Numerical cognition

# Sunday, October 02nd, 2011 [18:00 - 20:00]

## PS_3.060 - Biases in numerosity processing

Gebuis, T. & Reynvoet, B.

Laboratory of Experimental Psychology, Katholieke Universiteit Leuven

It has been suggested that proficiency in approximating numerosities is related to mathematical abilities. Insights in numerosity processing could therefore be of great value for intervention studies for children that have difficulties with mathematics. To date, many studies try to unravel the mechanisms underlying our ability to approximate numerosities. Most of these studies focus on the higher order stages of numerosity processing while paying little attention to the visual processes preceding numerosity processing. This is a potential problem as numerosity stimuli and their visual properties are highly correlated. To account for this problem, numerosity stimuli are generally created in such a manner that their visual properties are uninformative about number. Using electroencephalography data I demonstrate certain weaknesses of the predominant method and offer possibilities for improvements. First I present data revealing that visual cues can exert influence on event-related components that mimic results generally attributed to numerosity. Next I will show that when these visual cues are properly controlled, no significant effects of numerosity remain. Last, I will directly compare the event-related components related to passive viewing and approximation of numerosity.

## PS_3.061 - Are operands’ quantity representation automatically accessed during multiplication solving? Evidence from size congruity effects?

Estudillo Hidalgo, A. J. ^{1 } , García-Orza, J. ^{2 } & Damas-López, J. ^{2 }

1 University of Edinburgh

2 Universidad de Málaga

Some models assume that operands’ magnitude representations are activated during multiplication solving (McCloskey, 1992). Further models assume that multiplications are solved using verbal codes (Dehaene, 1992). In this research, the role of operands’ magnitude representations in multiplication problems was explored. To accomplish this we manipulated the size congruity effect. The physical and numerical magnitude of the operands within each problem was either congruent (the biggest numerical magnitude appears in bigger size), or incongruent (the smallest numerical magnitude appears in bigger size) or neutral (same physical size). Problem-size and order of the operands (8x9 vs. 9x8) were also manipulated. In our first experiment a verification task (e.g.: are the following problems correct?) was carried out. In the second experiment we employed a production task (e.g.: say the results of the following problems). Results showed longer response times in the incongruent condition than in the congruent conditions in both experiments. Although main effects of problem-size were also found, no interactions were observed between size congruity and the rest of variables. Operands’ magnitude representations are automatically activated even in the context of multiplication problems, however, the lack of interaction suggests that this activation is not related to the multiplication solving process.

## PS_3.062 - The Fast and the Inhibitory 2x3

Damas-Lopez, J. & Garcia-Orza, J.

Faculty of Psychology. Universidad de Málaga

Previous studies have shown faster responses naming Arabic digits primed with congruent multiplications (e.g., prime: 2x3=, target: 6) as compared with unrelated ones (e.g., prime: 4x8=, target: 6) using a masked priming paradigm (SOA = 50 ms). However, it is unclear whether this priming effect is a facilitatory process given by congruent multiplications or an inhibitory process given by incongruent ones, as well as the temporal course of this effect. In the present experiment we use the same paradigm, but including a neutral condition (e.g., prime: XxX=, target: 6), and also manipulating SOA (50 vs. 120 ms). The ANOVA showed an interaction between type of prime and SOA, showing longer response times for incongruent primes compared to congruent and neutral ones using the shortest SOA, but no differences regarding prime using the longest SOA. A visibility task ensured that participants were unaware of the primes. Results therefore suggest that multiplication priming is an inhibitory early effect.

## PS_3.063 - The influence of number sense acuity and mathematical expertise on mental addition strategies

Guillaume, M. , Nys, J. & Content, A.

Laboratoire Cognition, Langage et Développement. Université Libre de Bruxelles. Brussels, Belgium.

