Simple arithmetic processing: the question of automaticity

In adult simple arithmetic performance, it is commonly held that retrieval of solutions occurs automatically from a network of stored facts in memory. However, such an account of performance necessarily predicts a uniform reaction time for solution retrieval and is therefore not consistent with the robust finding that reaction time increases with problem size and difficulty. Additionally, past research into arithmetic performance has relied on tasks that may have actually induced and measured attentional processing, thereby possibly confounding previous results and conclusions pertaining to automaticity. The present study therefore, attempted to more reliably assess the influence of automatic processing in arithmetic performance by utilizing a variant of the well-established semantic word-priming procedure with a target-naming task. The overall results revealed significant facilitation in naming times at SOAs of 240 and 1000 ms for congruent targets i.e., targets that represented the correct solutions to problems presented as primes (e.g., 6+8 and 14). Significant inhibition in comparison to a neutral condition (0+0 and 17) was also observed at 120 and 240 ms SOAs in naming incongruent targets (e.g., 6+8 and 17). Furthermore, response times were found to vary as a function of both arithmetic fluency and problem size. Differences in performance to addition and multiplication operations and implications for cognitive research and education are considered.     

Simple arithmetic processing: surface form effects in a priming task

Models of numerical processing vary on whether they assume common or separate processing pathways for problems represented in different surface forms. The present study employed a priming procedure, with target naming task, in an investigation of surface form effects in simple addition and multiplication operations. Participants were presented with Arabic digit and number word problems in one of three prime-target relationships, including congruent (e.g., '2+3' and '5'), incongruent (e.g., '9+7' and '5') and neutral (e.g., 'X+Y' and '5') conditions. The results revealed significant facilitatory effects in response to congruent digit stimuli at SOAs of 300 and 1000ms, in both operations. In contrast, inhibitory effects were observed in response to incongruent word stimuli in both the addition and multiplication operations at 300ms, and in the addition operation at 1000ms. The overall priming effects observed in the digit condition were significantly greater than in the word condition at 1000ms in the multiplication operation and at 300ms in the addition operation. The results provide support to separate pathway accounts of simple arithmetic processing for problems represented in different surface forms. An explanation for variation in processing due to differences in access to visual and phonological representations is provided.     

Simple addition and multiplication: No comparison

Some models of memory for arithmetic facts (e.g., 5+2=7, 6×7=42) assume that only the max-left order is stored in memory (e.g., 5+2=7 is stored but not 2+5=7). These models further assume an initial comparison of the two operands so that either operand order (5+2 or 2+5) can be mapped to the common internal representation. We sought evidence of number comparison in simple addition and multiplication by manipulating size congruity. In number comparison tasks, performance costs occur when the physical and numerical size of numerals are incongruent (8 3) relative to when they are congruent (8 3). Sixty-four volunteers completed a number comparison task, an addition task, and a multiplication task with both size congruent and size incongruent stimuli. The comparison task demonstrated that our stimuli were capable of producing robust size congruity and split effects. In the addition and multiplication task, however, we were unable to detect any of the RT signatures of comparison or reordering processes despite ample statistical power: Specifically, there was no evidence of size congruity, split, or order effects in either the addition or multiplication data. We conclude that our participants did not routinely engage a comparison operation and did not consistently reorder the operands to a preferred orientation.     

Individual differences in the obligatory activation of addition facts

In two experiments, we found evidence for individual differences in the obligatory activation of addition facts. Subjects were required to verify the presence of a target digit (e. g., 4) in a previously presented pair (e. g., 5 + 4). Subjects rejected targets that formed the sum of the initial pair (e. g., 5+4 and 9) more slowly than they rejected unrelated targets (e. g., 5+4 and 7). This interference of the sum was largest for subjects who were relatively skilled at multidigit arithmetic. Less skilled subjects did not show statistically significant effects of obligatory activation. In comparison with less skilled subjects, skilled subjects showed differential interference on plus-one (e. g., 34 1) and standard (e. g, 2+3) problems when the plus sign was presented, and on ties (e. g., 22) when the plus sign was omitted. These results suggest that network models of arithmetic fact retrieval are appropriate for skilled subjects, but that alternative models need to be considered for less skilled individuals.     

