Neuroscience Letters 468 (2010) 220 224 Contents lists available at ScienceDirect Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet Event-related potentials findings differ between children and adults during arithmetic-fact retrieval Belén Prieto-Corona a,, Mario Rodríguez-Camacho a, Juan Silva-Pereyra a, Erzsébet Marosi a, Thalía Fernández b, Vicente Guerrero a a FES Iztacala, Universidad Nacional Autónoma de México, México b Instituto de Neurobiología, Universidad Nacional Autónoma de México, Campus Juriquilla, Querétaro, México article info abstract Article history: Received 19 August 2009 Received in revised form 16 October 2009 Accepted 30 October 2009 Keywords: Event-related potentials Arithmetic N400 effect LPC Arithmetical facts Arithmetic processing development Children Adults Some cognitive abilities of arithmetical calculation depend on retrieval of arithmetic facts from longterm memory. Arithmetic-fact retrieval has been studied in adults through Event-Related Potentials (ERP) experiments. Such information in children, however, has been scarce. It has been reported that from the age of 9 years, children employ a memory retrieval strategy for solving simple multiplication problems. The present study compared arithmetical-fact retrieval in children and adults while they were being subjected to ERP recording. The subjects were asked to make judgments about solutions to simple multiplication problems. Both groups of participants displayed the so-called arithmetic N400 effect for incorrect solutions relative to correct solutions. Adults showed a posterior N400 effect, while children showed a widely distributed N400 effect. Children displayed a larger amplitude and longer latency arithmetic N400 component than adults; this observation could be due to children exerting greater effort involving more widespread cortical activation than adults to solve the experimental problems. The Late Positive Component (LPC), which follows the arithmetic N400 and has been described previously in adult subjects, was observed in the present adult subjects, but was present in children only for correct solutions. These results may indicate that, relative to adults, children showed slower memory retrieval and a different pattern of a verification mechanism for correct and incorrect solutions. 2009 Elsevier Ireland Ltd. All rights reserved. There is a general agreement in the cognitive literature that when solving single-digit multiplication problems (i.e., 3 2), adults retrieve arithmetic facts from long-term memory [2]. A corresponding cognitive model assumes that arithmetic facts are stored as nodes in an associative network of data within long-term memory stores [1,9]. It has been proposed that the information retrieval mechanism is automatic in nature and involves an initial spread of activation through a network followed by a lateral inhibition, which enables the needed piece of information to be selected [5]. According to this model, the correct solution of a single-digit multiplication problem receives activation from both operands and hence its level of activation is greater than the other response nodes. Consistent with this model, subjects exhibit shorter reaction times and lesser errors when presented with unrelated wrong answers compared to related wrong answers (i.e., numbers that are multiples of either the first or the second operand) [4,15,21]. This difference can be attributed to the fact that related wrong Corresponding author at: FES Iztacala, UNAM, Av. de los Barrios 1, Los Reyes Iztacala, Tlalnepantla Estado de México, Mexico. Tel.: +52 55 56231333x39726. E-mail address: bemapado@gmail.com (B. Prieto-Corona). answers to operands compete more with the correct solutions than unrelated wrong answers. Incorrect solutions for single-digit multiplication problems in verification tasks have evoked an event-related brain potential (ERP) effect comparable to the semantic N400 [21 23]. This N400- like effect has its maximum amplitude between 300 and 500 ms in the centroparietal region, and has been called the arithmetic N400 [16,21 23]. The amplitude of the arithmetic N400 is smaller for correct than for incorrect solutions. These tasks have also been shown to elicit a positive component called the late positive component (LPC) which follows the N400. The LPC is also larger for incorrect than for correct solutions [16,21,23]. Children learn arithmetic facts of single-digit operations mainly through two kinds of strategies: procedure and memory retrieval [24]. The memory retrieval strategy involves a great deal of repetition of the multiplication tables, so that the data are stored in memory. Children from 9 to 12 years of age in Mexico and other countries have been reported to employ a procedural strategy for simple addition and subtraction, but to rely on a memory retrieval strategy for solving simple multiplication problems [8,15,19,24]. Several changes in neural development take place during childhood. These include plastic events such as synaptogenesis and 0304-3940/$ see front matter 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2009.10.094