In the field of numerical cognition, the acuity of the number sense has been associated with overall arithmetic performance from childhood to adulthood. Therefore, choosing an efficient and elaborate strategy during arithmetic processing might be facilitated by a more accurate number sense. In this study, we investigate the potential influence of the number sense on strategic choice and its relation to mathematical expertise. We set up an experiment composed of one complex addition resolution task and one non-symbolic comparison task. Participants were either Engineering or Psychology students. During the arithmetic task, they were asked to verbalize the strategy they used to solve each addition. Individual Weber fractions were computed from their performance in the comparison task as estimates of number sense acuity. Our results revealed that Engineering participants were more accurate in the comparison task than Psychology students. As for the strategic aspect, overall, the utilization of more elaborate calculation strategies was associated with higher comparison acuity. Moreover, Engineering students referred to memory retrieval to a greater extent and used more elaborate strategies than Psychology students did. Taken together, these results suggest that number sense accuracy is related to mathematical expertise and to the use of more elaborate strategies.

## PS_3.064 - What can the same-different task tell us about the development of magnitude representations?

Defever, E. ^{1, } ^{4 } , Sasanguie, D. ^{1, } ^{4 } , Vandewaetere, M. ^{2, } ^{3 } & Reynvoet, B. ^{1, } ^{4 }

1 Department of Psychology, K.U. Leuven, 3000 Leuven, Belgium

2 CIP&T, Centre for Instructional Psychology and Technology, K.U.Leuven, 3000 Leuven, Belgium

3 iTEC, Interdisciplinary Research on Technology, Communication and Education, K.U.Leuven, 8500 Kortrijk, Belgium

4 Subfaculty of Psychology and Educational Sciences, Department of Psychology, K.U.Leuven - Campus Kortrijk, 8500 Kortrijk, Belgium

We wanted to clarify the moderators (i.e. numerical distance, size, physical similarity) that influence adults’ and children’s responses when conducting a symbolic (i.e. digits) and non-symbolic (i.e. dot collections) same-different task and to investigate whether these influences change over development. In addition, we examined the relationship between these moderators and mathematical ability. Our findings demonstrate that the responses of the youngest children in the symbolic same-different task were equally influenced by the magnitude information and the physical similarity of the digits, while the older age groups mainly used the physical similarity. Apparently, a same-different task with digits is not an ideal measure to study the development of magnitude representations. In our non-symbolic task, the size of the distance effect was similar in all age groups, which suggests that the representations of non-symbolic numerosities are stable over development. The size of the distance effects was not influenced by subjects’ mathematical ability.

## PS_3.065 - Access to numbers quantity is not automatic: evidence from two versions of Indian numbers

García-Orza, J. ^{1 } , Perea, M. ^{2 } , Abu Mallouh, R. ^{3 } & Carreiras, M. ^{3, } ^{4 }

1 Universidad de Malaga, Spain

2 Universitat de Valencia, Spain

3 Basque Center for Cognition, Brain, and Language, Donostia-San Sebastian, Spain

4 IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

Numerical quantity seems to affect the response in any task that involves numbers, even when the task does not demand access to quantity (e.g., perceptual tasks). One piece of evidence in favour of this view comes from the “distance effect”: when comparing two numbers, reaction times are a function of the numerical distance between them. However, recent studies suggest that physical similarity between Arabic numbers and the numerical distance are strongly correlated, and the former might be a better predictor of RT data (Cohen, 2009). The present study explored the Persian and Arabic version of Indian numbers (Experiment 1 and 2, respectively). Naive participants (speakers from Spanish) and users of these notations participated in a same/different number matching task. The RTs of users of the Indian notation were regressed on perceptual similarity (estimated from the Spanish participants’ RTs) and the numerical distance effect. In Experiment 1, both distance and perceptual similarity alone were significant predictors of reaction times, however, when both variables were included in the regression, we only found a significant contribution of perceptual similarity. In Experiment 2, only perceptual similarity contributed to the regression. Thus, Indian integers do not automatically activate their quantity representation in simple, perceptual tasks.