Low-constraint facilitation in lexical decision with single-word contexts

Single-word, low-constraint adjective contexts were used to "prime" lexical decision to noun targets in Serbo-Croat. Semantically congruent situations consisted of adjective-noun pairs that were not highly predictable but were nonetheless plausible (e.g., GOOD-AUNT). Semantically incongruent situations used pairs that were implausible (e.g., SLOW-COAT). All adjective-noun pairs were grammatically congruent and were compared with a neutral XXX baseline. In Experiment 1, at a stimulus onset asynchrony of 300 ms, congruous situations showed 59 ms of facilitation while incongruous situations did not differ from the baseline. The same pattern was repeated in Experiment 2, at a stimulus onset asynchrony of 800 ms. Congruous situations were facilitated 67 ms. Results are discussed in terms of a message-level coherence check in Forster's (1979) model of autonomous levels of language processing.     

Mental representations of arithmetic facts: evidence from eye movement recordings supports the preferred operand-order-specific representation hypothesis

There are three main hypotheses about mental representations of arithmetic facts: the independent representation hypothesis, the operand-order-free single-representation hypothesis, and the operand-order-specific single-representation hypothesis. The current study used electrical recordings of eye movements to examine the organization of arithmetic facts in long-term memory. Subjects were presented single-digit addition and multiplication problems and were asked to report the solutions. Analyses of the horizontal electrooculograph (HEOG) showed an operand order effect for multiplication in the time windows 150-300?ms (larger negative potentials for smaller operand first problems than for larger operand first ones). The operand order effect was reversed in the time windows from 400 to 1,000?ms (i.e., larger operand first problems had larger negative potentials than smaller operand first problems). For addition, larger operand first problems had larger negative potentials than smaller operand first in the series of time windows from 300 to 1,000?ms, but the effect was smaller than that for multiplication. These results confirmed the dissociated representation of addition and multiplication facts and were consistent with the prediction of the preferred operand-order-specific representation hypothesis.     

Action-related objects influence the distribution of visuospatial attention

Previous studies have shown that attention is drawn to the location of manipulable objects and is distributed across pairs of objects that are positioned for action. Here, we investigate whether central, action-related objects can cue attention to peripheral targets. Experiment 1 compared the effect of uninformative arrow and object cues on a letter discrimination task. Arrow cues led to spatial-cueing benefits across a range of stimulus onset asynchronies (SOAs: 0?ms, 120?ms, 400?ms), but object-cueing benefits were slow to build and were only significant at the 400-ms SOA. Similar results were found in Experiment 2, in which the targets were objects that could be either congruent or incongruent with the cue (e.g., screwdriver and screw versus screwdriver and glass). Cueing benefits were not influenced by the congruence between the cue and target, suggesting that the cueing effects reflected the action implied by the central object, not the interaction between the objects. For Experiment 3 participants decided whether the cue and target objects were related. Here, the interaction between congruent (but not incongruent) targets led to significant cueing/positioning benefits at all three SOAs. Reduced cueing benefits were obtained in all three experiments when the object cue did not portray a legitimate action (e.g., a bottle pointing towards an upper location, since a bottle cannot pour upwards), suggesting that it is the perceived action that is critical, rather than the structural properties of individual objects. The data suggest that affordance for action modulates the allocation of visual attention.     

Skeletal structure of printed words: evidence from the stroop task

Do readers encode the sequencing of consonant (C) and vowel (V) phonemes (skeletal structure) in printed words? The authors used the Stroop task to examine readers' sensitivity to skeletal structure. In Experiment 1, CVC nonwords (e.g., pof) facilitated the naming of colors with congruent frames (e.g., red, a CVC word) but not with incongruent ones (e.g., green). In Experiment 2, the color black (a CCVC frame) was named faster with a congruent CCVC frame (e.g., grof) compared to either CCVCC (e.g., groft) or CVC (e.g., gof) incongruent controls. Finally, in Experiment 3, the color pink (a CVCC frame) was named faster with a CVCC frame (e.g., goft) compared to either CCVCC or CVC incongruent controls. In most cases, congruent frames shared no segments with the color name. These findings demonstrate that readers automatically assemble the skeletal structure of printed words.     

