Wednesday, 21 March 2012

Teaching using Computer Algebra Systems

Many academics and researchers get annoyed when students use computer algebra systems (CAS) such as Mathematica to evaluate simple integrals that they maintain should be done by hand. The question I ask is "At what point do you expect your students to switch over to using a computer?". Most mathematical examples are artificial in that closed-form expressions exist. However, in nearly any real problem, this is not the case.

Aside: see Closed-form expressionClosed forms: What they are and why they matter, and What is a Closed-Form Number?

I learnt mathematics using slide rules and tables, then calculators, then computers, then CAS. This is a useful and valid progression, but not one that everyone should have to go through. I feel that the only way true progress in teaching and learning can be made is if not all students have to learn the set of special rules (algorithms) for topics such as integration, that are better done by a CAS anyway. If we had to do calculus using Newton's geometrical constructs then progress would be very slow.

The real question is "what are the essential tools and lessons?". To me, deep understanding of the meaning of differentiation and integration ("mathematically" and "physically") is far more important than knowing how to compute a specific integral, or solving a particular differential equation.

Many people feel that reliance on a CAS means that students can't do calculus by hand and hence the really don't understand what's going on, just how to get the answer by computer. Calculus concepts are subtle. However, just knowing the mechanics of computing an integral or derivative does not imply understanding.

I believe that it is possible to have true understanding without knowing how to do algorithmic computation (see also Linear independence vs determinants), and so proper integration of CAS into mathematics courses is not only advisable, it is essential.

In a future world without computers, if all these human computational skills have been lost then it could take a long time to recover or re-discover them. In 1981, because of my physics background and experience using slide rules and tables, I was asked to navigate on a yacht sailing from Middle Harbour, Sydney, to Lord Howe Island. Learning how to use a sextant and reading GMT tables, with interpolation and hand computation, was straightforward. If there was no global GPS, I could survive again with these instruments, so the skills I learnt were not wasted. However, that still does not mean that everyone needs to have such skills.

Grammar and Style

This morning I had an interesting discussion (argument?) over breakfast with Carlo Margio about the use of an apostrophe in abbreviations. I argued that an apostrophe was not required for plurals of abbreviations, such as CDs, whereas Carlo insisted it was, and that this was a valid style choice.

Carlo considers the NY Times the final word on most style issues and, after breakfast, he looked it up, finding the following FAQ: Why Do Plural Abbreviations Have an Apostrophe?. The key issue here is the use of an apostrophe in the plural of abbreviations that include periods. So, I should use apostrophes for abbreviations that include period; except that I prefer PhD and BSc to Ph.D. and B.Sc. anyway, and I've been doing away with unnecessary periods (and apostrophes) for a long time now.

The "physics convention" for acronyms (e.g. the Phys. Rev. style) includes no punctuation, which I have always liked. However, they permit 's for abbreviations:
To form the plural of numbers add s (1980s), to symbols add 's (A's), and to abbreviations add 's or s (NMR's or NMRs).
I strongly prefer NMRs to NMR's.

I find some style choices to be more sensible than others. Style choice depends upon your favo(u)rite flavo(u)r of English. I strongly prefer the American (Harvard)—and Oxford—use of serial commas to the Times UK (+Australian) convention. And I have always been bothered by the following two style and grammar choices:
  1. The use of an preceding words beginning with h;
  2. The need for a common-gender singular pronoun.
To adress these in turn:

1. The case for a: Consider constructs such as 
"Surprisingly this is an hypothesis..."
"If you are doing a history subject, or tackling a question in any subject that has an historical dimension...".
It should be clear that the use of an to precede words beginning with h is rather clumsy. Surely, if the h is not silent then one should use a instead of an?

Consider the following (taken from The Decline of Grammar by Geoffrey Nunberg):
It should be a source of satisfaction that the grammar books of a hundred years hence will be decrying to good effect the tendency to misuse literally, or to confuse imply and infer.
I do not think that "...an hundred..." would read better. See also the Elegant Variation and All That by Jesse Sheidlower.

2. The case for they: I quote Neville March Hunnings from the (UK) Times of September 17, 1998:
A common-gender singular pronoun now needs an elegant solution. "Him/her" and "s/he" are ugly; "him" or "her" is cumbersome. On the other hand, "they" has a respectable grammatical precedent. We no longer object to an individual being addressed as "you" rather than "thou". Why not "they" instead of "s/he"?
UPDATE: Stephen Fry says it better than me: Kinetic Typography - Language

Tuesday, 20 March 2012

Top ten innovative archival documentaries

SBS's list of top ten innovative archival documentaries is interesting and eclectic. When I get some spare time I'll view these ...

