Archive for May, 2011

On teaching students to show their working

May 25, 2011

Karl F Gauss (1777 – 1855) “I have had my solutions for a long time, but I do not yet know how I am to arrive at them.”¹

I have struggled with the problem of persuading the talented students to show their thinking in any detail – the greater the gift, the less likely they are to want to explain the details.  After all, if it is blatantly obvious, who wants to discuss why it is so?

“Because I say so!” is a non-starter – too many of them can turn mulish.  The argument that it helps one to find one’s errors doesn’t work – they, having genius egos and little experience, do not really believe that they can be in error.

In literacy and other communication-loaded subjects, the argument that the details are needed to help the audience understand one’s thoughts may help.  Unfortunately, if the student feels that the teacher knows the details already, ve may logically respond that details are therefore not required.   More powerful for the score-motivated, however, was the clear opening statement that the person assessing one’s work will have a mental checklist of “things to give points for”, and that including those statements will get one points.  This was particularly important for a student, asked to discuss  a complex piece of writing, who skipped all the obvious bits (the teacher’s focus, of course!) to discuss subtleties in the subtext .  However, unless the teacher has written a very careful programme, has a very clear marking key linked to the topic, and has provided examples of pieces showing discussions of  “obvious bits” ,  and the student has attended, this leads to the lesson being that the teacher wants the student to guess what the teacher wants to see –

Now,  here is a win/win situation: that “unless” sounds like good teaching practice,   and the latter outcome reflects the reality of many test and workplace experiences .²

But then, there are those with much more internal motivations.   One approach for them which  I enjoyed involves a little history and psychology:

Many experts find they “know” but can’t easily explain why – like the soldier in Afghanistan who believes there is a trap, but can only say that “that street gives me a cold feeling” – not much help when training a rookie.   I knew a mathematician who had spent three years working on proving that two different areas of extreme geometry which were using different theorems could be reduced to one set of theorems – he “knew” they were linked, but had to prove it using both sets of theorems.  In higher maths, I myself often knew the answer to a problem and then had to work to choose the approach to showing that it was so.   

Even the great scientists and mathematicians experience this:  thus, the Gauss quote: Karl F Gauss (1777 – 1855) “I have had my solutions for a long time, but I do not yet know how I am to arrive at them.”¹ 

If all these people know things are so, then it is not surprising  that some  students will start to know also.  But how does it come to be so? 

When   one is learning to read, one remembers the shape-sound match, then sounds-out the letters, then links the sounds to find the word, and try to remember that one while reading the next word.   At each step, neurons are firing chemical messages and stimulating each other to grow and link across brain structures.  Later, the shape-sound match is known: neurons have made linkages, so the visual system gets the verbal system for the letter-sound doing its job below consciousness.   Then the sets of letters in each word start having neural networks, so the whole word is known.  Later, groups of words are linked, so that if a new word is made up of them, the set of activated networks means that the new word is known.  With much reading (and especially with good speed reading training) the networks may link so that entire sentences may be grasped by the expert neural systems rather than  read “word by word” by the conscious mind. 

In all aspects of learning, it comes to the same thing: neurons signalling and  linking and signalling.  What you practice is what you get good at.

If you practice just knowing, and you have made a faulty connection somewhere, that fault is strengthened.  That is the first reason to check the working consciously.

If you practice just knowing, you can unconsciously be using systems elsewhere in your brain – other expert systems can be involved without your knowledge.  This often happens where science uses mathematics, or any subject uses literacy.   Examining your processes can make surprising linkages available to make useful shortcuts – for example. having to remember only one of five physics formulae because they are all derived from one mathematically.  Making links where no-one else saw them is what gets people Nobel prizes.  That is a second reason to check the working consciously.

If you practice just knowing, you do not practice self-questioning.  To question one’s own inner processes is a valuable skill in later life, when more complex problems engage many neural networks – many adults spend long hours with psychologists, trying to figure why they make such bad decisions and how to improve their lives.    Start practicing with small things – like adding three-figure numbers – and develop the skills you will need for the big things later.  That is a third reason to check the working consciously.

Practicing just knowing means you cannot be sure that you have really grasped the whole of the problem.  In a hurried situation it is useful to be sure enough to gamble on, but where there is time –  conscious checking allows certainty.  That confidence is a fourth reason to check the working consciously.