B. Prieto-Corona et al. / Neuroscience Letters 468 (2010) 220 224 221 myelinization which lead to mature brain morphology and optimal functioning of central nervous system [14]. Some ERP components generally show clear developmental changes between childhood and adulthood in either latency, wave morphology, or topographic distribution [20]. ERP effects in children may be more widely distributed across the scalp than those found in adults [6]. The semantic N400, for example, exhibits decreases in amplitude and latency with age [13]. For the LPC component, antecedents are scarce. In a sentence listening paradigm, Juottonen et al. [17] reported that children did not display an LPC for incongruent sentences, as adults did. As there are virtually no prior cognitive arithmetic ERP studies in children that have shed light on the development of cognitive processes related to arithmetic, the aim of the present study was to investigate the characteristics and time course of ERPs elicited by correct and incorrect solutions to simple arithmetic problems in children and to compare the results with those of adults. We reasoned that if the consolidation of arithmetic knowledge is characterized by arithmetic-fact retrieval from memory, then retrieval arithmetic facts should improve with further cognitive development. Such a developmental change might also be observed in the amplitude of the N400 component generated during performance of an arithmetic verification task. Given that children from 9 to 12 years of age already retrieve arithmetic facts from memory, our hypothesis is that the arithmetic N400 effect and the LPC might be observed in these children although they will show larger amplitudes and longer latencies relative to the adult arithmetic N400 and LPC. These differences may reflect relatively immature juvenile processing related to anatomical and/or physiological differences between the brains of children vs. adults. Thus, the aim of the present study was to compare children s and adults performance in a verification task solving single-digit multiplication problems using ERP recording. Sixteen 4 6th grade boys were recruited from two elementary schools. Eighteen adult male volunteers were recruited from the undergraduate student body population at the National University of Mexico. All participants were right handed and native Spanish speakers. They had self-reported normal or corrected to normal vision. The mean age for the children was 10.3 years (0.79 S.D.) and the mean age for the adults was 26.11 years (5.06 S.D.). None of the participants had a history of psychiatric or neurological disease. Participants provided an informed consent. One hundred and twelve single-digit multiplication problems were presented to each subject. Multiplications involving 0 and 1 were excluded assuming that these would be solved applying a rule [18]. Ties (i.e., 2 2) were also eliminated because they have a processing advantage compared to non-tie problems of the same magnitude [3]. Observing these restrictions, a set of 56 different operand combinations remained. Each operation was presented twice, once with the correct solution (i.e., 4 7 = 28) and once with an incorrect solution (i.e., 4 7 = 31). Incorrect solutions were multiplication table unrelated wrong answers. Incorrect solutions were constructed by adding or subtracting 1 or 3 from the value of the correct solution. Visual stimuli consisted of Arabic numerals presented in light grey on a black background and were centered on the viewing screen (subtending a visual angle of 0.8 ) using a standard PC and a 17 in.-crt monitor (refresh rate of 75 Hz). In addition, there were 56 filler sums to prevent subjects from employing strategies. ERPs were only collected from subjects solving singledigit multiplication problems. The subjects were seated in a dimly lit, sound-attenuated room. Stimulus presentation was controlled by an STIM stimulus delivery system (Neurosoft, Inc.). Trials began with the presentation of a warning signal (a square) in the center of the screen for a duration of 300 ms. Five hundred milliseconds after the offset of the warning signal, the operation and solution appeared sequentially, each for 1000 ms, on the screen with an inter-stimulus interval of 500 ms. The solution was followed by a black screen that remained for 1000 ms and then a question mark. Subjects were asked to press a button as soon as possible after the appearance of the question mark. They had a maximum time of 1900 ms to respond, after which an omission would be recorded. Participants were instructed to make a judgment regarding the correctness of the solutions. Half of the participants in each age group were asked to click the left mouse button with their right index finger if the solution shown was correct, and to click