What makes fractions so vulgar?

Literature review

Not just in britain, but across europe there is increasing concern regarding the numeracy skills of adults. For example, the adult basic skills strategy unit, in concert with the european social fund, launched a numbers in everything campaign in 2004 to address the issue of adult numeracy (niace 2006). Respondents to the skills for life survey performed at lower levels on numeracy assessment than on literacy assessment (dfes 2003, 18). The adult math project addressed concern regarding numeracy issues amongst adults as far back as 1978 (evans 2000).
One of the reportedly most despised and difficult areas of mathematics in the minds of adults is fractions; many adults have difficulties with fractions as they had difficulty learning fractions as children, no longer practice them after leaving school, and rarely use fractional computations in their everyday life (chinn 2004).
Adults first have difficulty defining what a fraction entails; for most it is simply one number written above another with a line inbetween (chinn 2004). There is little understanding of the relationship inherent in fractions, or of fractions beyond a single unit as whole. Many separate the mathematical representation of fractions they learned in school from the deeper fractional concepts these mechanical manipulations represent (chinn 2004). Theunissen (2005) discusses the complexity of fractions, presenting them as division, as position, as process, and as algorithm. Few adults have this level of understanding of the definition or complexity of fractions. In addition, words used in fractions and related mathematics are often misused or present barriers to those attempting to learn (chinn 2004).
Mathematics instruction has traditionally focused on solving rather than understanding, particularly at the primary school level, where fractions are most typically introduced (evans 2000). In school, fraction computations are usually presented as a series of steps or methods to be memorized. The idea is that working these mathematical problems will lead the pupil to an understanding of the concpets behind them (gal 2002). However, this is often not the case. Gal (2002) contends it is “important to acknowledge the difference between mastery of computational and procedural skills and much broader understanding of principles and underlying ideas”(21).
In the area of cognition, learning fractions should lead to an understanding of proportional reasoning, a vital life skill (chinn 2004). Some adults were unable to master the computational processes of fractions when they were presented with them as children, but are able to master the computations when they approach the maths later in life (evans 2000). Unfortunately, “mathematical learning is a cumulative process so that a poorly developed concept of number can affect the acquisition of number facts and by the same token, poor arithmetic ability can compromise the growth of mathematical knowledge” (chinn 2004, vi). This can lead to poor self-efficacy in mathematics, difficulties in advanced maths, and math anxiety. Evans (2000), for example, provides extensive coverage of how math anxiety and other barriers to adult learning develop from childhood experiences.
Further, adults often question the usefulness of fractions in their everyday lives. Part of this results from emphasis on the computations of fractions rather than the cognitive understanding of proportional reasoning. Caunt (2001) contends “there is an overemphasis on the need for adults to have numerical skills to check that figures are correct, rather than on the need for numerical awareness to analyse and interpret what information is being presented”(19). “quantitative skills desired by employers are much broader than mere facility with the mechanics of addition, subtraction, multiplication and division and familiarity with basic number facts; they also include some knowledge of statistics, probability, mental computation strategies, some grasp of proportional reasoning or modeling relationships, and broad problem-solving and communication skills about quantitative issues” (gal 2002, 22).
To assist adults in developing these conceptual and computational skills, teaching methods and language that relate what is being taught to life experience is vital (chinn 2004). Experiential learning is an important method for education at any level, but must be reformatted in many cases to be appropriate for an adult learner. For example, pouring water and sand is fine for children, but may not be as readily accepted by adult pupils.
Overall, literature supports that most adults dislike fractions because they do not understand them. This makes working fraction problems mechanical and without meaning. Further, although they are likely to see them as less useful in their everyday lives, fractions represent an important conceptual area necessary for productive workers and citizens (niace 2006).

Methodology

As the reasons for adults' difficulties and dislike of fractions are likely to be complex, a qualitative research method is planned. Specifically, two focus groups are planned. The first focus group will consist of six to ten adults will be undertaken. This focus group will hopefully be comprised of adults from a spectrum of backgrounds, including different social classes, ethic backgrounds, and educational attainments. The unifying criteria of the group will be that all participants must have had difficulty learning fractions and dislike or disliked this area of mathematics. A set of open-ended questions will be designed to spur the group on to discussion regarding difficulties in mastering fractions, fractions' usefulness in everyday life, and various teaching methods experienced by participants. The second focus group will be of adult educators who teach mathematics. A series of open-ended questions will also be planned to guide this group, but with focus on teaching methods. Both focus groups' discussions will be recorded, with the transcript then coded and statistically evaluated.

References

Bsa 2001. The adult numeracy core curriculum. Basic skills agency.
Caunt, j.C. 2001. Adult numeracy. Adults learning, june 2001, 12(10): 19-20.
Chinn, s. 2004. The trouble with maths: a practical guide to helping learners with numeracy difficulties. London: routledgefalmer.
Dfes 2003. The skills for life survey. A national needs and impact survey of literacy, numeracy and ict skills. Norwich: her majesty's stationery office.
Evans, j. 2000. Mathematical thinking and emotions. London: routledgefalmer.
Gal i. 2002. Systemic needs in adult numeracy education. Adult basic education, spring 2002, 12(1): 20-33.
Niace 2006. Numbers in everything. Www.Numbersineverything.Org.Uk.
Theunissen, e. 2005. Revisiting fractions. Mathematics teaching, september 2005, 192: 45-47.