“2 x 3” primes naming “6”: Evidence from masked priming

It is a common assumption for multiplication-solving models that single-digit multiplications are automatically retrieved. However, the experimental evidence for this is based on paradigms under suspicion. In this research, we employed a new procedure with the aim of assessing the automatic retrieval of multiplication more directly. In two experiments, multiplication automatism was studied using briefly presented primes (stimulus onset asynchrony = 48 msec) in a number-naming task. In Experiment 1, in the congruent conditions, the target and the prime were the same numbers (e.g., prime, 6; target, 6) or the target was the solution to the multiplication prime (e.g., prime, 2×3=; target, 6). In the incongruent conditions, no relationship existed between the primes and the targets (e.g., prime, 32; target, 6; or prime, 4×8=; target, 6). Experiment 2 explored the relevance of the equal sign for the multiplication-priming effect. Data showed that naming was faster when the solution of the multiplication prime matched the target, as compared with the incongruent condition (multiplication-priming effect), and that these effects were found irrespective of the presence of the equal sign. The fact that this priming effect was found even though the participants were unaware of the presentation of the primes supports the automatic character of single-digit multiplication. We conclude by arguing that this procedure is highly valuable for exploring the mechanisms involved in simple arithmetic solving.     

Retrieval-induced forgetting of arithmetic facts but not rules

Retrieval of a multiplication fact (2×6 =12) can disrupt retrieval of its addition counterpart (2+6=8). We investigated whether this retrieval-induced forgetting effect applies to rule-governed arithmetic facts (i.e., 0×N=0, 1×N=N). Participants (n=40) practised rule-governed multiplication problems (e.g., 1×4, 0×5) and multiplication facts (e.g., 2×3, 4×5) for four blocks and then were tested on the addition counterparts (e.g., 1+4, 0+5, 2+3, 4+5) and control additions. Increased addition response times and errors relative to controls occurred only for problems corresponding to multiplication facts, with no problem-specific effects on addition counterparts of rule-governed multiplications. In contrast, the rule-governed 0+N problems provided evidence of generalisation of practice across items, whereas the fact-based 1+N problems did not. These findings support the theory that elementary arithmetic rules and facts involve distinct memory processes, and confirmed that previous, seemly inconsistent findings of RIF in arithmetic owed to the inclusion or exclusion of rule-governed problems.     

Mental representations of arithmetic facts: Evidence from eye movement recordings supports the preferred operand-order-specific representation hypothesis

There are three main hypotheses about mental representations of arithmetic facts: the independent representation hypothesis, the operand-order-free single-representation hypothesis, and the operand-order-specific single-representation hypothesis. The current study used electrical recordings of eye movements to examine the organization of arithmetic facts in long-term memory. Subjects were presented single-digit addition and multiplication problems and were asked to report the solutions. Analyses of the horizontal electrooculograph (HEOG) showed an operand order effect for multiplication in the time windows 150–300 ms (larger negative potentials for smaller operand first problems than for larger operand first ones). The operand order effect was reversed in the time windows from 400 to 1,000 ms (i.e., larger operand first problems had larger negative potentials than smaller operand first problems). For addition, larger operand first problems had larger negative potentials than smaller operand first in the series of time windows from 300 to 1,000 ms, but the effect was smaller than that for multiplication. These results confirmed the dissociated representation of addition and multiplication facts and were consistent with the prediction of the preferred operand-order-specific representation hypothesis.     

The role of color diagnosticity in object recognition and representation

The role of color diagnosticity in object recognition and representation was assessed in three Experiments. In Experiment 1a, participants named pictured objects that were strongly associated with a particular color (e.g., pumpkin and orange). Stimuli were presented in a congruent color, incongruent color, or grayscale. Results indicated that congruent color facilitated naming time, incongruent color impeded naming time, and naming times for grayscale items were situated between the congruent and incongruent conditions. Experiment 1b replicated Experiment 1a using a verification task. Experiment 2 employed a picture rebus paradigm in which participants read sentences one word at a time that included pictures of color diagnostic objects (i.e., pictures were substituted for critical nouns). Results indicated that the “reading” times of these pictures mirrored the pattern found in Experiment 1. In Experiment 3, an attempt was made to override color diagnosticity using linguistic context (e.g., a pumpkin was described as painted green). Linguistic context did not override color diagnosticity. Collectively, the results demonstrate that color information is regularly utilized in object recognition and representation for highly color diagnostic items.     

