Category Archives: education

Meta-knowledge: knowledge about knowledge

As engineers, we like to draw simple diagrams of the systems that we are attempting to analyse because most of us are pictorial problem-solvers and recording the key elements of a problem in a sketch helps us to identify the important issues and select an appropriate solution procedure [see ‘Meta-representational competence’ on May 13th, 2015].  Of course, these simple representations can be misleading if we omit parameters or features that dominate the behaviour of the system; so, there is considerable skill in idealising a system so that the analysis is tractable, i.e. can be solved.  Students find it especially difficult to acquire these skills [see ‘Learning problem-solving skills‘ on October 24th, 2018] and many appear to avoid drawing a meaningful sketch even when examinations marks are allocated to it [see ‘Depressed by exams‘ on January 31st, 2018].  Of course, in thermodynamics it is complicated by the entropy of the system being reduced when we omit parameters in order to idealise the system; because with fewer parameters to describe the system there are fewer microstates in which the system can exist and, hence according to Boltzmann, the entropy will be lower [see ‘Entropy on the brain‘ on November 29th, 2017].  Perhaps this is the inverse of realising that we understand less as we know more.  In other words, as our knowledge grows it reveals to us that there is more to know and understand than we can ever hope to comprehend [see ‘Expanding universe‘ on February 7th, 2018]. Is that the second law of thermodynamics at work again, creating more disorder to counter the small amount of order achieved in your brain?

Image: Sketch made during an example class

Knowledge explosions

Photo credit: Tom

When the next cohort of undergraduate students were born, Wikipedia had only just been founded [January 2001] and Google had been in existence for just over a decade [since 1998].  In their lifetime, the number of articles on Wikipedia has grown to nearly 6 million in the English language, which is equivalent to 2,500 print volumes of the Encyclopedia Britannica, and counting all language editions there are 48 million articles.  When Leonardo Da Vinci was born in 1452, Johan Gutenberg had just published his first Bible using moveable type.  By the time Leonardo Da Vinci was 20 years old, about 15 million books had been printed which was more than all of the scribes in Europe had produced in the previous 1500 years.  Are these comparable explosions in the availability of knowledge?  The proportion of the global population that is literate has changed dramatically from about 2%, when Leonardo was alive, to over 80% today which probably makes the arrival of the internet, Wikipedia and other online knowledge bases much more significant than the invention of the printing press.

Today what matters is not what you know but what you can do with the knowledge because access to the internet via your smart phone has made memorisation redundant.

Pluralistic ignorance

This semester I am teaching an introductory course in Thermodynamics to undergraduate students using a blended learning approach [see ‘Blended learning environments‘ on November 14th, 2018].  The blend includes formal lectures, example classes, homework assignments, assessed coursework questions and an on-line course, which I delivered as a MOOC a couple of years ago [see ‘Engaging learners on-line‘ on May 25th, 2016].  It is not unusual in a large class, nearly two hundred students this year, that no one asks questions during the lecture; although, at the end of each lecture and example class, a small group of students with questions always forms.  The on-line course has extensive opportunities for asking questions and discussing issues with the instructor and fellow learners.  These opportunities  were used heavily when the course was offered as a MOOC  with 6600 comments posted or 1 every 7.7 minutes!  However, this year the undergraduates have not made any on-line comments and it was a similar situation last year.  Is this a case of pluralistic ignorance?  The term was coined by psychologists Daniel Katz and Floyd Henry Allport in 1931 to describe students who pretend to understand everything explained in class and don’t ask any questions because they believe everyone else in the class has understood everything and they don’t want to damage their reputation with their peers.  Perhaps we have all done it and been very grateful when someone has asked the question that we wanted to ask but did not dare.  Would be it ethical to pretend to be a student and post questions on-line that I know from the MOOC they are likely to want to ask?

Sources:

Patterson EA, Using everyday engineering examples to engage learners on a massive open online course, IJ Mechanical Engineering Education, in press.

Katz D & Allport FH, Students’ attitude, Syracuse, NY: Craftsmann, 1931.

Origgi G, Reputation: what it is and why it matters, Princeton, NJ: Princeton University Press, 2018.

Image: Author speaking at National Tsing Hua University, Taiwan

Time at the heart of our problems

This week I started teaching thermodynamics to first year undergraduate students for the first time in twelve months.  I have had a break for a year because my course, which is only delivered once per year, was moved from first to second semester.  Although I have continued to teach postgraduate courses, it’s been like a sabbatical enforced by timetable changes.  Sadly, it’s over and I am back in the large lecture theatre in front of a couple of hundred of students – that makes it sound as if I don’t enjoy it which is not true but it does increase the intensity of the job because all of the other aspects of the role continue unabated.  So, for me time appears to accelerate as I attempt to jam more activities into a week.

Time lies at the heart of much of thermodynamics although we tend not to deal with it explicitly; however, it is implicit in our use of changes in the state of a system to understand it.  Quote Anaximander, the pre-Socratic philosopher & pupil of Thales of Miletus: ‘We understand the world by studying change, not by studying things’.  Time also lies at the centre of the tangle of problems found at the intersection of the theories of gravity, quantum mechanics and thermodynamics.  As Carlo Rovelli has remarked we are still in the dark about this tangle of problems; so, I will touch on it in my thermodynamics course but just to show students the limits of our knowledge and perhaps inspire one or two of them to think about tackling them in postgraduate studies.

Meanwhile, I plan tackle my challenges with time by slowing it down once a week with a walk in the Clwydian Hills where the landscape appears unchanging so that time stands still allowing me to relax.

Sources:

Rovelli C, Seven brief lessons on physics, London, Penguin Books. 2016.

Wohllerben P, The hidden life of trees, London, William Collins, 2017.