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

Abstract

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.

Keywords

Number magnitude comparison Parallel processing Eye-tracking Unit–decade compatibility effect

Get full access to this article

View all access options for this article.

References

Baayen

R. H.

Davidson

D. J.

Bates

D. M.

(2006). Mixed-effects modeling with crossed random effects for subjects and items Manuscript submitted for publication.

Brysbaert

(1995). Arabic number reading: On the nature of the numerical scale and the origin of phonological recoding. Journal of Experimental Psychology: General 124, 434–452.

Comrie

(2006). Numbers, language and culture Jyvaskyla, FinlandJune Talk held at the NUMBRA (Numeracy and Brain Development) Summer School.

Dehaene

(1989). The psychophysics of number comparison: A reexamination of apparently incompatible data. Perception and Psychophysics 46, 72–80.

Dehaene

Dupoux

Mehler

(1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance 16, 626–641.

Dehaene

Mehler

(1992). Cross-linguistic regularities in the frequency of number words. Cognition 43, 1–29.

Frazier

Rayner

(1982). Making and correcting errors during sentence comprehension: Eye movements in the analysis of structurally ambiguous sentences. Cognitive Psychology 14, 178–210.

Green

H. J.

Lemaire

Dufau

(2007). Eye movement correlates of younger and older adults’ strategies for complex addition. Acta Psychologica 125, 257–278.

Knops

(2006). On the structure and neural correlates of the numerical magnitude representation and its influence in the assessment of verbal working memory Germany: Technical University (RWTH) Aachen Unpublished doctoral dissertation.

10.

Korvorst

Damian

M. F.

(in press). The differential influence of decades and units on multi-digit number comparison. Quarterly Journal of Experimental Psychology.

11.

Liu

Wang

Corbly

C. R.

Zhang

Joseph

J. E.

(2006). The involvement of the inferior parietal cortex in the numerical Stroop effect and the distance effect in a two-digit number comparison task. Journal of Cognitive Neuroscience 18, 1518–1530.

12.

Lorch

R. F.

Jr. Myers

J. L.

(1990). Regression analyses of repeated measures data in cognition research. Journal of Experimental Psychology: Learning, Memory, and Cognition 16, 149–157.

13.

Nuerk

H.-C.

Kaufmann

Zoppoth

Willmes

(2004a). On the development of the mental number line: More, less, or never holistic with increasing age?. Developmental Psychology 40, 1199–1211.

14.

Nuerk

H.-C.

Weger

Willmes

(2001). Decade breaks in the mental number line? Putting the tens and units back into different bins. Cognition 82, B25–B33.

15.

Nuerk

H.-C.

Weger

Willmes

(2002). A unit–decade compatibility effect in German number words. Current Psychology Letters: Behaviour, Brain, & Cognition 2, 19–38.

16.

Nuerk

H.-C.

Weger

Willmes

(2004b). On the perceptual generality of the unit–decade compatibility effect. Experimental Psychology 51, 72–79.

17.

Nuerk

H.-C.

Weger

Willmes

(2005). Language effects in magnitude comparison: Small but not irrelevant. Brain and Language 92, 262–277.

18.

Nuerk

H.-C.

Willmes

(2005). On the magnitude representations of two-digit numbers. Psychology Science 47, 52–72.

19.

Poltrock

S. E.

Schwartz

D. R.

(1984). Comparative judgement of multi-digit numbers. Journal of Experimental Psychology: Learning, Memory, and Cognition 10, 32–45.

20.

Ratinckx

Nuerk

H.-C.

van Dijk

J.-P.

Willmes

(2006). Effects of interhemispheric communication on two-digit number processing. Cortex 42, 1128–1137.

21.

Rayner

(1998). Eye movements in reading and information processing: Twenty years of research. Psychological Bulletin 124, 372–422.

22.

Rayner

Carlson

Frazier

(1983). The interaction of syntax and semantics during sentence processing: Eye movements in the analysis of semantically biased sentences. Journal of Verbal Learning and Verbal Behavior 22, 358–374.

23.

Rayner

Sereno

S. C.

(1994). Regressive eye movements and sentence parsing: On the use of regression contingent analyses. Memory & Cognition 22, 281–285.

24.

Restle

(1970). Speed of adding and comparing numbers. Journal of Experimental Psychology 83, 32–45.

25.

Verguts

De Moor

(2005). Two-digit comparison decomposed, holistic or hybrid?. Experimental Psychology 52, 195–200.

26.

Wood

Nuerk

H.-C.

Willmes

(2006). Neural representations of two-digit numbers: A parametric fMRI study. NeuroImage 29, 358–367.

27.

Zhang

Norman

D. A.

(1995). A representational analysis of numeration systems. Cognition 57, 271–295.

28.

Zhang

Wang

(2005). The effect of external representation on numeric tasks. Quarterly Journal of Experimental Psychology 58A, 817–838.

29.

Zhou

Chen

Dong

(in press). Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number matching task. Cognition.