A Comparison of Mathematics, Numeracy, and Functional Mathematics: What do they Mean for Adult Numeracy Practitioners?

Abstract

What is Mathematics? The discipline of mathematics has evolved over time and across different civilizations to become the abstract, professionalized body of knowledge within an international community of practice that we know today, and it will continue to evolve as new knowledge is developed and existing knowledge is superseded. The discourse of mathematics in all its various specializations involves certain ways of thinking and acting. From a given, axiomatic, starting point, logical deductions are made. In mathematical modeling, for example, problems are formulated in mathematical terms. However, in order to be useful, the mathematical solution needs to take into account the industrial, social, environmental, etc. contexts. Yet, the optimal mathematical solution may not be most useful in a sense and compromises must be made. There is not one single absolute and infallible mathematic, but rather, a plurality of mathematics which operates on a pragmatic basis, linked to time and place. Academic mathematics as we know it evolved through the confluence of certain socio-cultural conditions, such as the rise of commerce, the need for timesaving devices such as algorithms, as well as the spread of printed material (Restivo, 1992). Unfortunately, the public image of this mathematics is generally a cold, dehumanized process, which as Davis and Hersh (1986, 1988) point out, is actually intrinsic to the fundamental intellectual processes that are inherent to the discipline. However, a paradox exists in the seeming 'demathematization' of society. As technology becomes more sophisticated, there is an apparent reduction in the amount of explicit mathematical knowledge required for its operation, while the amount of implicit mathematics increases. Although the explicit uses in business and industry are generally valorized, they are mostly concealed from view and, with the exception of arithmetic, not visible to the general public except through their experiences of school mathematics. (For further discussion on mathematics, see FitzSimons, 2002.) What is Functional Mathematics? In the United Kingdom, the Qualifications and Curriculum Authority (QCA) website defines functional skills as practical skills in English, Information and Communication Technology (ICT), and Mathematics, that allow individuals to work confidently, effectively and independently in life. Assessment of these applied skills will include electronic and on-screen approaches, and will be based primarily on task-based scenario questions with a limited duration, delivered in a controlled environment. Assessments will use and reinforce skills-based, problem-solving learning techniques. (See Functional Skills website in reference list). The QCA website on mathematics (see Solving Problems in reference list) defines functional mathematics in terms of logical creativity: Mathematics is a creative discipline. The language of mathematics is international. The subject transcends cultural boundaries and its importance is universally recognized. Mathematics has developed over time as a means of solving problems and also for its own sake. Mathematics can stimulate moments of pleasure and wonder when pupils solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Pupils develop their knowledge and understanding of mathematics through activities, exploration and discussion, learning to talk about their methods and explain their reasoning. A workshop on functional mathematics for 14- to 19-year-olds proposed several key themes: (a) relevance of content materials, (b) development of thinking skills, (c) conceptual understanding of mathematics, (d) integrated use of information technology, and (e) comprehensive assessment, including a sustained activity for learners to demonstrate their relatively straightforward mathematical abilities in complex contexts. …