Action-related objects influence the distribution of visuospatial attention

Previous studies have shown that attention is drawn to the location of manipulable objects and is distributed across pairs of objects that are positioned for action. Here, we investigate whether central, action-related objects can cue attention to peripheral targets. Experiment 1 compared the effect of uninformative arrow and object cues on a letter discrimination task. Arrow cues led to spatial-cueing benefits across a range of stimulus onset asynchronies (SOAs: 0 ms, 120 ms, 400 ms), but object-cueing benefits were slow to build and were only significant at the 400-ms SOA. Similar results were found in Experiment 2, in which the targets were objects that could be either congruent or incongruent with the cue (e.g., screwdriver and screw versus screwdriver and glass). Cueing benefits were not influenced by the congruence between the cue and target, suggesting that the cueing effects reflected the action implied by the central object, not the interaction between the objects. For Experiment 3 participants decided whether the cue and target objects were related. Here, the interaction between congruent (but not incongruent) targets led to significant cueing/positioning benefits at all three SOAs. Reduced cueing benefits were obtained in all three experiments when the object cue did not portray a legitimate action (e.g., a bottle pointing towards an upper location, since a bottle cannot pour upwards), suggesting that it is the perceived action that is critical, rather than the structural properties of individual objects. The data suggest that affordance for action modulates the allocation of visual attention.     

假字的Stroop效应:汉字部件对颜色命名的影响

通过变化左、右部件和上、中、下部件而制作的假字,采用两因素被试内设计,共80名大学生参加两个实验,考察汉字部件的Stroop效应。结果发现:(1)由"红"、"黄"两字不同部件所构成的假字分别影响对红、黄颜色的命名;(2)不同位置的部件所构成的假字,其产生的Stroop效应不同,即左部件比右部件,上部件比中、下部件产生的影响更明显。最后在平行分布式加工模型的范畴内讨论了其加工机制。     

The influence of spatial representation on valence judgements: An event-related potential study

The present study used event-related potentials (ERPs) to explore the nature of space-valence congruency effects. We presented participants with up or down arrows at the centre of the screen and then asked participants to identify whether the following target words had the emotional valence. The target words included positive emotional words (e.g., “happy” and “delight”), negative emotional words (e.g., “sad” and “depressive”) and neutral words (e.g., “history” and “country”). Behavioural data showed that the positive targets were identified faster when they are primed by up arrows than when primed by down arrows, whereas the negative targets were identified faster when they are primed by down arrows than when primed by up arrows. The ERP analysis showed larger P2 amplitudes were found in the congruent condition (i.e., the positive targets following up arrows or the negative targets following down arrows) than in the incongruent condition (i.e., the positive targets following down arrows or the negative targets following up arrows). Furthermore, larger N400 amplitudes were found in the incongruent condition compared with the congruent condition. Moreover, larger LPC amplitudes were found in the congruent condition compared with the incongruent condition. Therefore, in addition to replicating the space-valence congruency effects in a neutral/emotional judgement task, our study also extended previous studies by showing that spatial information modulates the processing of the emotional words at multiple stages.     

Evaluative priming of naming and semantic categorization responses revisited: a mutual facilitation explanation

The evaluative priming effect (i.e., faster target responses following evaluatively congruent compared with evaluatively incongruent primes) in nonevaluative priming tasks (such as naming or semantic categorization tasks) is considered important for the question of how evaluative connotations are represented in memory. However, the empirical evidence is rather ambiguous: Positive effects as well as null results and negatively signed effects have been found. We tested the assumption that different processes are responsible for these results. In particular, we argue that positive effects are due to target-encoding facilitation (caused by a congruent prime), while negative effects are due to prime-activation maintenance (caused by a congruent target) and subsequent response conflict. In 4 experiments, we used a negative prime-target stimulus-onset asynchrony (SOA) to minimize target-encoding facilitation and maximize prime maintenance. In a naming task (Experiment 1), we found a negatively signed evaluative priming effect if prime and target competed for naming responses. In a semantic categorization task (i.e., person vs. animal; Experiments 2 and 3), response conflicts between prime and target were significantly larger in case of evaluative congruence compared with incongruence. These results corroborate the theory that a prime has more potential to interfere with the target response if its activation is maintained by an evaluatively congruent target. Experiment 4a/b indicated valence specificity of the effect. Implications for the memory representation of valence are discussed.     

