The construct and measurement of spontaneous attention to a number

Abstract

The Spontaneous Attention to a Number (SAN) construct serves a different purpose than Hannula-Sormunen and colleagues’ Spontaneous Focus on Number (SFON) construct. As an extension of Eleanor J. Gibson’s differentiation theory, the premise of SAN is that children’s step-wise construction of small number concepts enables them to perceptually differentiate among increasingly larger numbers—to distinguish reliably between “oneness” or “twoness” and larger numbers, then between “threeness” and “larger numbers,” and eventually between “fourness” and larger numbers. In contrast, SFON refers to the tendency to attend to numbers in general—an attentional process that, unlike SAN, is separate from enumeration skill. Not surprisingly, then, although the prototype for both the SAN and SFON tasks is Nancy C. Jordan and colleagues’ non-directive nonverbal number task, the independent development of the SAN and SFON tasks resulted in key differences in how they are administered and scored and to whom they are administered.

Key words:

• Spontaneous attention to number
• differentiation theory
• early childhood
• number development
• mathematics learning.

Notes

1. Dr Hannula has long claimed that the nonverbal production task developed by Jordan and colleagues (1992) and Huttenlocher et al. (1994) are not the prototype for SFON tasks—that SFON tasks are the original means for assessing unguided attention to number. In a personal communication dated July 28, 2006, she noted:

I’d like to correct [a] clear misunderstanding … Any of the 15 SFON [tasks] that we have developed [are] not Huttenlocher et al. [nonverbal production] task, in which children’s attention is clearly directed to the number aspect of the task. If you read the method of the study, [it specifies] “the child was asked to place an appropriate number of disks on his or her mat” (emphasis added). This is not a SFON task at all! … The … SFON [tasks provide] … no hints towards number.

Dr Hannula's claim was based on an understandable, but unfortunate, misinterpretation of Jordan and colleagues’ (1992) and Huttenlocher et al. (1994) incomplete description of their task. The phrase cited above in italics is a “description of what the child was supposed to do,” not what participants were actually told to do (N. Jordan, personal communication, August 7, 2015). Hannula et al. (2010) subsequently described Huttenlocher et al.'s instruction correctly but inaccurately maintained that task specifically guided a child’s attention toward number, because of the demonstration/practice trials with one and two. Hannula et al.’s (2010) criticism would be valid if the demonstration or feedback (e.g., placing the correct amount on the child’s mat) had, for example, included non-examples that eliminated competing non-numerical features from consideration. In conclusion, it would be fair to say that Hannula and colleagues were the first to intentionally measure spontaneous attention to number. However, SFON tasks are more akin to Jordan and colleagues’ (1992) and Huttenlocher et al. (1994) nonverbal production task than the non-verbal matching SAN task in two ways: the task demands of maintaining a mental representation of a collection and the (relative) absence of competing qualitative or non-numerical features.