the right mouse button with their right middle finger if it was incorrect. These instructions were reversed for the other half of the participants such that the left and right button pressings were counterbalanced across the sessions. A delayed verification task, rather than a production task or a standard verification task, was used in the ERP experiment in order to prevent motor responses while the subjects were perceiving and processing the operands. Accuracy and reaction time of correct responses were recorded. Stimuli were presented block-wise (12 blocks of 14 trials in each experimental run). An obligatory break of at least 10 s separated the blocks. After a 10-trial practice round, subjects initiated the first experimental trial by clicking one of the two mouse buttons. Multiplication problems presented in the practice blocks were not used during the experiment proper. Electroencephalogram (EEG) recordings were collected using a SCAN system (Neurosoft, Inc. USA) with 31 silver/silver chloride sintered electrodes inserted in a Quick-cap (NeuroScan Inc.). All EEG channels were referenced to linked earlobes, and the ground electrode was placed 1.5 cm anterior to midline frontal electrode (Fz). Additional electrodes were attached along the outer edge and the supraorbital region of the left eye for horizontal and vertical electro-oculogram recording. Impedances were kept below 5 k. The recordings were made in a 0.3 30 Hz bandwidth. The EEG sampling interval was 5 ms. Ocular artifacts were corrected using a NeuroScanEDIT algorithm. After correction of ocular artifacts, continuous EEG data were segmented into epochs that extended from 100 ms prestimulus (baseline) to 1180 ms poststimulus. The EEG data were detrended and baseline-corrected. Incorrect responses or epochs in which EEG activity exceeded ±75 V in any electrode site were excluded from the analysis. Artifact-free ERP data were extracted from each subject by averaging trials separately for each experimental condition. The same number of EEG segments was taken into consideration for the averages for each experimental condition across subjects. The behavioral data consisted of reaction times and correct response rates. The mean reaction time and correct response rates were calculated for each subject group (children and adults) and each condition. Repeated measures (rm) ANOVAs were performed with performance measure data and the mean percentage of hits for each condition. ERPs for 10 regions of interest (ROIs) were computed from data collected from the 30 electrodes (Fpz was not included in the analysis). Each ROI ERP was computed from the average of a group of 3 electrodes. The following ROIs were examined based on data from the indicated electrodes: left lateral anterior (F7, Ft1, T3), left lateral posterior (T31, P7, O1), left paracentral anterior (FP1, F3, C3a), left paracentral posterior (C3, C3p, P3), medial anterior (Fz, Cza, Cz), medial posterior (Pza, Pz, Oz), right paracentral anterior (Fp2, F4, C4a), right paracentral posterior (C4, C4p, P4), right lateral anterior (F8, Ft2, T4), and right lateral posterior (T41, P8, O2) (see Fig. 1). Topographic N400 maps were created using NeuroScan software. N400 Latency: To determine the onset of the N400 effect, a consecutive 50-ms time-windows analysis was carried out for each group separately. After the 50-ms time-windows analysis, the peak latency of N400 was measured as the more negative deflection at the midline ROIs in the 250 400 ms interval for adults and
222 B. Prieto-Corona et al. / Neuroscience Letters 468 (2010) 220 224 Fig. 1. (A) Grand average ERP responses to correct (black lines) and incorrect (grey lines) solutions in children (lower left panel) and in adults (upper left panel) in the central anterior region. (B) An ERP graph comparing the two age groups is shown at the center of the figure. Adults (black line) showed a smaller amplitude and shorter latency N400 than that exhibited by children (grey line). A diagrammatic scheme of the ROIs and electrode placements is provided below the graphs. (C) N400 effect standardized Z maps for children (lower right panel) and adults (upper right panel). 350 450 ms interval for children, for both conditions and groups, in order to assess differences between the groups using rm-anova with the following factors: 2 groups (adults and children) 2 conditions (correct and incorrect solutions) 2 ROIs (medial anterior and medial posterior). Post hoc analyses were performed by applying Least Significance Difference (LSD) tests. N400 and LPC amplitude: To determine the onset of N400 and LPC effects, a consecutive 50-ms time-windows analysis was carried out for each group separately. N400 was defined as having mean amplitude within the 250 400 ms poststimulus time range for adults and within the 350 450 ms poststimulus time range for children. The LPC was defined as having a mean amplitude value in the 450 650 ms range for adults and in the 500 650 