Tag Archives: MOOC

Depressed by exams

I am not feeling very creative this week, because I am in middle of marking examination scripts; so, this post is going to be short.  I have 20 days to grade at least 1100 questions and award a maximum of 28,400 marks – that’s a lot of decisions for my neurons to handle without being asked to find new ways to network and generate original thoughts for this blog [see my post on ‘Digital hive mind‘ on November 30th, 2016].

It is a depressing task discovering how little I have managed to teach students about thermodynamics, or maybe I should say, how little they have learned.  However, I suspect these feelings are a consequence of the asymmetry of my brain, which has many more sites capable of attributing blame and only one for assigning praise [see my post entitled ‘Happenstance, not engineering‘ on November 9th, 2016].  So, I tend to focus on the performance of the students at the lower end of the spectrum rather than the stars who spot the elegant solutions to the exam problems.

Sources:

Ngo L, Kelly M, Coutlee CG, Carter RM , Sinnott-Armstrong W & Huettel SA, Two distinct moral mechanisms for ascribing and denying intentionality, Scientific Reports, 5:17390, 2015.

Bruek H, Human brains are wired to blame rather than to praise, Fortune, December 4th 2015.

How many repeats do we need?

This is a question that both my undergraduate students and a group of taught post-graduates have struggled with this month.  In thermodynamics, my undergraduate students were estimating absolute zero in degrees Celsius using a simple manometer and a digital thermometer (this is an experiment from my MOOC: Energy – Thermodynamics in Everyday Life).  They needed to know how many times to repeat the experiment in order to determine whether their result was significantly different to the theoretical value: -273 degrees Celsius [see my post entitled ‘Arbitrary zero‘ on February 13th, 2013 and ‘Beyond  zero‘ the following week]. Meanwhile, the post-graduate students were measuring the strain distribution in a metal plate with a central hole that was loaded in tension. They needed to know how many times to repeat the experiment to obtain meaningful results that would allow a decision to be made about the validity of their computer simulation of the experiment [see my post entitled ‘Getting smarter‘ on June 21st, 2017].

The simple answer is six repeats are needed if you want 98% confidence in the conclusion and you are happy to accept that the margin of error and the standard deviation of your sample are equal.  The latter implies that error bars of the mean plus and minus one standard deviation are also 98% confidence limits, which is often convenient.  Not surprisingly, only a few undergraduate students figured that out and repeated their experiment six times; and the post-graduates pooled their data to give them a large enough sample size.

The justification for this answer lies in an equation that relates the number in a sample, n to the margin of error, MOE, the standard deviation of the sample, σ, and the shape of the normal distribution described by the z-score or z-statistic, z*: The margin of error, MOE, is the maximum expected difference between the true value of a parameter and the sample estimate of the parameter which is usually the mean of the sample.  While the standard deviation, σ,  describes the difference between the data values in the sample and the mean value of the sample, μ.  If we don’t know one of these quantities then we can simplify the equation by assuming that they are equal; and then n ≥ (z*)².

The z-statistic is the number of standard deviations from the mean that a data value lies, i.e, the distance from the mean in a Normal distribution, as shown in the graphic [for more on the Normal distribution, see my post entitled ‘Uncertainty about Bayesian methods‘ on June 7th, 2017].  We can specify its value so that the interval defined by its positive and negative value contains 98% of the distribution.  The values of z for 90%, 95%, 98% and 99% are shown in the table in the graphic with corresponding values of (z*)², which are equivalent to minimum values of the sample size, n (the number of repeats).

Confidence limits are defined as: but when n = , this simplifies to μ ± σ.  So, with a sample size of six (6 = n   for 98% confidence) we can state with 98% confidence that there is no significant difference between our mean estimate and the theoretical value of absolute zero when that difference is less than the standard deviation of our six estimates.

BTW –  the apparatus for the thermodynamics experiments costs less than £10.  The instruction sheet is available here – it is not quite an Everyday Engineering Example but the experiment is designed to be performed in your kitchen rather than a laboratory.