If you practice just knowing, you can be manipulated by events elsewhere in your brain.  If conscious checking gives an answer different from your knowledge, you have a starting point for finding out what you know (in the normal sense) which contradicts your conscious thinking.  Sometimes, there is a fault which can derail your life (see the psychologist’s work, as above.)  And, from experts in fields from medicine to farming, there is another case:  if you know the area really well, your gut feeling is often right – and finding out why is the path to excellence.    That is a last reason to check the working consciously.

Finally, the more complex the problem, the more useful it is to do the working in writing and in a careful format, so that each step can be checked over again.  Doing this gets easier with practice – so practice doing it in writing, neatly, and in the standard form for the subject.

 Go, and justify your answers from now on.  Or I will go over this again.


1.  K.F.Guauss, cited by Paul Williams (2010) p.338.  In Afterword in Sturgeon, N. (Ed.) Case and the Dreamer (pp.327-354)
Berkeley: North Atlantic Press

2. A teacher’s view of this fact of life, and advice on teaching students to live with it:  Mark Lopez “The Little Black School Book ” Vols. 1 and 2, 2008 and 2011, Connor Court Australia.

Frightened to touch – is that good for your class?

May 16, 2011

Combine  the ideas in  David Brook’s address to the Commonwealth Club of California, Harlow’s research on the rhesus monkey’s need for comforting touch,  the recognition of the need for affective touch leading to the development of special cuddleable robots for hospitalised children,   the recognition by the marketing community of the importance of touch in selling (extend it to selling a person as being caring),  the link between childhood experiences of touch and adolescent social and emotional development, and the link between physical aggression and touch deprivation including touch in adolescence.  Stir in a dose of any of the films of primates de-escalating tense situations, or doing “group bonding activities”.  Add awareness of the busy family using electronics to babysit, and of  families where non-aggressive, non-sexual touch is rare for less socially accepted reasons.

What does this  say about the no-touch approach in school?  What are the effects of the policy being stronger  after the children are 8 years old, and its being stronger for men in teaching?

Entirely apart from the failure to use a strong reinforcer (oxytocin release) with known links to opinion change, calming, and later cooperative behaviour;  and ignoring the chance to help children at risk of later developmental problems –

I see an unintended lesson:  teachers, especially men, are perverts, who must be prevented from molesting you by rules against their touching you.  Another blow to the social status of teachers.

All rather sad, really.  I’m sure the fashion will change eventually, but at the moment – so sad.

Fortune favours the well prepared, well-mannered, and hard-working

May 10, 2011

 How British horse chestnuts influenced the foundation of Israel.

There is a tale of a British politician in WWI  who had a policy of having tea with a wide range of people, and one day had tea with a  White Russian (refugee from destruction of Czarist Russia) Jew.  It happened that conversation turned to the problems of the military, as their main source of acetone –   an ingredient in cordite  for munitions – was lost through the war.  The refugee said ” I can help you there – I have a way to make acetone from horse-chestnuts”  .    The government invested in his method, and was able to make the shells needed to continue the war.  Later, grateful for his assistance, the British listened to his arguments in support of the creation of Israel.

This sounds like chance favouring the politician who was willing to meet odd people and listened to a refugee grumble , and the refugee who met the politician – but the reality is more complex.  The politician was Lloyd George, the “refugee” was Chaim Weizmann.

According to Wikipedia, “Weizmann studied chemistry at the Polytechnic Institute of Darmstadt, Germany, and University of Freiburg, Switzerland. In 1899, he was awarded a doctorate with honors. In 1901, he was appointed assistant lecturer at the University of Geneva and, in 1904, senior lecturer at the University of Manchester.”

Weizmann had become interested in the bacteriology of fermentation, and sent many years testing cultures for the ability to produce useful chemicals like butyl alcohol from fermenting maize.  This was complicated by commercial restrictions on other scientists sharing processes and cultures.  One of his cultures (later named ‘Clostridium aceto-butylicum Weizmann’) produced good amounts of butyl alcohol, but also fair amounts of acetone.

At the same time, he was strongly involved in the more militant branch of Zionism, weary of centuries of racism.  He was invited to tea with a middle-class, well-assimilated Jewish family, and there met another guest – a distinguished journalist. Through conversation with this gentleman he gained introductions to senior politicians, arguing for his cause.

In  1915, through a series of contacts suggested by scientific friends, and through demonstrations of the laboratory-level success of his bacillus and brewing and distillation techniques, he became one of three scientists separately funded to develop methods for manufacturing acetone.   He made modest requests for immediate funding,  accepting later payment in order to support the war effort, with a gentlemanly manner much appreciated by the Government.    He rapidly scaled up the process from kilogram to tonne output, and found ways to ferment carbohydrate sources other than maize.

