Comprehension of algebraic expressions by experienced users of mathematics

Little is known about how people comprehend mathematical expressions. In the present study we investigate the internal representations used by experienced users of mathematics to encode algebraic expressions. Initially, a memory recognition task was conducted that examined the role of mathematical syntax in the encoding of algebraic expressions. The results indicate that participants could more readily identify those parts of a previously seen expression that were syntactically well formed than those that were not well formed, suggesting that syntax plays an important role. To determine the level of syntactic structure involved, a second recognition task was conducted. The results indicate that algebraic expressions are encoded into components that represent the phrasal constituents of the expression. However, the results of these experiments did not rule out the possibility that the visual processes of perceptual organization were used to encode the expressions, or that the data were a consequence of a mathematical “lexicon” of common mathematical “phrases”. Three further experiments were conducted to examine this, the results of which indicate that the encoding of algebraic expressions is based primarily on processes that occur beyond the level of visual or “lexical” processing. This is consistent with our finding that syntactic structure plays a key role.     

Planning in sentence production: Evidence for the phrase as a default planning scope

Controversy remains as to the scope of advanced planning in language production. Smith and Wheeldon (1999) found significantly longer onset latencies when subjects described moving-picture displays by producing sentences beginning with a complex noun phrase than for matched sentences beginning with a simple noun phrase. While these findings are consistent with a phrasal scope of planning, they might also be explained on the basis of: (1) greater retrieval fluency for the second content word in the simple initial noun phrase sentences and (2) visual grouping factors. In Experiments 1 and 2, retrieval fluency for the second content word was equated for the complex and simple initial noun phrase conditions. Experiments 3 and 4 addressed the visual grouping hypothesis by using stationary displays and by comparing onset latencies for the same display for sentence and list productions. Longer onset latencies for the sentences beginning with a complex noun phrase were obtained in all experiments, supporting the phrasal scope of planning hypothesis. The results indicate that in speech, as in other motor production domains, planning occurs beyond the minimal production unit.     

The sausage machine: A new two-stage parsing model

It is proposed that the human sentence parsing device assigns phrase structure to word strings in two steps. The first stage parser assigns lexical and phrasal nodes to substrings of roughly six words. The second stage parser then adds higher nodes to link these phrasal packages together into a complete phrase marker.This model of the parser is compared with ATN models, and with the two-stage models of Kimball (1973) and Fodor, Bever and Garrett (1974). Our assumption that the units which are shunted from the first stage to the second stage are defined by their length, rather than by their syntactic type, explains the effects of constituent length on perceptual complexity in center embedded sentences and in sentences of the kind that fall under Kimball's principle of Right Association. The particular division of labor between the two parsing units allows us to explain, without appeal to any ad hoc parsing strategies, why the parser makes certain ‘shortsighted’ errors even though, in general, it is able to make intelligent use of all the information that is available to it.     

A neutral face is not neutral even if you have not seen it: social anxiety disorder and affective priming with facial expressions

Cognitive theories suggest that social anxiety disorder (SAD) is characterized by biased processing of negative facial expressions. Recently, however, it has been proposed that the fear of positive evaluation may play an additional, important role. In order to investigate which specific expressions evoke biased processing, 15 patients diagnosed with SAD and 15 non-anxious controls (NACs) completed an affective priming procedure: they rated neutral symbols which were preceded by sub-optimally presented primes of angry, neutral, and smiling faces. Patients with SAD rated the symbols significantly more negatively than NACs when they were primed with a neutral face. In addition, SAD patients tended to rate all symbols significantly more negatively suggesting that all faces (negative, positive, and neutral) are threatening to SAD patients.     

Lexical or syntactic control of sentence formulation? Structural generalizations from idiom production

To compare abstract structural and lexicalist accounts of syntactic processes in sentence formulation, we examined the effectiveness of nonidiomatic and idiomatic phrasal verbs in inducing structural generalizations. Three experiments made use of a syntactic priming paradigm in which participants recalled sentences they had read in rapid serial visual presentation. Prime and target sentences contained phrasal verbs with particles directly following the verb (pull off a sweatshirt) or following the direct object (pull a sweatshirt off). Idiomatic primes used verbs whose figurative meaning cannot be straightforwardly derived from the literal meaning of the main verb (e.g., pull off a robbery) and are commonly treated as stored lexical units. Particle placement in sentences was primed by both nonidiomatic and idiomatic verbs. Experiment 1 showed that the syntax of idiomatic and nonidiomatic phrasal verbs is amenable to priming, and Experiments 2 and 3 compared the priming patterns created by idiomatic and nonidiomatic primes. Despite differences in idiomaticity and structural flexibility, both types of phrasal verbs induced structural generalizations and differed little in their ability to do so. The findings are interpreted in terms of the role of abstract structural processes in language production.     

