Diagrams in the UK National School Curriculum

We review the use of diagrams in the UK National School Curriculum (NC) and assess it in the light of current research on childrens’ graph comprehension. It is noted that some diagrams are very ubiquitous (e.g. illustrations and bar graphs) whereas other representations which are potentially appropriate for younger children (e.g. hierarchies) are relatively rarely used. We also query some of the teaching practices advocated in the NC in that, for example, diagrammatic representations are conflated with figurative illustrations (pictographs). Suggestions for improving the NC are offered in the conclusion. 1 Diagrams in the UK National Curriculum Despite the calls for a graphicacy curriculum and the growing evidence on children’s diagrammatic abilities (e.g. [2], [6], [7]), it seems that it has yet to influence the UK National Curriculum (NC). We discuss this by presenting (1) results from a survey of the use of different external representations (ERs) in the NC activities, and (2) recommendations from the literature about students’ use of some ERs. These two points are discussed and some recommendations to educators are made about how ERs should be used in the UK school curriculum. The NC sets out the subjects that children should study at each of four key stages (KS) across ages ranging from 5 to 16 years. Each KS identifies a band of school years, with children’s performance assessed at the end of each band. The assessment includes a national test (SAT, Standard Assessment Task) for KS 2 and KS 3. The attainments, knowledge and skills for each subject are outlined in the “Program of Study”. However, the content of each subject is not overly specified in terms of detail. This allows educators to follow other NC guidelines and to freely decide which teaching methods are appropriate for their students. Our focus is upon the National Curriculum in Action [5] because it explicitly presents ER-related classroom activities. ? Corresponding author. 1 For the purpose of this paper, we define them as those graphical representations listed in Table 1 and based on Harris’ diagrammatic taxonomy [3]. 2 See: http://www.qca.org.uk/qca_7124.aspx 3 Such as the “Schemes of Work”: http://www.standards.dfes.gov.uk/schemes3/ 4 http://curriculum.qca.org.uk/index.aspx 2 Grecia Garcia Garcia and Richard Cox Classification of Data Activities were selected and categorized by subject and year. This resulted in a list of activity examples together with descriptions and, in most cases, an example of pupils’ work. The activity examples and their associated sets of ERs were examined, and their representations were categorized and named based on [3] (see Table 1). KS 4 data is not included because our focus is on children below 14 years. Additionally, examples from the subjects ‘Modern Foreign Languages’ and ‘Citizenship’ were excluded because they do not appear in all of the NC key stages. Table 1 shows the ERs found across school years 1-9. The gray boxes indicate that at least one of that table cell’s representations was conflated with pictograms. The practice of conflating diagrammatic and figurative illustrations could be implicated as a cause of misconceptions such as ‘graph-as-picture’ (discussed below). Table 1. External representations found in key stages 1, 2 and 3. ‘Other graphs’ refers to ‘frequency and distribution graph’, ‘radar graph’ and ‘scatter graph’ as in [3]. KS stands for Key Stage. Total KS 1 KS 2 KS 3 Age: 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 Representation vs Year 1 2 3 4 5 6 7 8 9 Illustration chart 137 15 24 7 10 13 20 13 17 18 Table 95 3 7 7 8 11 15 15 11 18 List 32 1 9 3 2 2 3 7 5 Bar graph 29 5 3 4 3 1 6 2 1 4 Map 27 2 3 1 4 2 2 1 4 8 Line graph 15 3 5 1 6 Conceptual diagram 11 1 1 1 1 5 2 Block diagram 10 1 1 1 1 4 2 Flow chart 8 2 2 3 1 Tree diagram 7 2 1 4 Other graphs 5 1 1 3 Tally chart 5 1 2 1 1 Venn diagram 5 2 1 2 Network diagram 3 1 2 Pie chart 3 1 2 Relationship diagram 3 3 Time line chart 3 2 1 Calculation chart/tree 1 1 Cartesian coordinates 1 1 Graph theory 1 1 TOTAL 401 27 53 26 30 33 57 42 56 77 Table 1 shows which ERs are ubiquitous across the 3 key stages. It is interesting to note that there is an increase in the number of different ERs used at the end of each KS (when SAT-type assessment tests are administered). It seems that children are exposed to a wider variety of ERs during those periods. Additionally, mixtures of pictorial and diagrammatic representations were found for several representational forms in the early years. Figure 1 presents an example