# Mathematics: Functional or Not?

By Cowley, David | Mathematics Teaching, March 2006 | Go to article overview

# Mathematics: Functional or Not?

Cowley, David, Mathematics Teaching

As I write this article, the mathematics education community is being asked to consider proposals for 'functional mathematics'. In this context, I am not the first, nor shall I be the last, to ask the question 'What is mathematics?', but is my 2006 perspective different to others?

Mathematics has its roots in practical requirements. Around 1500 years after Babylonian algebraic texts, the Greeks took the subject to a new level and Euclid, amongst others, laid down the foundations for mathematics as a deductive science.

Buxton, debating the nature and purpose of mathematics in 1984, identified varieties of maths in terms of purpose: mathematics for survival; useful mathematics; direct applications of mathematics; mathematics as a language and a tool; mathematics for its own sake and mathematics for personal development.

Perhaps my favourite exposition on the topic of what is mathematics comes from Davis and Hersch (1980), who concluded that:

'The definition of mathematics changes. Each generation and each thoughtful mathematician Jbrmulates a definition according to his lights.'

This gives mathematicians the freedom to define their field in any way they want. It enables the primary teacher who is encouraging the use of mathematics as a language, the secondary teacher who is asking fifteen-year-olds to be creative and pose their own questions, the university lecturer encouraging proofs to be rigorous and the would-be Andrew Wiles extending the subject to solve hitherto unsolvable problems, all to be united under the banner of mathematics. In fact, isn't that why the subject is so important? There are far more people using mathematics in this world than there are using the English language.

So, when I am asked to consider 'functional mathematics', I ask the questions 'functional for whom? …

## The rest of this article is only available to active members of Questia

Already a member? Log in now.

### Notes for this article

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this article

#### Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

#### Cited article

Mathematics: Functional or Not?
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.
Print this page

#### Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this article
• Highlights & Notes
• Citations
Some of your highlights are legacy items.

## Questia reader help

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

Buy instant access to save your work.

Already a member? Log in now.

Search by...
Show...

### Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.