ms range for children. Repeated measures ANOVAs were performed with mean amplitude values using the ROIs based on these two ERP time windows. A 5-way rm-anova was performed on the mean amplitudes of the full study cohort data. Variables included 2 groups (adults and children) 2 conditions (correct solutions and incorrect solutions) 2 antero-posterior ROIs (lateral anterior paracentral anterior and lateral posterior paracentral posterior) 2 hemispheres (left and right) 2 laterality locations (lateral and paracentral). For midline regions, an ANOVA was carried out with the following factors: 2 groups (adults and children) 2 conditions (correct and incorrect solutions) 2 ROIs (medial anterior and medial posterior). Post hoc analyses were performed by applying Least Significance Difference tests. The topography of the N400 effect was assessed in a manner similar to that of other studies (i.e., [21,25]). After calculating the difference (incorrect minus correct solution) waves, amplitude values were standardized across electrodes. Z scores were analyzed in the topographical analyses. A main effect of group was observed in the correct response rate (F (1,32) = 10.43, p = 0.003). Adults had a higher percentage of hits than children for both correct (94.54% vs. 86.03%) and incorrect (95.44% vs. 86.24%) solutions. Adults and children had similar reaction times (F (1,32) = 0.219, p = 0.64): for correct solutions (391.08 ms vs. 418.09 ms, respectively) and incorrect solutions (400.58 ms vs. 438.15 ms, respectively). Grand average ERPs produced in response to incorrect and correct solutions are shown in Fig. 1. Visual inspection of the ERP revealed a larger negativity for incorrect solutions than for correct solutions. This negativity was followed by a positive wave that was greater for the incorrect than the correct solutions in adults, but not in children. Children displayed longer N400 latencies than adults (Fig. 1). A significant Group Condition Anterior posterior interaction was observed (F (1,32) = 4.73, p = 0.037). LSD analysis indicated that children exhibited longer latencies than adults in both correct and incorrect solution conditions (MD = 102.61 ms, p = 0.001). The children s mean N400 latencies were 406.56 ms in the medial anterior region and 398 ms in the medial posterior region for correct solutions, and were 395 ms in the medial anterior region and 393.75 ms in the medial posterior region for incorrect solutions. The adults mean N400 latencies were 289.72 ms in the medial anterior region and 286.39 ms in medial posterior region for correct solutions, and were 310.55 ms in the medial anterior region and 296.94 ms in the medial posterior region for incorrect solutions. Five-way ANOVA revealed a significant Condition Anteroposterior Laterality Group interaction in the N400 amplitude data (F (1,32) = 5.25, p = 0.029). LSD post hoc tests revealed that children showed a widely distributed N400 effect over lateral anterior regions (mean difference (MD) = 1.81, p = 0.002), lateral posterior regions (MD = 1.93, p = 0.001), paracentral anterior regions (MD = 3.32, p = 0.001), and paracentral posterior regions (MD = 4.78, p = 0.001), while adults showed the N400 effect in lateral posterior regions (MD = 2.31, p = 0.001) and paracentral posterior regions (MD = 2.721, p = 0.002). A main effect of condition was significant in midline regions (F (1,32) = 46.32, p = 0.0001). The topography of the N400 effect is shown in standardized (Z score transformed) maps in Fig. 1. This topography was tested on Z scores by Group Antero-posterior Hemispheres Laterality position ANOVA. A significant Group Antero-posterior interaction was observed (F (1,32) = 3.95, p = 0.05). LSD post hoc test revealed that adults showed a mean amplitude of the N400 effect that was more negative in the posterior (mean = 1.25 V) than in the anterior region (mean = 0.511 V) (MD = 0.735 ms, p < 0.000), while children showed an N400 effect in both the anterior and posterior regions (mean anterior region = 0.388 V; mean posterior region = 0.693 V). The N400 was followed by a typical LPC in adults but not children (Group Condition F (1,32) = 5.89, p = 0.021). Specifically, as shown in Fig. 1, the LPC was larger in amplitude for incorrect solutions than for correct solutions in central regions (Group Condition Laterality F (1,32) = 15.84, p = 0.001). LSD post hoc test indicated that adults showed an LPC effect in lateral regions (MD = 1.15, p = 0.05) and paracentral regions (MD = 1.57, p = 0.03). There was a significant Group Condition interaction for midline regions (F (1,32) = 7.76, p = 0.009). LSD post hoc test revealed a LPC