Listening with your eyes shut

I am in the London Underground onboard a train on my way to a conference on ‘New Approaches to Higher Education’ organised by the Institution of Engineering and Technology and the Engineering Professors’ Council.  The lady opposite has her eyes closed but she is not asleep because she opens them periodically as we come into stations to check whether it’s her stop.  I wonder if she is trying to reproduce John Hull’s experience of the depth of sounds as a blind person [see my post entitled ‘Rain brings out the contours in everything‘ on February 22, 2017].  For the second time in recent weeks, I close my eyes and try it for myself.  It is surprising how in a crowded train, I can’t hear anyone, just the noise made by the train.  It’s like a wobble board that’s joined by a whole percussion section of an orchestra when we go around a bend or over points.  The first time I closed my eyes was at a concert at the Philharmonic Hall in Liverpool.  My view of the orchestra was obstructed by the person in front of me so, rather than stare at the back of their head, I closed my eyes and allowed the music to dominate my mind.  Switching off the stream of images seemed to release more of my brain cells to register the depth and richness of Bach’s Harpsichord Concerto No. 5.  I was classified as tone deaf at school when I was kicked out of the choir and I learned no musical instruments, so the additional texture and dimensionality in the music was a revelation to me.

Back to the London Underground – many of my fellow passengers were plugged into their phones or tablets via their ears and eyes.  I wondered if any were following the MOOC on Understanding Super Structures that we launched recently.  Unlikely I know, but it’s a bit different, because it is mainly audio clips and not videos.  We’re trying to tap into some of the time many people spend with earbuds plugged into their ears but also make the MOOC more accessible in countries where internet access is mainly via mobile phones.  My recent experiences of listening with my eyes closed, make me realize that perhaps we should ask people to close their eyes when listening to our audio clips so that they can fully appreciate them.  If they are sitting on the train then that’s fine but not recommended if you are walking across campus or in town!

We are all citizens of the world

A longer post this week because I was invited to write an article for the Citizens of Everywhere project being organised by the Centre for New and International Writing at the University of Liverpool. The article is reproduced below:

