Making sense of realistic word problems: portraying working class ‘failure’ on a division with remainder problem

Abstract

Children of 10–11 years of age were interviewed while undertaking a range of mathematic problems, most of which embedded mathematical operations in textually represented realistic settings. One problem, concerning a lift moving people in the morning rush, comprised a division‐with‐remainder problem in which children are required, conventionally, to introduce a particular realistic consideration in order to produce the ‘correct’ answer. Another problem was an extended version of this, requiring children to comment on four competing answers produced by other children. Analysis of responses to the first of these two problems demonstrated that it was working class children who were especially likely to fail to produce the conventionally required answer. Having shown this, the paper concentrates on portraying the ways in which ‘failing’ working class children interpret and respond to the two problems. Our purpose here is to contribute to understanding the difficulties working class children appear to have in negotiating the demands of contextualized problems.

Notes

1. The original item was set for 13‐ to 14‐year‐olds, but with more difficult numbers than we use here with 10‐ to 11‐year‐olds (Schools Examinations and Assessment Council, 1992). In the terminology of the English National Curriculum in mathematics, the source item, with the more difficult numbers, was rated as Attainment Level 4. Current government targets for children’s achievement at the end of primary schooling, i.e., for 10‐ to 11‐year‐olds, are that 85% should reach Level 4 by 2004.

2. There has been, of course, a longstanding and ongoing debate about the conceptualization (even the existence) of social class and also about measures of socio‐economic status (Marshall et al., 1988; Hauser & Warren, 1997; Rose & Pevalin, 2001). We believe that the value of occupationally based measures for a variety of purposes has been demonstrated (Erikson & Goldthorpe, 1993). We also hold, as a working assumption, that there is likely to be a continuing relation in class‐differentiated societies, as there has in the past (Kohn & Schooler, 1969, 1983; Holland, 1981; Bourdieu, 1986), between parents’ occupational experiences and their childrearing practices, with resulting class‐linked consequences for children’s thinking. It is of course possible, even likely, that social change in recent decades (Roberts et al., 1977) has diminished the strength of such relationships. At root, this is an empirical question. The particular parental social class categories used in the current study are taken from Goldthorpe and Heath (1992) and Erikson and Goldthorpe (1993). Their dominance approach, which recognizes the contribution of both parents while taking account of their respective commitment to the paid labour market, has been used (Erikson & Goldthorpe, 1993, p. 238). We have only a snapshot at one point in time of parents’ occupational trajectories, and this limitation should be borne in mind (Featherman et al., 1988). The service class comprises: (1) higher grade professionals, administrators and officials; managers in large industrial establishments; large proprietors; and (2) lower grade professionals, administrators and officials; higher grade technicians; managers in small industrial establishments; supervisors of non‐manual employees. The intermediate class comprises (3) routine non‐manual employees; (4) personal service workers; (5) small proprietors with employees; (6) small proprietors without employees; (7) farmers and smallholders; and (8) foremen and technicians. The working class comprises (9) skilled manual workers; (10) semi‐ and unskilled manual workers; and (11) agricultural workers.

3. However, we should note that the sample does not meet the ideal conditions for using this technique. It is small and, more importantly, not simply random. These results should therefore be regarded as indicative of a possible social class ‘effect’. They offer some support for this, but they clearly do not establish it beyond doubt. In addition, ideally we would want a measure of ‘ability’ here rather than prior achievement.

4. More exactly, 37.8% on Cox and Snell R square, and 51.1% on Nagelkerke R square.

5. Using forward conditional logistic regression, social class is entered on Step 1, and prior mathematics achievement on Step 2.

6. A case could be made for placing him in Cell 1.

7. The placement of Scott in Table 5 is difficult. We have decided to enter him in Cell 6, but a good case could be made for Cell 3.