The effect of horizontal versus vertical 1 RUNNING HEAD: CHILDREN’S PERFORMANCE IN COORDINATE TASKS The effect of horizontal versus vertical task presentation on children’s performance in coordinate tasks

Empirical work on children’s ability to understand spatial coordinates has focused on the factors that increase children’s proficiency. When interpreting performance, it should be considered that presenting a coordinate task on a horizontal surface might constrain the responses that children make because some target positions are further away from the child than others. Vertical task presentation removes this constraint. Threeto nine-year-old children were presented with an interpretative coordinate task administered on a touchscreen, presented in an egocentric-vertical position or -horizontal position. The results show that for 5to 7-year old children vertical presentation led to far more correct responses than horizontal presentation. Analysis of the children’s errors suggested that this may arise due to the fact that vertical presentation suppresses children’s bias towards responding in relation to one rather than both coordinates. Taken together these findings contribute to understanding why children’s performance in xy coordination tasks is highly contextually sensitive. The effect of horizontal versus vertical 3 There exists much debate over the age at which children are believed to possess the skills required to coordinate spatial dimensions, and the developmental acquisition of the necessary components of Euclidean awareness required for this. Piaget and Inhelder (1956) outline three levels in children’s spatial development; topological, projective and Euclidean. Although proficiency in the coordination of dimensions does not develop until the Euclidean stage, concepts acquired at the preceding stages are prerequisites for the resolution of coordinate problems. A coordinate reference consists of two orthogonal dimensions, one horizontal and one vertical, that give reference to a point in space at their point of intersection. In order to accurately coordinate horizontal and vertical dimensions, a child is required to identify the horizontal and vertical axes, extrapolate straight lines from the orthogonal axes (a characteristic of the projective stage), and coordinate these two lines to find their point of intersection. Further task demands include aspects of working memory, in order to imagine where the two lines indicated by the orthogonal markers intersect. A task administered by Piaget Inhelder and Szeminska (1960) indicated that children were unable to use a coordinate system to locate a point in space until the age of eight or nine years, once the stage of concrete operational thought had been reached. Children were presented with two rectangular pieces The effect of horizontal versus vertical 4 of paper, differing in orientation, at opposite ends of a table. Children were required to reproduce a point (P1) from sheet 1 (S1) onto sheet 2 (S2), being provided with a ruler and strips of paper, lengths of thread and a stick. It was not until the age of eight or nine years that children spontaneously used a coordinate system to make the transformation. However, this task was ambiguous in its requirement of the use of a coordinate system. In the task, children were required to recognise that using a coordinate system would provide a potential solution to the problem, which may be a possible explanation for why children did not succeed until the age of nine years. Whilst Piaget et al. may have been correct in asserting that spontaneous coordinate use does not develop until the age of eight or nine years, this initial study provides little insight into the age at which children can use a coordinate system if it is presented to them (Somerville & Bryant, 1985). More recent research using a variety of methodologies and task contexts has demonstrated successful performance in coordinate tasks in much younger children, in some cases from the age of four years. Children’s proficiency is increased in cases where the task is made less abstract (for example replacing letters and numbers as grid references with coloured circles as reported by Blades & Spencer, 1989). Children also perform well where the task makes more ‘human sense’, such as where the dimensions to be coordinated are the The effect of horizontal versus vertical 5 imagined paths that two model people would walk (Bremner, Andreasen, Kendall & Adams, 1993). Children also demonstrate the ability to provide the coordinate references for a given point in space in ‘construction’ tasks (e.g. Cochran & Davis, 2005; Lidster & Bremner, 1999) and coordinate dimensions in arrays with up to 16 target positions (e.g. Blades & Spencer, 1989). It has been proposed by many researchers (e.g. Blades and Spencer, 1989; Bryant and Somerville, 1986; Somerville & Bryant, 1985) that such adeptness in the utilisation of rectangular coordinate systems serves as an illustration of young children’s understanding of Euclidean geometry. This understanding of Euclidean space can therefore be seen as a precursor for the development of further spatial awareness. These