of a ‘pure’ diagrammatic form and an example of a conflated pictorialdiagrammatic representation. They are representative of those found throughout the NC in Action. Considering the number of ERs in each subject area, it is apparent that illustration charts, tables and lists represent more than 56% of the representaDiagrams in the UK National Curriculum 3 tions in all subjects except in Geography and Physical Education. It would be interesting to establish whether the ubiquity of charts, tables and lists makes the use of representations in the NC too homogeneous. An increased variety of representations in the NC might improve it. For example, [2] has shown that hierarchies can be effectively used in educational contexts by children as young as 7 years. ‘Graphical literacy’ is directly targeted in some subjects. For example, the ICT Schemes of Work (Unit 1E Representing information graphically: pictograms) states: “In this unit children learn how to use ICT to represent information graphically. They learn how to create pictograms and how to answer simple questions on the data shown in their pictograms.” However, it is not clear what is meant precisely by the terms ‘pictogram’ and ‘represent information graphically’. Fig. 1. A scatter graph and a tally chart. Note tally chart includes pictograms. 2 Discussion use of ERs by primary students An issue with curriculum implications concerns children’s graphicacy readiness. Research on children’s ability to use bar graphs indicates that 9 year old pupils have difficulties with comprehension [6]. It seems that children can identify labels in a graph, but they experience difficulties when doing operations and drawing inferences [6]. Nevertheless, first graders are encouraged to use them in the UK NC (see Table 1). In the case of line graphs, 7 and 8 year olds are able to interpret them [7]. However, examples of the use of that ER are not found at that stage (Table 1). Similarly, hierarchies are relegated to the very end of primary school, despite research evidence which shows that children aged 7, 9 and 11 years are able to understand and construct them [2]. As far as we know, the NC contains no clear suggestions to teachers for using hierarchies in teaching and learning contexts. Another area of relevant research is that on children’s misconceptions. In the case of line graphs, it has been noted that some of the students’ difficulties include slope/height confusion (graphs), interpreting intervals, and the graph-as-picture misconception, among others [1, 4, 5 http://www.standards.dfes.gov.uk/schemes2/it/itx1e/?view=get 4 Grecia Garcia Garcia and Richard Cox 7]. In particular, the graph-as-picture misconception seems quite prevalent [1]. Children who have this misconception confuse an abstract, diagrammatic ER with another kind of representation (e.g. confusing a line graph with a map, or a line graph with picture of a mountain range). We suspect that the graphas-picture misconception may be partially due to the frequent use of pictorial representations in conjunction with ‘purer’ diagram forms such as line graphs. Thus, in attempt to introduce formal diagrammatic forms via the inclusion of familiar pictorial images, it is possible that teachers might inadvertently seed pictorial/diagrammatic representational confusions in students’ minds by confounding two entirely different forms of representations (Table 1 gray boxes). In the survey of representations used in the NC there is a disparity between the very prevalent use of illustration charts and bar graphs and other potentially useful alternative forms. Ubiquitous forms potentially ‘displace’ alternative appropriate forms. The NC’s attempt to ‘bridge’ pictorial and diagrammatic representations by combining them might be counterproductive and may engender misconceptions such as the graph-as-picture misconception. The results also suggests that students would probably benefit from earlier instruction in the use of hierarchies and line graphs. A systematic trend was for the variety of representations used in the NC to increase markedly at the end of each key stage (when national achievement tests are administered). To develop their graphical skills, children need broad experience with a varied mix of representations across the curriculum. Research-based ‘graphicacy development’ guidelines could be produced to help instructors. These might include information about methods of teaching representational skills and the matching of representations to tasks. They might also help to prevent the development of graphical misconceptions by students.