The status of teachers

In raise status of teachers, add some authority and watch our students blossom, Frank Furedi argues that
Many of the universities I visit now provide remedial courses for their new intake of undergraduates to compensate for their knowledge deficit.
Certainly this true at UWA. The article is worth reading in full, but here are some selected quotes, with my added emphasis:
The most important cultural influence on children's school performance is the expectation their teachers, parents and communities communicate towards them. The reason East Asian school systems tend to outperform Anglo-American ones is not that they have a superb strategy for mentoring or training teachers, but because they perform within a culture of high expectation. In these societies, schools expect all children to take their studies seriously. As a result, their work rate is significantly higher than those of their peers in Western societies. Not surprisingly, high standards of performance often co-exist with equity.
A serious commitment to the value of education is far more important than any pedagogic system or technique. That is why children from Hong Kong, China and Korea outperform their Western peers even when they attend schools in Australia, the US or Europe.
Anglo-American pedagogy has embraced an anti-academic and anti-intellectual ethos: Accordingly the main objective of schools is to motivate youngsters, rather than drive the acquisition of knowledge. One of the hallmarks of this focus is the devaluation of academic subject-based learning. Opponents of subject-based teaching enthuse about motivating children through engaging them in broad themes and projects. In reality, the shift from academic subject-based teaching is underpinned by a dogma of low expectations that decries such education as elitist and too abstract.
..."compartmentalised" subjects—mathematics, history, biology—are the intellectual foundation for real education. Indeed, one of the symptoms of educational malaise in English-speaking societies is the lack of affirmation for subject-based education.
Occasionally, the Grattan report recognises the key role of subject-based education. For example, it notes that a strong focus on subject content is responsible for Singaporeans' success in mathematics. In Singapore, mathematics university graduates actually teach their subject to young people! Subject-based education is not simply the most effective way of transmitting the intellectual and cultural legacy of a community. It is through mastering an academic subject that a teacher acquires authority in the classroom.
The current trend towards "broadening education" and diminishing the role of academic subjects devalues the professional status of teachers, whose authority rests on their mastery of a particular subject. Without this intellectual foundation they have to rely on gimmicks and a variety of class management skills. But motivational techniques do not compensate for the impact intellectual authority makes on a classroom.
In Australia a regrettable erosion of the professional status of teachers is intimately connected to school performance. It also undermines the appeal the profession has for potential recruits. Is it any surprise that bright young graduates are less inclined to view teaching as their profession of choice? Shortages of properly educated maths and science teachers in Australian schools emphasise the need to enhance the status and authority of this important profession. Raising the status of teachers is the first step towards promoting a culture of high expectations in the classroom. Such a step tells us and our children that we take education very seriously.

Academics v Administrators

In push for academic promotion may cost us more than we gain Peter van Onselen makes the case that
Dean and head of school positions should jettison their administrative responsibilities, instead operating as board positions. This would free those academics to teach and conduct research in a way that they currently cannot. School and faculty managers should take over many of the administrative responsibilities academics currently have, creating a similar splitting up of responsibilities as occurs between the chairman of a board and the company's chief executive. 
With any luck increased responsibilities for such professional administrators would increase the talent pool prepared to embark on such a career. 
A lot more work would need to be done to make such a change of management viable. But it is a worthy restructure to consider.

Monday, 19 March 2012

6 Mitchell Street

In 1964 my family moved from East Cannington to 6 Mitchell Street Maylands (now part of Mount Lawley). Presently for sale, it is described as having a sublime location within walking distance to CBD—a little optimistic, I think—at the "fantastic price" of $1,450,000.





The real estate agents write:
This large double-storey character home set on 1012sqm and located in the sought-after Mt Lawley/East Perth river precinct is the perfect family home. 
Offering a flexible floor- plan with both formal and informal living areas, plus glimpses of both the river and city skyline from the upper level. There is a large, private front verandah on which you can sit with a cup of tea and a large covered terrace at the rear of the home overlooking the lap pool (the pool is a combination of lap and leisure pool). 
It also has wonderful access to the Graham Farmer freeway, CBD and Claisebrook Cove where you will find all manner of restaurants, café’s and bars overlooking the beautiful Swan River. Banks Reserve, beautiful parkland on the river, is a 2 minute walk with cycleways and walkways all along the river. Many local residents take the opportunity to walk to work from here. 
This is a lovely quiet area in which to live.

Sistine Chapel

It takes some time to load, but the Vatican's virtual Sistine Chapel is quite impressive.

Wednesday, 14 March 2012

Inner-city Sydney galleries

Galleries on the go featured some galleries to visit the next time I'm in Sydney:
The article led me to the Hg2 and their iPhone app, which I ended up buying.

Tuesday, 6 March 2012

Growler

First saw a 'growler' at the Botannical in Melbourne. They had the Colonial Growler from Colonial Brewing Margaret River, which surprised (and impressed) me. It is disappointing that there is only limited availability in WA.