publication by the realization that others were catching up with us [see blog post and conference paper].  Our title does not give much away: ‘Characterisation of metal fatigue by optical second harmonic generation‘.

Second harmonic generation or frequency doubling occurs when photons interact with a non-linear material and are combined to produce new photons with twice the energy, and hence, twice the frequency and half the wavelength of the original photons.  Photons are discrete packets of energy that, in our case, are supplied in pulses of 2 picoseconds from a laser operating at a wavelength of 800 nanometres (nm).  The photons strike the surface, are reflected, and then collected in a spectrograph to allow us to evaluate the wavelength of the reflected photons.  We look for ones at 400 nm, i.e. a shift from red to blue.

The key finding of our research is that the second harmonic generation from material in the plastic zone ahead of a propagating fatigue crack is different to virgin material that has experienced no plastic deformation.  This is significant because the shape and size of the crack tip plastic zone determines the rate and direction of crack propagation; so, information about the plastic zone can be used to predict the life of a component.  At first sight, this capability appears similar to thermoelastic stress analysis that I have described in Instructive Update on October 4th, 2017; however, the significant potential advantage of second harmonic generation is that the component does not have to be subject to a cyclic load during the measurement, which implies we could study behaviour during a load cycle as well as conduct forensic investigations.  We have some work to do to realise this potential including developing an instrument for routine measurements in an engineering laboratory, rather than an optics lab.

Last week, I promised weekly links to posts on relevant Thermodynamics topics for students following my undergraduate module; so here are three: ‘Emergent properties‘, ‘Problem-solving in Thermodynamics‘, and ‘Running away from tigers‘.


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.


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.