findings have important educational implications. The principles involved in the coordination of dimensions are not introduced into the UK National Curriculum until the ages of seven to eight, and children are not expected to read and plot coordinates until the ages of nine to ten. The age at which these concepts are introduced is, not surprisingly, in line with the age at which Piaget suggested children possess the necessary understanding (Davis, 2003). However, more recent demonstrations of proficiency in much younger children have led to suggestions that the concepts underlying the use of The effect of horizontal versus vertical 6 coordinates can be introduced at a very young age (e.g. Blades & Spencer, 1989; Lidster & Bremner, 1999). However, it is important to consider that such successful performance in young children may well be because of their ability on certain types of trials. Lidster and Bremner (1999) found differences in children’s ability to coordinate dimensions for different trial types, in particular superior performance on nearnear trials, where the target is in the quadrant that is close to the horizontal and vertical pointers. Far-far trials, where the target quadrant is far from both pointers were the most difficult. Similar differences were also found by Cochran and Davis (2005) in a constructive coordinate task, where children were required to indicate the correct orthogonal pointers for a given target quadrant. The most plausible interpretation of these findings is that they serve as an illustration of children’s difficulty in extrapolating the imaginary lines of intersection to targets in a distal position to the pointers (Bremner et al., 1993), with children having little difficulty in trials where target positions are proximal to the pointers. Whilst above-chance performance in coordinate tasks has been demonstrated by young children, errors are still prevalent. Of interest are the types of error children make, and what this reveals about the strategies children employ in a coordinate task. Bremner et al. (1993) conducted an analysis of the The effect of horizontal versus vertical 7 types of errors children make in an interpretative coordinate task with a 2x2 grid, suggesting that when children make an error they attend to only one of the two pointers (i.e. only one axis) and select a target position in relation to that pointer. Errors were classified as either next to one pointer in the near-far dimension, next to one pointer in the left-right dimension, far from one pointer in the near-far dimension, far from one pointer in the left-right dimension, or not in line with either pointer. They found that the dominant error type was selecting a position next to one of the pointers, suggesting this to be the strategy that children use in these tasks. Consistent application of a next-to-pointer strategy would lead to 100% success on near-near trials, 50% success on nearfar and far-near trials, and 0% success on far-far trials. Bremner et al. observed that the performance of the 4-year-old children they tested closely approximated this pattern on a standard coordinate task. Here we see another possible explanation for the pattern of success in different trial types explained above. Although near-ceiling performance is often observed in near-near trials, this might not necessarily reflect children’s ability to coordinate the two dimensions. Instead, success on these trials could arise simply by children applying a next-to-pointer strategy. Cochran (2006) found similar distributions of error types, with next-to-pointer errors being the most frequent type (72% of all errors). These two reports of error analyses, along with similar findings by The effect of horizontal versus vertical 8 Blades and Spencer (1989), indicate that children’s errors are far from random. This suggests that children might be consistently employing a strategy in such tasks, and that errors and correct responses might be the result of the application of the same strategy. If this is indeed the case, task presentation factors could have an effect on the strategies children employ. Previous studies examining children’s strategy use in a coordinate task, due to the use of table-top apparatus, have administered the task on a horizontal surface (e.g. Bremner et al., 1993; Cochran, 2006). With such horizontal presentation, irrespective of where the child is sitting or standing, and irrespective of the size of the array, some of the target positions will be further away from the child than others. For this reason, we suggest that presenting a task to children on a horizontal surface might constrain their responses and if so might influence their response strategy. In the experiment presented here, we wanted to compare performance on an egocentric-horizontal presentation with an egocentric-vertical presentation where all target positions and pointers are equidistant from the child. We expect fewer errors to be made in the vertical condition when compared to the horizontal condition, and predict that condition might influence the strategies children use in order to complete the task. The effect of horizontal versus vertical 9