Number Representation: A Question of Look? The Distance Effect in Comparison of English and Turkish Number Words

Order processing of number symbols is influenced by direction, but not format

This study probed the cognitive mechanisms that underlie order processing for number symbols, specifically the extent to which the direction and format in which number symbols are presented influence the processing of numerical order, as well as the extent to which the relationship between numerical order processing and mathematical achievement is specific to Arabic numerals or generalisable to other notational formats. Seventy adults who were bilingual in English and Chinese completed a Numerical Ordinality Task, using number sequences of various directional conditions (i.e., ascending, descending, mixed) and notational formats (i.e., Arabic numerals, English number words, and Chinese number words). Order processing was found to occur for ascending and descending number sequences (i.e., ordered but not non-ordered trials), with the overall pattern of data supporting the theoretical perspective that the strength and closeness of associations between items in the number sequence could underlie numerical order processing. However, order processing was found to be independent of the notational format in which the numerical stimuli were presented, suggesting that the psychological representations and processes associated with numerical order are abstract across different formats of number symbols. In addition, a relationship between the processing speed for numerical order judgements and mathematical achievement was observed for Arabic numerals and Chinese number words, and to a weaker extent, English number words. Together, our findings have started to uncover the cognitive mechanisms that could underlie order processing for different formats of number symbols, and raise new questions about the generalisability of these findings to other notational formats.

Verbal count sequence knowledge underpins numeral order processing in children

Recent research has suggested that numeral order processing - the speed and accuracy with which individuals can determine whether a set of digits is in numerical order or not - is related to arithmetic and mathematics outcomes. It has therefore been proposed that ordinal relations are a fundamental property of symbolic numeral representations. However, order information is also inherent in the verbal count sequence, and thus verbal count sequence knowledge may instead explain the relationship between performance on numeral order tasks and arithmetic. We explored this question with 62 children aged 6- to 8-years-old. We found that performance on a verbal count sequence knowledge task explained the relationship between numeral order processing and arithmetic. Moreover many children appeared to explicitly base their judgments of numerical order on count sequence information. This suggests that insufficient attention may have been paid to verbal number knowledge in understanding the sources of information that give meaning to numbers.

Magnitude processing of written number words is influenced by task, rather than notation

The extent to which task and notation influence the processing of numerical magnitude is under theoretical and empirical debate. To date, behavioural studies have yielded a mixed body of evidence. Using the case of written number words in English and Chinese, we re-examined this issue. Thirty-nine bilingual participants who showed a balanced profile of language dominance in English and Chinese completed three tasks of numerical processing (Magnitude Comparison, Numerical Matching, and Language Matching) with pure English, pure Chinese, and mixed notation number words. We conducted frequentist and Bayesian statistics on the data. Magnitude processing, as indexed by the numerical distance effect (NDE), was found to be dependent on task. Specifically, the NDE occurred in all notation conditions in the Magnitude Comparison Task and mixed notation trials in the Numerical Matching Task only. However, the data indicated that magnitude processing was independent of notation. Task and notation had an interactive influence on overall speed of processing, where participants responded to Chinese number words significantly faster than other notations for the Magnitude Comparison and Numerical Matching Tasks only. Finally, Bayesian analyses indicated that task and notation do not interact to affect magnitude processing. Specifically, the Bayes Factor and posterior model probabilities of the Bayesian ANOVA yielded strongest support for the model with three main effects (Task, Notation, Numerical Distance) and two two-way interactions (Task × Numerical Distance, Task × Notation). These findings highlight the critical role of task in numerical magnitude processing, provide support for a notation-independent account of magnitude processing, and suggest that linguistic/orthographic factors, combined with task, may interact to affect overall speed of processing.