Scientists seek to discover and describe knowledge, while engineers seek to apply and deploy the same knowledge by creating technology that supports our global society.  In their quests, both scientists and engineers are dependent on each other and on those that have gone before them.  On each other, because scientists increasingly need technology in order make discoveries, and because engineers need new scientific discoveries to drive innovation; and both groups stand on the shoulders of their predecessors, to mis-quote Isaac Newton who said he was able to see further by standing on the shoulders of his predecessors.  Scientists and engineers have to build on the achievements of their predecessors, otherwise nothing would be achieved in a single lifetime.  This process is enabled by the global dissemination of knowledge and understanding in our society, which does not recognise any boundaries and flows around the world largely unimpeded by the efforts of nation states and private corporations.  As Poincaré is reputed to have said ‘the scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful’.  The feeling of delight is a reward for hours of intense study; but, the realization that you are the first to recognise or discover a new scientific fact generates so much excitement that you want to tell everyone.  Scientists have always met to share their findings and discuss the implications.  As a young researcher, I had a postcard above my desk showing a photograph of the attendees at the 5th Solvay Conference in 1927 at which 29 scientists from around the world met to debate the latest discoveries relating to electrons and photons.  Seventeen of the 29 attendees at this conference went on to receive Nobel prizes.  Not all scientific meetings are as famous, or perhaps as significant, as the Solvay conference; but, today they are happening all around the world involving thousands of researchers from scores of countries.  Besides the bureaucratic burden of obtaining visas, national boundaries have little impact on these exchanges of scientific and technological knowledge and understanding.  If you are a researcher working in the subject with sufficient funding then you can attend; and if your work is sufficiently novel, rigorous and significant, as judged by your peers, then you can present it at one of these meetings.  You can also listen to the world’s leading experts in the field, have a discussion over a coffee, or even a meal, with them before going back to your laboratory or office and attempting to add to society’s knowledge and understanding.  Most scientists and engineers work as part of a global community contributing to, and exploiting, a shared knowledge and understanding of natural and manufactured phenomena; and in this process, as global citizens, we are relatively unaware and uninfluenced by the national boundaries drawn and fought over by politicians and leaders.  Of course, I have described a utopian world to which reality does not conform, because in practice corporations attempt to protect their intellectual property for profit and national governments to classify information in the national interests and sometimes restrict the movement of scientists and technologist to and from states considered to be not playing by the right set of rules.  However, on the timescale of scientific discovery, these actions are relatively short-term and rarely totally effective.  Perhaps this is because the delight in the beauty of discovery overcomes these obstacles, or because the benefits of altruistic sharing outweigh the selfish gain from restrictive practices.  (Of course, the scientific community has its charlatans, fraudsters and free-loaders; but, these counterfeiters tend to operate on a global stage so that even their fake science impacts on the world-wide community of scientists and engineers.)  Participation in this global exchange of ideas and information makes many of us feel part of a world-wide community, or citizens of the world, who are enfranchised by our contributions and interactions with other citizens and international organisations.  Of course, along with everyone else, we are also inhabitants of the world; and these two actions, namely enfranchisement and inhabiting, are key characteristics of a citizen, as defined by the Shorter Oxford English Dictionary.  Theresa May in her speech last October, at the Conservative party conference said: ‘If you believe you’re a citizen of the world, you’re a citizen of nowhere.’  If she is right, then she rendered many scientists and engineers as aliens; however, I don’t think she is, because citizenship of the world does not exclude us from also being citizens of other, local communities; even though politicians may want to redraw the boundaries of these communities and larger unions to which they belong.  However, in practice, it is hard to avoid the fact that we are all inhabitants of planet Earth and have a responsibility for ensuring that it remains habitable for our grand-children and great-grandchildren; so, we are all citizens of the world with its associated responsibilities.

When I was a student, thirty years ago, James Lovelock published his famous book, ‘Gaia’ in which he postulated that the world was a unified living system with feedback control that preserved its own stability but not necessarily the conditions for the survival of the human race.  More recently, Max Tegmark, in his book ‘Our Mathematical Universe’, has used the analogy of spaceship Earth stocked with large but limited supplies of water, food and fuel, and equipped with both an atmospheric shield and a magnetic field to protect us from life-threatening ultra-violet and cosmic rays, respectively.  Our spaceship has no captain; and we spend next to nothing on maintenance such as avoiding onboard explosions, overheating, ultra-violet shield deterioration or premature depletion of supplies.  Lovelock and Tegmark are part of a movement away from a reductionist approach to science that has dominated since Descartes and Newton, and towards systems thinking, in which it is recognised that the whole is more than the sum of the parts.  It’s hard for most of us to adopt this new thinking, because our education was configured around dividing everything into its smallest constituent parts in order to analyse and understand their function; but, this approach often misses, or even destroys, the emergent behaviour of the complex system – it’s like trying to understand the functioning of the brain by physically dissecting it.  Recently reported statements about citizens of the world and about climate change, suggest that some world leaders and politicians find it easier, or more convenient, to use reductionism to ignore or deny the potential for complex systems, such as our global society and planet Earth, to exhibit emergent behaviour.

Thomas L. Friedmann in his book, ‘The World is Flat’ warned that ‘every young American would be wise to think of themselves competing against every young Chinese, Indian or Brazilian’.  He was right; we cannot turn back the globalisation of knowledge.  The hunger for knowledge and understanding is shared by all and courses provided over the internet are democratizing knowledge to an unprecedented level.  For instance, I recently taught a course on undergraduate thermodynamics – not normally a popular subject; but, it was made available globally as a massive open on-line course (MOOC) and taken by thousands of learners in more than 130 countries.  The citizens of the world are becoming empowered by knowledge and simultaneously more networked.  Large complex networks are systems that exhibit emergent behaviour, which tends to be unexpected and surprising, especially if you only consider their constituents.