Toddlers' Spontaneous Attention to Number

Abstract

Hannula and Lehtinen (2001, 2005) defined spontaneous focusing on numerosity (SFON) as the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these “intuitive numbers” in everyday situations—even before they acquire language. If so, their tendency to attend to two and three should be comparable. If language in the form of the first few number words facilitates the construction of these number concepts, then toddlers' tendency to focus on two and three should parallel the staggered development of verbal number skills. The present study is the first to systematically examine if and how the size and makeup of a collection affect toddlers' tendencies to focus on number. For each of two types of attention tasks, each of 37 participants between the ages of 2 and 4.25 years old was shown 36 different collections of 2, 3, and 4 items that were homogeneous, semihomogeneous (the same shape but two different colors), or heterogeneous (two different shapes and two different colors). Age, size, and makeup had a significant effect on participants' tendency to attend to number. The significant drop off in this tendency with collections of more than two items is inconsistent with the nativists' hypothesis of an innate cardinal concept of three.

The research described was supported, in part, by a grant from the National Science Foundation (BCS-0111829), the Spencer Foundation (Major Grant 200400033), and the National Institutes of Health (1 R01 HD051538-01). The opinions expressed in the present manuscript are solely those of the authors and do not necessarily reflect the position, policy, or endorsement of the National Science Foundation, the Spencer Foundation, or the National Institutes of Health.

Notes

1. For instance, the training (habituation) procedures used in infant and animal studies might enable participants to form a number-like category or even a number category, if only temporarily. That is, extant infant and animal research may simply be revealing learning potential or transient learning, not innate knowledge of cardinal numbers (Baroody, 1992).

2. Starkey and Cooper's (1995) participants compared arrays that were one less than, equal to, or one more than a standard array of one to six items (one, two, and one trials, respectively, for each standard) and indicated whether an array was “the same” or “not the same” as the standard array. Two year olds successfully compared one and two when one was the standard (1-to-1 and 2-to-1 trials) with at least 92% accuracy. Likewise, except for the single 3-to-2 trial (75% success rate), they successfully made comparisons on trials involving two as the standard (the single 1-to-2 and the two 2-to-2 comparisons) with at least 92% accuracy. However, except for the 2-to-3 comparison (100%), the 2 year olds successfully made comparisons involving three (comparing 3 to 3 twice and 4 to 3 once) with only 67% to 79% accuracy. (A 50% success rate could be expected by chance alone.) Although nine of the twelve 2 year olds were successful on the majority of the four trials in which three was the standard (p < .025, binomial theorem), some of these participants may have gotten three or four items correct by chance alone (cumulative probability = .3125; expected value by chance = 3.75 participants), and others may have done so by using an inexact representation of three.

3. The collections of three and four we composed from two forms and two colors (e.g., two blue T-Rexes and a red Triceratops or two blue T-Rexes and two red Triceratops) might better be called partially heterogeneous or semiheterogeneous because each element of the collection did not differ in appearance from all other elements in the collection. However, for the sake of simplicity, we use the term heterogeneous for these collections as well.