www.whyslopes.com > Volume 1B,  Mathematics Curriculum Notes,  1996  >   2 For & Against Math     [ Back ] [ Next ]

Chapter 2
For and Against Mathematics

Previous: Chapter 1, Introduction

Motivations from philosophy, daily life and science or technology or business can be offered for the study of mathematics. They are described next with some links to reason. This chapter ends with paragraphs which discusses why students avoid mathematics.

1. For some past philosophers and thinkers, the definitions and conclusion reaching methods in Euclid's books on geometry provided the most certain model for rule-based reason, or how to argue if you must. Geometric knowledge was based on rules, patterns and definitions which seemed self-evident once said or described. Euclid's books or elements were composed two thousand years ago. Modern translations of them exist. The translations are recommended to specialists in geometry only, as today newer presentations of geometry and other ideas of mathematics are favoured in the classroom. For students wanting to understand whatever they may be doing, if not why, the Euclidean organization of mathematical disciplines can be attractive. This is a link to the love of rule-based reason, if not knowledge.

2. For the person in the street a few centuries ago, writing, reading and figuring skills were signs of knowledge or education. Before the seventeenth century A.D., if not later, the absence of a good notation for arithmetic made figuring hard, except perhaps in areas where the abacus was readily available. Since the seventeenth century the development of the printing press and of arithmetic based on decimal notation, the skills of writing, reading and figuring have become common. For the person in the street, these skills are useful in correspondence and in the buying and selling of goods, property and services. Counting, decimal arithmetic and the use of simple formulas provide people with repeatable and therefore verifiable rules for arriving at conclusions. Figuring on paper or in the head is also part of rule-based thought and reason. This link to rule-based reason needs to be remembered.

3. The decision of what or how to calculate in business, science and technology often depends on an algebraic way of writing and thinking for describing (or changing) calculations, numbers and quantities. The latter appears as a reasoning tool. But this tool is part of the mystery surrounding mathematics and reason for many people in school and out. Implication rules with the algebraic way of writing and thinking, if clearly explained, provide a foundation for both mathematical thought and also rule-based reason in all disciplines. A student may be encouraged to study mathematics in the hope of understanding whatever he or she might be doing and why, and to have the option of mastering numerical disciplines in science, technology or commerce. For better or worse, this is a link to rule-based reason in modern life.

At least four further motivations for studying mathematics exist. First, teachers and writers in all disciplines may have the goal of identifying and imparting some worthwhile knowledge - an incentive for this writer. Second, researchers in mathematics may identify the goal of extending the boundaries and form of mathematical thought. Third, some people were attracted to mathematics instruction and research just as a means to a livelihood in some shape or manner. Fourth, some find an enthusiasm for mathematical thought or mathematical recreations sufficient.
No single motivation can satisfy everyone. A motivation that is meaningful for one may seem vacuous to another, and some motivations are not positive.

In modern society or times, science and technology are used to justify ecological and ethical acts which appall some students. Students see that the environment is under threat. Many leading elements of our society busily trying to survive today have the attitude that tomorrow does not count. Students see the use of technology and science in the creation of war machines. Students fear that there will be no jobs regardless of what they study. And students excelling in literature and word-based subjects may find the symbolic and algebraic exposition of mathematics itself and of quantitative disciplines alienating – an abstract art. Their teachers in schools and colleges may be powerless and insecure cogs in bureaucracies that go forward without allowing initiative. Not all is well. Schools may be like assembly lines, impersonally processing students or livestock to be moved on and out. Given the fears that students may acquire, many rational students will turn away in despair from studies or planning for the future. [1]

[1] As a student and then as an adult I had a fear and despaired of the ever-present possibility of nuclear war. Much to my own surprise, thirty years later in 1996, I am still alive but have refrained from having children. This refrain may continue due to my ecological pessimism.

In education and society, give students hope or pay the consequences in the classroom, in the streets and in the morgue – circumstances hopeless or lacking purpose may lead students to harm (glue sniffing, drugs, crime or suicide). Compulsory education is absurd and pointless without care for these other factors.

Next: Chapter 3, Algebraic Thought- What is it

www.whyslopes.com > Volume 1B,  Mathematics Curriculum Notes,  1996   >   2 For & Against Math     [ Back ] [ Next ]

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby,  All Rights Reserved.