Two-digit Number Processing Research Articles

Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking

While reaction time data have shown that decomposed processing of two-digit numbers occurs, there is little evidence about how decomposed processing functions. Poltrock and Schwartz (1984) argued that multi-digit numbers are compared in a sequential digit-by-digit fashion starting at the leftmost digit pair. In contrast, Nuerk and Willmes (2005) favoured parallel processing of the digits constituting a number. These models (i.e., sequential decomposition, parallel decomposition) make different predictions regarding the fixation pattern in a two-digit number magnitude comparison task and can therefore be differentiated by eye fixation data. We tested these models by evaluating participants' eye fixation behaviour while selecting the larger of two numbers. The stimulus set consisted of within-decade comparisons (e.g., 53_57) and between-decade comparisons (e.g., 42_57). The between-decade comparisons were further divided into compatible and incompatible trials (cf. Nuerk, Weger, & Willmes, 2001) and trials with different decade and unit distances. The observed fixation pattern implies that the comparison of two-digit numbers is not executed by sequentially comparing decade and unit digits as proposed by Poltrock and Schwartz (1984) but rather in a decomposed but parallel fashion. Moreover, the present fixation data provide first evidence that digit processing in multi-digit numbers is not a pure bottom-up effect, but is also influenced by top-down factors. Finally, implications for multi-digit number processing beyond the range of two-digit numbers are discussed.

Decomposed but Parallel Processing of Two-Digit Numbers in 1st Graders

It has been suggested that decomposed processing of two-digit numbers develops from sequential (left-to-right) to parallel with age (Nuerk et al., 2004). However, task demands may have provoked sequential processing as a specific rather than a universal processing style. In the current study a standard unit-decade compatibility effect observed in two-digit number magnitude comparison indicated that first graders were already able to process the single digit magnitudes of tens and units separately and in parallel. Consequently, previous findings of sequential processing may be specific for stimulus characteristics in which such a processing style is useful. It is concluded that even first graders seem to be able to adapt their individual processing styles depending on stimulus properties. More generally, this suggests that the manner by which children process two-digit numbers is strategically adaptive rather than fixed at a particular developmental stage.

Impairments of the mental number line for two-digit numbers in neglect

Humans represent numbers along a left-to-right oriented Mental Number Line (MNL). Neglect patients seem to neglect the left part of the MNL, namely the smaller numbers within a given numerical interval. However, until now all studies examining numerical representation have focussed on single-digit numbers or two-digit numbers smaller than 50. In this study, the full range of two-digit numbers was assessed in neglect patients and two control groups. Participants were presented with number triplets (e.g., 10_13_18) and asked whether or not the central number is also the arithmetical middle of the interval. The factors manipulated were decade crossing (e.g., 22_25_28 vs 25_28_31), distance to the arithmetical middle (e.g., 18_19_32 vs 18_24_32), and, most importantly, whether the central number was smaller or larger than the arithmetical middle (e.g., 11_12_19 vs 11_18_19). Neglect patients differed from controls in that they benefited less when the middle number was smaller than the arithmetical middle of the interval. Neglect patients thus seem to have particular problems when accessing the left side of numerical intervals, also when adjusted to two-digit numbers. Such an impaired magnitude representation in neglect seems to have detrimental effects on two-digit number processing as the helpful spatial metric of magnitude cannot be properly activated.