A validation of eye movements as a measure of elementary school children's developing number sense
Section snippets
The number line estimation task as a measure of number sense
As a very broad construct, number sense can be measured in several ways (Berch, 2005; Jordan, Kaplan, Oláh, & Locuniak, 2006). One way, suggested by Siegler and Opfer (2003), is especially useful. Siegler and Opfer asked children to estimate the positions of given numbers on an external number line where only the starting and the end points were labeled. They interpreted the patterns of estimates as indicative of children's representation of magnitudes on their internal number line. These
The added value of eye-tracking
Despite its potential benefits, the number line estimation task has a major drawback. Although it is easy to measure such products of children's estimation processes as accuracy, solution times and estimate patterns, it is hard to investigate the processes themselves that children employ to construct their solutions.
In a cross-sectional study with children in Grades 1–3, Petitto (1990) identified two types of solution strategies. To find the magnitude represented by a position on the line, most
The current study
Research on the development of children's number sense and its relations to other competencies, we propose, may benefit from the inclusion of eye-movement data because of their objectivity and their potential to reveal underlying processes. However, the validity of eye-movement data for the number line estimation task is as yet unclear and must be established. Furthermore, as noted earlier, little is known about the relation between number sense and the addition skills of typically developing
Participants
Sixty-six children from two public primary schools in Berlin participated in the study. Both schools are attended by mostly Caucasian middle-class to upper middle-class children. At each grade level, half of the children were recruited from one school, the other half from the other. The schools did not differ with respect to instructional approaches. All children were selected by teachers on the basis of average or above-average mathematical achievement. This was done to reduce error variance
Results
Results by grade level are shown in Table 1. Each of the three variables shows significant increases across grade levels. Addition accuracy increases most strongly from 15 to 91% and has the highest proportion of explained variance, as indicated by η2 values. The effect sizes also show that grade-related increases in knowledge are more clearly reflected by estimation accuracy than by fixation accuracy. Of the three variables, fixation accuracy shows the least change and the smallest, albeit
Discussion
The present results suggest that eye-tracking data collected with the number line estimation task are a valid, detailed, and sensitive indicator of children's developing number sense. We presented five pieces of empirical evidence in support of this claim, which correspond to our five research questions. Children's fixations (a) validly reflect grade-related competence increases, (b) are closely related, in Grades 2 and 3, to manual solutions of estimation tasks, (c) are related, in Grade 2, to
Acknowledgements
This work was supported by a grant from the German Federal Ministry of Education and Research (BMBF), funded under the interdisciplinary research initiative Neuroscience, Instruction, Learning (NIL). It was additionally funded by the GOA grant 2006/1 from the Research Fund K.U.Leuven, Belgium.
We thank Katharina Tempel for her assistance with data collection. Bert De Smedt and Joke Torbeyns are Postdoctoral Fellows of the Fund for Scientific Research-Flanders (Belgium).
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