Semantic facilitation with pictures and words

The present experiments explored the role of processing level and strategic factors in cross-form (word-picture and picture-word) and within-form (picture-picture and word-word) semantic facilitation. Previous studies have produced mixed results. The findings presented in this article indicate that semantic facilitation depends on the task and on the subjects' strategies. When the task required semantic processing of both picture and word targets (e.g., category verification), equivalent facilitation was obtained across all modality combinations. When the task required name processing (e.g., name verification, naming), facilitation was obtained for the picture targets. In contrast, with word targets, facilitation was obtained only when the situation emphasized semantic processing. The results are consistent with models that propose a common semantic representation for both picture and words but that also include assumptions regarding differential order of access to semantic and phonemic features for these stimulus modalities.     

Mixed emotions: holistic and analytic perception of facial expressions

In the face literature, it is debated whether the identification of facial expressions requires holistic (i.e., whole face) or analytic (i.e., parts-based) information. In this study, happy and angry composite expressions were created in which the top and bottom face halves formed either an incongruent (e.g., angry top + happy bottom) or congruent composite expression (e.g., happy top + happy bottom). Participants reported the expression in the target top or bottom half of the face. In Experiment 1, the target half in the incongruent condition was identified less accurately and more slowly relative to the baseline isolated expression or neutral face conditions. In contrast, no differences were found between congruent and the baseline conditions. In Experiment 2, the effects of exposure duration were tested by presenting faces for 20, 60, 100 and 120 ms. Interference effects for the incongruent faces appeared at the earliest 20 ms interval and persisted for the 60, 100 and 120 ms intervals. In contrast, no differences were found between the congruent and baseline face conditions at any exposure interval. In Experiment 3, it was found that spatial alignment impaired the recognition of incongruent expressions, but had no effect on congruent expressions. These results are discussed in terms of holistic and analytic processing of facial expressions.     

RT distribution analysis of category congruence effects with masked primes

Macquarie University, Sydney, New South Wales, Australia In the number magnitude decision task (“Is the number bigger/smaller than 5?”), response to a target (e.g., 3) is faster following a masked prime congruent with the target (e.g., 1) than it is following an incongruent prime (e.g., 9). This category congruence effect has been reported to be “interference-dominant” relative to a neutral prime (e.g., the # sign, the number 5) on the basis of the analysis of mean response time (RT). Using RT distribution analysis as well as mean RTs, we identified two bases for this pattern. One relates to the choice of neutral baseline: The # prime, unlike the digit prime, does not factor in the cost of perceptual transition between the prime and target, and therefore underestimates facilitation and overestimates the interference effect. The second basis of the interference-dominant pattern is a disproportionate slowdown of congruent trials in the slow RT bins. Furthermore, this slowdown is greater for primes that had been used as targets than it is with “novel” primes that have not been responded to as targets. We interpret the results as suggesting that the category congruence effect has two components with different time courses—one based on stimulus-response mapping, and the other on semantic categorization.     

Mixed emotions: Holistic and analytic perception of facial expressions

In the face literature, it is debated whether the identification of facial expressions requires holistic (i.e., whole face) or analytic (i.e., parts-based) information. In this study, happy and angry composite expressions were created in which the top and bottom face halves formed either an incongruent (e.g., angry top + happy bottom) or congruent composite expression (e.g., happy top + happy bottom). Participants reported the expression in the target top or bottom half of the face. In Experiment 1, the target half in the incongruent condition was identified less accurately and more slowly relative to the baseline isolated expression or neutral face conditions. In contrast, no differences were found between congruent and the baseline conditions. In Experiment 2, the effects of exposure duration were tested by presenting faces for 20, 60, 100 and 120 ms. Interference effects for the incongruent faces appeared at the earliest 20 ms interval and persisted for the 60, 100 and 120 ms intervals. In contrast, no differences were found between the congruent and baseline face conditions at any exposure interval. In Experiment 3, it was found that spatial alignment impaired the recognition of incongruent expressions, but had no effect on congruent expressions. These results are discussed in terms of holistic and analytic processing of facial expressions.