By Dr Leonard Bezzina from the Dept. of Mathematics & Science Education
This is Part 2 of 3 of a series of articles about the importance of learning mathematics. Part 1 can be revisited through this link.
There’s much beyond the academic interest in Mathematics
One must consider the issue of why knowledge of mathematics is considered to be so crucial by so many people. If knowledge of mathematics is deemed to be of fundamental importance, then one can safely assume that there must be something in its very nature that makes it so. This leads us to consider yet another question: what is mathematics?
It could be argued that such a question, though of undoubted interest to philosophers of mathematics, is largely academic to everyone else. Some would even go further and argue that if there is widespread agreement that mathematics is essential there is no need to answer this question (Ziegler & Loos, 2017).
But is the issue of the nature of mathematics just of academic interest? The answer is clearly no. How mathematics is conceptualised is of fundamental significance especially within education circles (Ernest, 1991). Research shows that divergent conceptions of mathematics play a significant, though sometimes subtle, function in shaping teachers’ behaviour (Thompson, 1984; Dossey, 1992).
Different views of mathematics not only lead to different perspectives on why and how mathematics should be taught but also to divergent perspectives on the social, political, and moral values of mathematics as well as the related social, political, and moral responsibility of those who teach it (Ernest, 1991).
Mathematics as a product or as a process
Conceptions of mathematics that view it primarily as a ‘product’ - a body of infallible, incontestable, value-free, and objective truth that is independent of man and society (Ernest, 1991) and which grows through a process of accretion - would tend to emphasise transmission methods of teaching, passive autonomous learning, knowledge of mathematical products especially facts, skills & techniques, and concepts, and, one-off summative assessment methods such as tests and examinations that emphasise ‘knowing’ and ‘reproducing’.
On the other hand, conceptions of mathematics that view it mainly as a ‘process’ – a body of fallible, questionable, value-laden, and subjective (von Glasersfeld, 1995) or intersubjective (Ernest, 1991) knowledge, very much a product of man’s creation (Ernest, 1991; Hersh, 1998) which grows not only through accretion but also through correction and revision would tend to emphasise inquiry methods of learning, active collaborative learning, knowledge of mathematical processes, especially solving and investigating strategies, and, continuous formative assessment methods such as assignments and projects.
Which view is the correct one? Both of them are! Mathematics can be viewed as being both a product as well as a process – a product of great human ingenuity made up of a series of rich, interconnected conceptual structures derived through a process of inquiry, significant mental effort, and sheer dogged determination and perseverance. The chief driving force underlying much of mathematics has been the search for abstract patterns – patterns in ideas derived from observation or through the workings of the mind. One can say that mathematics is the science and art of patterns and mathematicians are essentially makers of patterns (Hardy, 1967).
Helping us interact with the world around us
As the science and art of patterns mathematics equips us with the requisite knowledge for understanding and interacting with the world around us – a world that is steeped in patterns such as those found in numbers, shapes, space, position, motion, change, chance, and population characteristics (Devlin, 2000). This has made mathematics exceedingly useful. It is an indispensable tool that has greatly aided the development of other fields of knowledge such as the sciences, technology, engineering, architecture, economics, and geography as well as activities such as commerce, manufacturing, and banking.
It’s a concise, unambiguous and powerful language
Mathematics is also useful because it is a concise, unambiguous, and powerful language (Cockcroft, 1982) that enables us to communicate ideas that are difficult to express through other means. A mathematical statement such as ‘4 x 5 = 20’ can be used to represent diverse situations such as the total cost of 4 objects at 5€ each or the area of a patio 4m by 5m or the total number of oranges in four bags containing five oranges each, as well as various other possible real or abstract situations. This shows how rich, unique, versatile, and functional the language of mathematics can be. Numbers, letters, equations, graphs, tables, geometrical figures, and other modes of representation allow us to encode ideas and relationships not only in a variety of ways but, more importantly, precisely, and succinctly. Moreover, as a universally understood and accepted medium of communication that prevails over cultural, linguistic, and social barriers mathematics allows us to share these ideas not only through space but also through time. Mathematics connects people together!
Part 3 will focus on the indispensability of Mathematics as a tool that can be used universally.
Disclaimer: Opinions and thoughts expressed within this article do not necessarily reflect those of the University of Malta.