B. Prieto-Corona et al. / Neuroscience Letters 468 (2010) 220 224 223 effect for adults in the anterior medial (MD = 1.83, p = 0.015) and posterior medial (MD = 1.64, p = 0.048) regions. In the present study, incorrect solutions elicited a larger ERP negativity than correct solutions. Adults showed the N400 effect in central regions, while children showed a broader N400 effect. Children displayed longer N400 latencies than adults in both correct and incorrect solution conditions. In adults, the N400 negativity was followed by an LPC that was greater for incorrect than correct solutions. In contrast, an LPC was observed in children only in the correct solutions condition, but not in the incorrect solutions condition. The arithmetic N400 effect obtained for adults in this experiment was similar to that reported in previous studies [16,21,23,22]. It has been suggested that this N400 is elicited by incorrect solutions for multiplication problems in a verification task because a representation of a solution does not fit with the precedent equation. Incorrect solutions elicited a larger ERP negative component than correct solutions in the children. This negativity was similar to the N400 effect observed in adults. This electrophysiological finding is consistent with reports indicating that children 9 years of age and older retrieve arithmetic solutions from memory [15,19]. According to the model proposed by Ashcraft [2], in principle, children are similar to adults in the way that they retrieve arithmetic data from memory to solve simple multiplication problems. Nevertheless, differences in arithmetic N400 characteristics between children and adults were observed in our study. Our finding that children showed greater arithmetic N400 amplitudes and latencies than adults can likely be understood by an explanation similar to those put forth for other ERP components [12,17]. Briefly, children may exert greater effort and thus may recruit more widespread cortical activation than adults when solving experimental problems [7]. It is noteworthy that the N400 topography differed between adults and children. Children displayed a much wider distributed negativity than adults, whose N400 negativity had a more posterior distribution similar to previously described arithmetic N400 component [16,21,22,23]. Hence the involvement of more cortical areas [7] in the presently employed task could be reflected in a more widely distributed topography of the arithmetic N400 in children. Alternatively, the differences in the topography of N400 effects may be explained by the readily observable anatomical and/or physiological differences between the brains of children and adults. Greater arithmetic N400 amplitude in children may reflect the use of more resources to identify a result, relative to adults. Both greater amplitude and longer latency for the arithmetic N400 in children may be electrophysiological signs of a greater cognitive effort. Furthermore, these findings may reflect slower and more effortful memory retrieval for children. This phenomenon would be similar to the observation that, in verification tasks, the N400 is small for correct solutions presumably because this type of solutions may benefit from the spread of activation associated with the processing of primes (i.e., operands). If the prime is followed by an incorrect solution, there is no such benefit and more resources would presumably be required to solve the problem. Hence, the use of these extra resources may be what is reflected by the larger N400 seen in incorrect solution conditions [4,23]. Prior ERP studies in adults have reported that the arithmetic N400 is followed by an LPC with a centro-parietal distribution. The adults in this study showed larger LPC amplitude for incorrect than for correct solutions, consistent with the findings of prior studies [21 23,25]. On the other hand, the children in this study only displayed an LPC for correct solutions. The LPC in verification tasks could be a reflection of the subjects being surprised by incorrect solutions or a sign of implausibility [21,23]. The finding of an inverse pattern of results for the LPC in children and adults might be due to children not being totally confident about the arithmetic-fact information stored in their memories and thus having a tendency to verify those solutions that are more familiar to them, or that they recognize better (i.e., correct but not incorrect solutions). For children, this verification processing could be reflected in the LPC only for correct solutions. On the other hand, adults tend to verify information when it does not fit with preceding context, as in case for incorrect solutions, thus producing this component only for incorrect solutions. Confidence in one s response [10,15] and the decision making process [11] could be associated with LPC modulation. The whole arithmetic cognitive process can be interpreted by considering our N400 effect results in light of these two cognitive processes. That is, in adults, a representation of the solution such as it is could be activated and the N400 elicited, then a subsequent verification mechanism could be invoked to test the status of the solution. It is assumed that this extra activity is reflected in the arithmetic LPC. For a correct