The other two methods proved less successful, and, with the strict rationing required later in WWI, the ability  to ferment horse-chestnuts was a strong factor in Weizmann’s popularity: children would collect the nuts for shipping to the factory, “helping the war effort.”  Thus,the Government’s willingness to support early-stage science paid off, even though two in three did not pan out.  They prepared for later needs by seeking out appropriate science,  were courteous in dealing with the scientists, and  dealt with the bureaucratic labour involved – so fortune later favoured them.

And Weizmann?  From a great deal of hard work, a gentlemanly approach, and knowing influential people on more than a scientific basis; with a good public profile and with the British Government in his (moral) debt, as the head of the British Zionist Federation and later the World Zionist Organisation he dealt with British (and other)  politicians.    This took up a great deal of his time between the wars (WWI and WWII), while he continued his research, industrial production of fermentation products, and development of what became the Weizmann Institute of Science in what became Israel.

Weizmann became the first President of the new state of Israel in 1949.

Fortune favoured the well-prepared, well-mannered,  and hard-working.


This blog entry was made possible through talking with a friend who watched a documentary on the Atlantic, through Wikipedia, and through my paying an annual fee to have access, through a University library, to online versions of journal articles. In this case, particularly to J. Reinharz (1985) Science in the service of politics:the case of Chaim Weizmann during the First World War. English Historical Review Vol. 100, No. 396 (Jul., 1985): 572-603. doi: 10.1093/ehr/C.CCCXCVI.572: .  This is worth reading in its entirety.

The title derives from “Dans les champs de l’observation le hasard ne favorise que les esprits préparés.”  (In the fields of observation chance favoors only the prepared mind) : Louis Pasteur, Lecture, University of Lille (7 December 1854)

The topic here is a wider field than observational science, but I assert that the concept still applies.

From book launch to class investigation and Civics discussion

May 3, 2011

Public radio prompts many ideas for class projects. Here is one on the problems facing the politicians trying to improve the lives of Aboriginal Australians:

Aboriginal self-determination: The Whiteman’s dream  examines the history of Australian attempts at “Bridging the gap”  and encouraging Aboriginal self-determination.  It was launched with speeches from Mal Brough,  former Minister for Families, Community Services and Indigenous Affairs, who is a person of Aboriginal background, and Gary Johns, the author.   Mr Brough initiated “the NT  Intervention”, and is seen as a very right-wing thinker, but my interest here is not in is particular political views (although, given his family contacts with remote locality Aboriginal lives,  his speech is worth listening to.)   I want to look at one particular  point raised by speeches at the launch (via ABC RN Counterpoint, in the program aired on 02 May 2011).

According to the speeches, the book reports that the Royal Commission into Aboriginal Deaths in Custody  found, in the first 6 weeks, that the statistics for death rates (per year per  thousand, I assume) in custody were not significantly different between Aboriginal and other prisoners.  The Commission continued to investigate the events surrounding Aboriginal deaths in custody, and issued its influential report.

Questions for a class to consider:

  • How can we test the veracity of the  statement that the death rates were the same?
  • From your current knowledge, do you think the causes of deaths in custody are likely to be the same for those of Aboriginal, White Australian, and other ethnic appearances?
  • How could the Government of the time find out what was really happening?
  • What arguments can you think of for and against the Royal Commission continuing the investigation into Aboriginal deaths in particular?
  • What arguments can you think of for and against publicising, at the time of the Royal Commision, the general nature of the rate of deaths in custody?
  • Given the arguments for and against, do you feel that the decisions made were right as far as they went?
  • What else would you have done?

Follow up:

  • How can we find out what statistics are currently available on death rates per ethnic group in and out of custody?
  • What information can we find on historical changes in these rates?
  • Have there been changes in these rates following the Royal Commission?
  • How could a social scientist test whether the death rates over time are affected by Governments’ attempts to change the way Aboriginals are handled in custody, or by other changes in society?

Further follow-up

  • Has this experience changed your ideas on the way Governments work?  If so, what has changed?

I don’t have a class of the age for this, but I’d love to try it someday.  The topic is going to be around for years;  use of the internet to search Government and NGO sites for official statistics, and the class contacting  the Australian Bureau of Statistics to ask for an expert’s advice, are examples of research serious thinkers on controversial matters must do;  and the political problem of choosing how much to make public is  one the voting public must consider if they are to judge politicians’ actions.  All these are things direcly related to the voter’s civic responsibility – and thus well raised in school.