How reliable is the Give-a-Number task?

• In Event: New Developments in the Science of Numerical Thinking

Abstract

The Give-a-Number task has become a gold standard of children’s number word comprehension in developmental psychology. In the task, the experimenter provides a child with a set of counters (e.g., 10 toy apples), and asks them to give specific numbers of things – e.g., “Can you put one apple on the plate?”. Next, they proceed to other numbers, with the goal of identifying the highest number word that the child understands (i.e., their “knower level”). The importance of the task stems in part from its use to document a sequence of knower level stages, which has been reported across different labs, languages, and cultures. Also, recently, researchers have begun to use the task as a predictor of other developmental milestones. This raises the question of how reliable the task is, since test-retest reliability of any measure places an upper bound on the size of reliable correlations that can be found between it and other measures. In Experiment 1, we presented 81 2- to 5-year-old children with Wynn’s (1992) titrated version of the Give-a-Number task twice within a single session. In this titrated version, if a child responds correctly to a request (e.g., giving exactly 2 objects when asked for two), they are then tested with the next largest number (e.g., three), whereas if they fail, they are tested on a smaller number. This procedure is repeated until the experimenter is able to identify the highest number that a child can consistently succeed at. We found that the reliability of this version of the task was high overall (kappa = 0.866; Figure 1), but varied importantly across different knower levels, and was very low for some knower levels, especially among higher subset-knower stages (i.e., 3-,4-,5-knowers), placing into question the robustness of these higher stages, and their utility as predictors in statistical models. In Experiment 2, we assessed the test-retest reliability of the non-titrated version of the Give-a-Number task, with another group of 81 children. In the non-titrated version of Give-a-Number, participants are tested on all numbers of interest (e.g., 1, 2, 3) three times each in pseudo-random order. Similar to Experiment 1, we found that the reliability of the non-titrated version was overall high (kappa = 0.815; Figure 2) but differed across individual knower-levels. Finally, in Experiment 3, we asked whether the two versions of Give-a-Number generated different knower levels within-subjects, by testing 75 children with both tasks in a single session. Also, we asked whether either version better predicted a third commonly used test of number knowledge, the “What’s-On-This-Card?” (WOC) task. We found that overall, the titrated and non-titrated versions of Give-a-Number yielded similar knower levels (kappa=0.706), and that neither was more closely related to the WOC task. In fact, both Give-a-number versions generated lower knower levels than WOC. We discuss implications of these results for the knower level stage theory and recommendations regarding when to use each version of the Give-a-Number task, and how to best use knower levels as predictors in statistical models.

Authors

• Elisabeth Marchand, University of California - San Diego
  Presenting Author

• David A Barner, University of California - San Diego
  Non-Presenting Author