solution, no extra processing would be required. Our ERP results are consistent with the possibility that the aforementioned mechanism could function in children, but perhaps only for correct solutions. Because children are less apt to be totally confident about the arithmetic-fact information stored in their memories, they may tend to need to verify those solutions. The present study showed that incorrect solutions for simple multiplication problems elicited greater arithmetic N400 amplitudes than correct solutions in both adults and children. Children displayed larger amplitude and longer latency N400s than adults, probably due to slower memory retrieval; meanwhile the inverse LPC pattern observed in children with respect to adults could signify a verification mechanism for correcting previously recognized solutions. Acknowledgements This research was supported by DGAPA (UNAM) IN303507, CONACYT 59066, PAPCA 2006 2007. References [1] M. Ashcraft, Cognitive arithmetic: a review of data and theory, Cognition 44 (1992) 75 106. [2] M. Ashcraft, Cognitive psychology and simple arithmetic: a review and summary of new directions, Math. Cognit. 1 (1995) 3 34. [3] S. Blankenberger, The arithmetic tie effect is mainly encoding-based, Cognition 82 (2001) B15 24. [4] J. Campbell, Conditions of error priming in number fact retrieval, Mem. Cognit. 19 (1991) 197 209. [5] A. Collins, E. Loftus, A spreading activation theory of semantic processing, Psychol. Rev. 82 (1975) 407 428. [6] E. Courchesne, Cognitive components of the event-related potentials: changes associates with development, in: A.W. Gaillart, W. Ritter (Eds.), Tutorials in ERP Research: Endogenous Components, Holland, Amsterdam, 1983. [7] T. DeBoer, L. Scott, C. Nelson, ERPs in developmental populations, in: T. Handy (Ed.), Event-Related Potentials: A Methods Handbook, MIT Press, 2005, pp. 263 298. [8] S. Dehaene, L. Cohen, Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic, Cortex 33 (1997) 219 250. [9] F. Domahs, M. Delazer, Some assumptions and facts about arithmetic facts, Psychol. Sci. 47 (2005) 96 111. [10] S. Finnigan, M. Humphreys, S. Dennis, G. Geffen, ERP old/new effects: memory strength and decisional factor(s), Neuropsychologia 40 (2002) 2288 2304. [11] G. Frishkoff, Hemispheric differences in strong versus weak semantic priming: evidence from event-related brain potentials, Brain Lang. 100 (2007) 23 43. [12] A. Hahne, K. Eckstein, A. Friederici, Brain signatures of syntactic and semantic processes during Children s language development, Cognit. Brain Res. 16 (2004) 1302 1318. [13] P.J. Holcomb, D. Coffey, H. Neville, The effects of context on visual and auditory sentence processing: a developmental analysis using event-related brain potentials, Dev. Neuropsychol. 8 (1992) 203 241. [14] P. Huttenlocher, Basic Neuroscience research has important implications for child development, Nat. Neurosci. 6 (2003) 541. [15] I. Imbo, A. Vandierendonck, Effects of problem size, operation, and workingmemory span on simple arithmetic strategies: differences between children and adults? Psychol. Res. 72 (2008) 331 346.
224 B. Prieto-Corona et al. / Neuroscience Letters 468 (2010) 220 224 [16] K Jost, E. Hennighausen, F. Rösler, Comparing arithmetic and semantic fact retrieval: effects of problem size and sentence constraint on event-related potentials, Psychophysiology 41 (2004) 46 59. [17] K. Juottonen, A. Revonsuo, H. Lang, Dissimilar age influences on two ERP waveforms (LPC and N400) reflecting semantic context effect, Cognit. Brain Res. 4 (1996) 99 107. [18] J. LeFevre, J. Bisanz, K. Daley, L. Buffone, S. Greenham, G. Sadesky, Multiple routes to solution of single-digit multiplication problems, J. Exp. Psychol. Gen. 125 (1996) 284 306. [19] M. McCloskey, W. Harley, S. Sokol, Models of arithmetic fact retrieval: an evolution in light of finding from normal and brain-damaged subjects, J. Exp. Psychol. Learn. Mem. Cognit. 17 (1991) 377 399. [20] H. Neville, Developmental specificity in neurocognitive development in humans, in: M.S. Gazzaniga (Ed.), The Cognitive Neurosciences, MIT Press, Cambridge, MA, 1995, pp. 219 231. [21] M. Nieddegen, F. Rosler, N400 effects reflect activation spread during retrieval of arithmetic facts, Psychol. Sci. 10 (1999) 271 276. [22] M. Niedeggen, F. Rösler, N400 effects related to incongruities in mental calculation problems, Psychophysiology 33 (1999) S65. [23] M. Niedeggen, F. Rösler, K. Jost, Processing of incongruous mental calculation problems: evidence for an arithmetic N400 effect, Psychophysiology 36 (1999) 307 324. [24] J. Roussel, M. Fayol, P. Barrouillet, Procedural vs. direct retrieval strategies in arithmetic: a comparison between additive and multiplicative problem solving, Eur. J. Cognit. Psychol. 14 (2002) 61 104. [25] D. Szúcs, V. Csépe, The effect of numerical distance and stimulus probability on ERP components elicited by numerical incongruencies in mental addition, Cognit. Brain Res. 22 (2005) 289 300.