Fortnightly Mailing

Poincaré's "Mathematical Creation" - via a review by Jim Holt of Nicholas Carr's "The Shallows"

I did not enjoy Nicolas Carr's "The Shallows - How the Internet Is Changing the Way We Think, Read and Remember" (in the US the strapline is the much brasher "What the Internet Is Doing to Our Brains".....), which seemed to veer between coherent scientific investigation and journalistic hyperbole.

There is an interesting review of The Shallows in the current issue of the LRB by science writer Jim Holt (who from his self-description comes across as someone who is not exactly an inveterate user of the Web). Holt's review gently and playfully points out several of the weaknesses in Carr's argument.

But this does not mean that Holt is calm about the impact of the Web on thought.

To cut a long story short, Holt argues that the connection between memory and creativity ought to make us wary of the web. What bothers Holt is the way that the Web allows you to avoid internalising facts and concepts, because you can look things up on demand, without needing to learn them, thereby denying your unconscious mind the chance to turn over learned facts and concepts to generate new ideas. This, Holt argues, is the process that is at the heart of creativity, which he illustrates with a short quotation from the French mathematician Henry Poincaré's essay "Mathematical Creation":

Having reached Coutances, we entered an omnibus to go some place or other. At the moment I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’s sake, I verified the result at my leisure.

Digging on the Web led me to the February 2ooo issue of Resonance, an Indian journal of science education, and the whole accessibly written essay by Poincaré.

 

 

 

Dylan Wiliam - Formativeness as a potential property of an assessment

I heard "inside the black box" Dylan Wiliam speak at an LSIS event today for the current cohort of Research Development Fellows. Wiliam was fascinating as always. For example here is his definition of formative, which he sees as a property of (some, and only some) assessments:

"An assessment functions formatively to the extent that evidence about student achievement elicited by the assessment is interpreted and used to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions that would have been taken in the absence of that evidence."

Statistical literacy - ARTIST - a resources site

ARTIST - "Our goal is to help teachers assess statistical literacy, statistical reasoning, and statistical thinking in first courses of statistics. This Web site provides a variety of assessment resources for teaching first courses in Statistics."

Peer Instruction in the Humanities and Arts a resource from Monash University

The diagram below is from an area of the Monash University Philosophy Department's web pages devoted to peer instruction in the humanities, mostly dated 2008.

For more on Eric Mazur's peer instruction, go to Data is not the plural of anecdote, this two-minute overview, or the Mazur Group web site. Or read the book.

Source

Cognitive neuroscientific insights into training

A novel approach to minimize error in the medical domain: Cognitive neuroscientific insights into training [link to article home page] is a newly published paper by Dr Itiel Dror, whose work I've featured previously in Fortnightly Mailing.

Here is the abstract:

Medical errors are an inevitable outcome of the human cognitive system working within the environment and demands of practising medicine. Training can play a pivotal role in minimizing error, but the prevailing training is not as effective because it directly focuses on error reduction. Based on an understanding of cognitive architecture and how the brain processes information, a new approach is suggested: focusing training on error recovery. This entails specific training in error detection and error mitigation. Such training will not only enable better responses when errors occur, but it is also a more effective way to achieve error reduction. The suggested design for error recovery training is to begin with detecting errors in others. Starting off with highly visible and even exaggerated errors, and advancing to more challenging detections and finally requiring to detect errors within oneself rather than in others. The error mitigation training starts with providing the learners with the correct remedial actions (after they have detected the error). With training, the learners are required to select the appropriate actions within multiple choice alternatives, and eventually are required to generate the appropriate remedial responses themselves. These can be used for instruction as well as for assessment purposes. Time pressure, distractions, competitions and other elements are included so as to make the training more challenging and interactive.

Two-minute video overview of Eric Mazur's approach to large group teaching

Last year I pointed to a talk by Eric Mazur about peer-based instruction. The video above provides a clear and accessible overview of Mazur's approach.

Conditions for Successful Innovation – A Baker’s Dozen Checklist

This checklist was developed by participants in a workshop – Beware Geeks Bearing Gifts – at the LSIS Embracing Technology for Success conference held in Birmingham on 2 February 2011.

Comments are welcome.

[Innovation = change for the better that helps solve a problem that need solving and which is capable of being solved.]

Innovation within an organisation tends to be successful when ……

1. there is buy-in from users and when those who have to change their practices are doing so willingly rather than by diktat (willingness and diktat are extreme ends of the spectrum, and willingness can be developed through advocacy by people in positions of influence);
2. there are clear objectives – kept in mind at all times – with all the main people involved able to answer clearly the questions “what are we doing?” and “why are we doing it?”
3.  it is capable of being done at a large enough scale for financial savings or effectiveness improvements to accrue;
4. people are given time to do it – thus resource controllers need to be sufficiently convinced of the benefits to provide time for implementation (time might be planning time, implementation time, professional development time, and last by not least, testing time);
5. those leading and/or promoting innovation need to be savvy about true costs and benefits – otherwise changes will be made that are unsustainable;
6. there is a clear business case (but this does also run counter to the other truth that some valuable inventions can arise when there is no business need whatever);
7. risk, recognition, and reward are part of the local climate (if there is fear of occasional failure then people will tend not to take risks – but do not forget that the banks failed partly because they rewarded risk-taking……..);
8.  innovation is seen as a key part of an organisation’s strategy (but this is not a sufficient condition: plenty of organisations that do not innovate have “we innovate” writ large in their strategy);
9. it is monitored and evaluated (with appropriate evaluation criteria that are not applied inflexibly), and when things that do not work are killed off – but not too quickly – rather than being left to fester;
10. resource controllers are able to spot “fantasy business plans”, and have their eyes open for those who are too personally or politically invested in a particular innovation (but remember: many innovations happen precisely because someone is personally invested!)
11. there is a continuous process of prioritising and re-prioritising – this is especially important when an innovation concerns a complex and possibly changing mix of issues – and appraisal should not stop when a product or service is launched);
12. you keep the horse (the innovation) in front of cart (the problem that it is designed to solve) at all times, and ensure that the innovation has a strong focus on clients/users/consumers;
13. every project needs a communication channel, successes and failures should be honestly and routinely communicated (negative news sticks and travels further and faster than good news).

Miscellaneous points

a. There is no point expecting technically dependent innovation to be successful if the technical infrastructure is not reliable.

b. One problem solved may create others. (This links to 11 above).

c. The checklist relates mainly to “incremental or diffusive innovation” rather than to “disruptive innovation”. It should not be assumed that the former is a more important form of innovation than the latter.