Cactus presentation style.

Hyde, Hartley ; Spencer, Toby

This article is designed to help you prepare material for your students. Some readers will regard these issues as pedantic, however, most teachers are perfectionists and like to know they are correct.

Users of Microsoft Word are generally familiar with the concept of style sheets (normal, Heading 1, etc.). Many are predefined by Microsoft but the default values can be changed as needed.

Using style sheets not only means consistency throughout one or more documents, but it also makes changing the document much quicker and easier; e.g., changing a heading style sheet will apply changes throughout a document, rather than you having to change many individual headings.

Sometimes style is simply a personal preference and sometimes we have to experiment, but usually there are logical guidelines to setting out in order to present work in the best way. For many years, the "normal" style of AMT has specified 10 point Bookman. Despite its far too elaborate upper case "Q", this is the font that best matches the Symbol font--the expression sin 28 using Bookman looks better than sin 28 using Times.

Most publishing houses and organisations have a style manual which details spelling standards, citation formats, ways of presenting various levels of headings, contents pages, captions, dates, numbers and references. While there is broad agreement, there are small differences that often depend on a fashion at the time or may relate to geographical location (e.g., American versus Australian conventions).

So: how do we know what is "correct"? Fortunately, there are authoritative sources to help us. The International Organisation for Standardization (ISO; www.iso.org) is the world's largest developer and publisher of international standards. Macquarie University also has an enormous influence on the way we speak and write in Australia. Staff prepare the Macquarie Dictionary, advise the ABC Standing Committee on Spoken English and for many years they have distributed a very useful guide called Australian Style--available as PDF from: www.ling.mq.edu.au/news/australian_style.htm. They also contribute to a surprisingly interesting book: the Australian Government's Style Manual. Much of this article is based on the current sixth edition.

The important thing about all of these Macquarie publications is that they are based on continuing research about what is happening in different parts of Australia. The advice therefore slowly changes along with observed usage, changing standards and, sometimes, legislation.

Numerals

In the fourth edition, the Style Manual quotes the Australian Standard AS 1000-1979 to claim that a "billion" is a "million million" ([10.sup.12], traditionally a UK English usage), but by the sixth edition they prefer to recommend standard (AS ISO 1000:1998) where a billion is now only a "thousand million" ([10.sup.9], traditionally a US usage). Both editions recommend using "powers of ten to clarify critical amounts". One wonders under what conditions a missing factor of 1000 would be considered non-critical!

A use of spaces instead of commas to aid the recognition of numerals larger than 9999 (e.g., 12 345.678 99) was recommended by the Metric Conversion Board in 1974 and incorporated into AS 1000. Later editions of the Style Manual note a continuing use of commas. This has not been helped when both Microsoft and Macintosh operating systems have set their Australian defaults to commas, mirroring the American system. Commas are still recommended when large numerals are expressed in words, e.g., "nine thousand, seven hundred and two". English grammar conventions suggest that a sentence should not start with numerals and that any number between one and nine be written as a word while any number 10 and above be written using numerals. However, mathematical writing often requires the use of numerals; when determining which to use, a rough guide might be to distinguish between "five" as an amount of something and "5" the numeral in an expression.

Time and dates

Progress toward standardisation is much slower for time and date formats. American publishers recommend a time format such as 8:45 PM where the letters PM are in capitals of a smaller font size. Australian usage prefers 8.45 pm. One advantage of the American system is that it avoids confusion with the decimal fraction 8.45.

Most Australians are aware that US citizens would read 04/06/10 as 6 April 2010 instead of 4 June; but all six permutations are in use in various countries. This is clearly a problem for efficient trade and ISO 8601 recommends we all use 2010-06-04.

The full ISO standard recommends a combined format 2010-04-06T20:45:00 for 8.45 pm on 4 June 2010. The advantages of this standard are that:

* it allows easy sorting because it lists larger units before smaller units;

* we can cut this format short or extend it to whatever precision we require;

* it is language independent;

* it has constant length; and

* it can be easily modified to express local time using an offset to UTC.

Confusion over abbreviated dates can be removed by writing a date in full. The Australian standard is still to use "4 June 2010" (note no "th" is used--which Word tends to insert by default) which quite efficiently does away with any extraneous commas such as in the American convention: June 4, 2010.

Aware that most Australians use twelve hour clocks, the Style Manual recommends a use of the words "midnight" and "noon" to avoid confusion about 12.00 am and 12.00 pm.

Fractions

Where there are more than four digits after a decimal point, they should be grouped using spaces as shown previously. Where a decimal fraction is less than one we should use a leading zero (0.63 rather than .63).

For non-decimal fractions it is better to insert a fraction using Equation Editor (a cut-down version of MathType that has come bundled with Word for many versions) than to use a forward slash to separate numerator and denominator: 2 3/4 is confusing.

