Graph interpretation skills among lower-achieving school leavers

Research in Education, Nov 1998 by Swan, Malcolm, Phillips, Richard

at mathematical skills does everybody need to operate in the real world? Alongside the need to understand money and measurement, most people's list would include the ability to interpret simple graphs and charts. Their prevalence in newspapers, on television and in other media makes them an essential part of modern life. Traditionally the school curriculum has emphasised graph construction skills (e.g. the ability to plot a graph from a table of values) but in the real world graph interpretation skills are probably of greater importance. This article reports on the graph interpretation skills of a group of lower-achieving school leavers in England. The study questions how well the school system has delivered these important skills.

In the past a number of studies have drawn attention to the inadequate graph interpretation skills of secondary and older students (e.g. Vernon, 1946; Kerslake, 1981; Padilla et al., 1986; Swatton and Taylor, 1994; McFarlane, 1994). Generally these report data where a substantial proportion fail to answer graph interpretation tasks set by the researcher. The reasons for failure are not easy to analyse. The context of a graph is of considerable importance: this is demonstrated by Preece and Janvier (1993), where 14 and 15 year olds interpreted two graphs with the same syntax but with different contexts.

Bell et al. (1987) applied diagnostic teaching methods to graphical interpretation. They identified the following main areas of difficulty in the understanding of graphs by 14 year olds: Interpreting a graph as if it were a picture. Co-ordinating two variables.

Identifying the type of variation (e.g. linear v. non-linear). Interpreting intervals and gradients. Whereas most discussions of secondary school students emphasise their failure, some recent studies reviewed by Phillips (1997) show that children as young as 7 or 8 can sometimes understand line graphs and scatter graphs to a greater extent than was previously supposed. It is important that students have sufficient time and support for the context to become familiar, and most of the successful activities make some use of computers (e.g. Corcoran, 1991; Pratt, 1994). It is not easy to reconcile these reports with the more pessimistic statements about older students. A number of recent changes in England may have improved the level of graph interpretation among school leavers. They include changes in examination syllabuses, in the National Curriculum, in the availability of textbooks and other material supporting graph interpretation activities, and the increased frequency of computer-based activities with graphs.

The English National Curriculum now requires graph work at Key Stage 2 (from age 7 upwards) and graph interpretation questions now feature regularly in GCSE mathematics examinations (taken at age 16). Innovative ideas for teaching graph interpretation (e.g. Swan, 1986) are increasingly appearing in mainstream mathematics textbooks. Although information technology work with graphs is patchy in schools, it does occur in a number of different contexts: in data logging activities, with databases and spreadsheets, in simulation and modelling software, as well as in software specifically written to develop graph interpretation skills. Some of these activities use graphing calculators as well as computers. Although information technology is not the main focus of this article, it is of importance and could be investigated more fully in future research.

The present study analyses data from a group of lower-achieving school leavers in an attempt to offer a balanced and current picture of their understanding of graphs.

Method Sample The test was given to 101 students who had gained a grade D or E in the GCSE mathematics examination and who were planning to resit. These grades cover roughly the forty-fifth to the eightieth percentiles. The sample was drawn from the first year in seven mathematics classes at four further education colleges in the Nottingham area. The purpose behind identifying this sample was formative. We intended to adapt the repeat GCSE courses to improve the facility of students in this field. Students with grades D and E constitute the majority on such courses.

Test The aim of the graph test was to assess a broad range of skills involving the production and interpretation of graphs, including some understanding of function. Contexts were chosen to be familiar to students. The test was specially developed for this study but adapted a number of items from a tests used by Hart et al. (1985) and Brekke (1987) and from Swan (1986). Fuller details of the test are reported by Swan (1997, 1998). No interviews were conducted with students, but for a fuller picture of students' misconceptions see the specimen responses reported by Brekke (1987) and Swan (1990). Other questions Five other questions were included in the test but, because of limitations of space, are not reported in detail. 'A journey to college' (question 3) asked students to write a written description of a journey from a distance/time graph. The skill of putting a story to a graph is of considerable importance in graph interpretation, because a full understanding of a graph often depends on surmising extra information that is not explicit in the graph. It is not an easy skill and it is confounded by the problem that students may not regard the creative activity of story telling as an appropriate activity for mathematics lessons. Only 16 per cent succeeded, while 21 per cent made a classic error of reading the graph as if it were a picture (see Janvier, 1978).