The size of your fractions may depend on context, personal preference and line spacing in your document.

Formulae and operations

Personal computers have made inserting specific mathematical symbols into documents much simpler: now we simply need to "insert symbol". There really is no excuse for such shortcuts as using an "x" for a multiplication sign! Many fonts include special symbols in the font set, and then there are also specific fonts such as the appropriately named Symbol--Greek letters, arrows and others are no longer a problem!

Using applications such as Equation Editor make formatting much simpler: templates allow numbers and symbols to be inserted in the correct place, at appropriate sizes and with adequate spacing.

[ILLUSTRATION OMITTED]

General mathematical conventions suggest that variables should be italic and equality symbols should be aligned.

Dashes

The correct use of the various horizontal bars is discussed under punctuation in the Style Manual. The hyphen "-" is used specifically for word punctuation. While that section makes interesting reading it is far too extensive to review here. The em dash ("--" so called because historically it was the width of a typeset letter "m") should be used to signify an abrupt change or to set apart parenthetic elements. It is frequently mis-used in place of a colon.

The en dash ("-" so called because historically--you guessed it--it was the width of a typeset letter "n") should be used, rather than a hyphen, to indicate subtraction or to shown that a numeral is negative (3 - 7 = -4). When used to indicate a negative numeral there is no space between the en dash and the following digit. Use of the macron ("4) to indicate a negative numeral (as in the Algebra Skills Kit) is no longer recommended.

The en dash is used to show spans as in pages 45-56 or May-July. However, if we need to add extra information, the en dash should be spaced as in 78 BCE - 34 BCE.

The en dash is also used to show an association between words that retain their separate identities (e.g. Asia-Pacific region).

SI units

Having started teaching in 1966, I have treasured the documents that introduced us to decimal currency on 14 February of that year. Some years later came the flood of documentation when we slowly "went metric" in the early seventies.

Looking through that material, I am amazed how well the style promoted by the Metric Conversion Board has stood the test of time. The most obvious change has been that we lowered the decimal point from its established position half way up the x-height, as in 2 5, because when we started to used microcomputers we had to use a full stop instead.

The table of Base Units shown in the Style Manual is identical to the one distributed in 1973. From the base units are defined the derived units, described by ISO 31:1992.

When writing a measurement, we should leave a space between the quantity and the unit (0.34 m). We do not use plurals because 50 ms might be mistaken for 50 m/s.

SI derived units are defined in terms of base units. Thus acceleration is measured in metres per second squared and denoted by m/[s.sup.2] or m x [s.sup.-2]. Interestingly, in 1973 we wrote m.[s.sup.-2] and now we find that the raised dot is recommended for "multiplying" units. Derived units can also be expressed in terms of other derived units or in terms of base units--e.g., an inductance of 3.41 Henry can also be written 3.41 H or, using other derived units as 3.41 Wb/A or, using base units as 3.41 [m.sup.2] * kg * [s.sup.-2] * [A.sup.-2]. Use of negative indices is preferred to using a forward slash.

Units are capitalised where they are named after a person; the larger prefixes are also capitalised (see Scrapbook p. 12). The litre is not an SI unit, but we should write either 5 litres or 5 L because a lower case L might be mistaken for a one when using some fonts ("L" is the general Australian usage). Other non-SI units are needed for specific industries. Aviation uses imperial measures because the USA is not metric.

Abbreviations

In Australia, the general convention with abbreviations is to use a full stop if the condensed word does not finish with the final letter of the original word; hence, the abbreviation of "editor" is "ed." but "eds" is the abbreviation of "editors". This abbreviation in particular often comes into conflict with many American referencing systems such as that of the American Psychological Association (APA) which is commonly used in academic mathematics publishing (and is used in AAMT journals) where the American convention is to use a full stop with all abbreviations.

It is worth noting that standard units such as "m" for metre or "s" for second are regarded as symbols, not abbreviations.

This article has of necessity considered issues relating specifically to mathematics, which often requires special usage and presentation with regards to conventional English grammar. However, there are many other standards relating to the style with which we present our written work. Many students learn these concepts in computing and desktop publishing classes. Just as we take care to avoid spelling errors, students are becoming equally critical if we have used a hyphen where we should have used an en dash.

While there are other authorities on what makes for clear presentation, you will probably best serve the needs of your students if you follow the Australian Government Style Manual. If there is not a copy in your library, recommend that they buy one. If you would like your own copy, they cost about $50.

Remember that what you are generally trying to do is communicate your thoughts and ideas to others--so format to aid understanding. In general, if you stick to common conventions and keep your formatting simple, you cannot go wrong!

Hartley Hyde & Toby Spencer

cactus.pages@internode.on.net