The Effect of Phonemic Repetition on Syntactic Ambiguity Resolution: Implications for Models of Working Memory

Two reading experiments investigated the extent to which the presence of phonemic repetition in sentences influenced processing difficulty during syntactic ambiguity resolution. In both experiments, participants read sentences silently as reading time was measured. Reading time on sentences containing a temporary syntactic ambiguity was compared to reading time on unambiguous control sentences. Sentences either did or did not contain repeated phonemes. The results showed that reading time was longer for sentences containing a syntactic ambiguity than for unambiguous control sentences. Reading time was also longer on sentences containing repeated phonemes than on sentences that did not contain repeated phonemes. Phonemic repetition did not increase the time taken for syntactic ambiguity resolution; rather, the effects of syntactic ambiguity and phonemic repetition were temporally distinct, with the effect of phonemic repetition following the effect of syntactic ambiguity. Implications for theories of working memory are discussed.     

Working memory and planning during sentence production

Speakers retrieve conceptual, syntactic and lexical information in advance of articulation during sentence production. What type of working memory (WM) store is used to hold the planned information before speaking? To address this question, we measured onset latencies when subjects produced sentences that began with either a complex or a simple initial noun phrase, while holding semantic, phonological or spatial information in WM. Although we found that subjects had longer onset latencies for sentences beginning with a complex noun phrase, showing a phrasal scope of planning, the magnitude of this complexity effect was not affected by any type of WM load. However, subjects made more syntactic errors (but not lexical errors) for sentences beginning with a complex noun phrase, suggesting that advance planning for these phrases occurs at a syntactic rather than lexical–semantic level, which may account for the lack of effect with various types of WM load in the current study.     

Young children's use of prosody in sentence parsing

Korean children's ability to use prosodic phrasing in sentence comprehension was studied using two types of ambiguity. First, we examined a word-segmentation ambiguity in which placement of the phrasal boundary leads to different interpretations of a sentence. Next, we examined a syntactic ambiguity in which the same words were differently grouped into syntactic phrases by prosodic demarcation. Children aged 3 or 4 years showed that they could use prosodic information to segment utterances and to derive the meaning of ambiguous sentences when the sentences only contained a word-segmentation ambiguity. However, even 5- to 6-year-old children were not able to reliably resolve the second type of ambiguity, an ambiguity of phrasal grouping, by using prosodic information. The results demonstrate that children's difficulties in dealing with structural ambiguity are not due to their inability to use prosodic information.     

From exemplar to grammar: a probabilistic analogy-based model of language learning

While rules and exemplars are usually viewed as opposites, this paper argues that they form end points of the same distribution. By representing both rules and exemplars as (partial) trees, we can take into account the fluid middle ground between the two extremes. This insight is the starting point for a new theory of language learning that is based on the following idea: If a language learner does not know which phrase-structure trees should be assigned to initial sentences, s/he allows (implicitly) for all possible trees and lets linguistic experience decide which is the "best" tree for each sentence. The best tree is obtained by maximizing "structural analogy" between a sentence and previous sentences, which is formalized by the most probable shortest combination of subtrees from all trees of previous sentences. Corpus-based experiments with this model on the Penn Treebank and the Childes database indicate that it can learn both exemplar-based and rule-based aspects of language, ranging from phrasal verbs to auxiliary fronting. By having learned the syntactic structures of sentences, we have also learned the grammar implicit in these structures, which can in turn be used to produce new sentences. We show that our model mimicks children's language development from item-based constructions to abstract constructions, and that the model can simulate some of the errors made by children in producing complex questions.     

Not Propositions

Current computational accounts of meaning in the cognitive sciences are based on abstract, amodal symbols (e.g., nodes, links, propositions) that are arbitrarily related to their referents. We argue that such accounts lack convincing empirical support and that they do not provide a satisfactory account for linguistic meaning. One historic set of results supporting the abstract symbol view has come from investigation into comprehension of negated sentences, such as “The buttons are not black.” These sentences are presumed to be understood as two propositions composed of abstract symbols. One proposition corresponds to “the buttons are black,” and it is embedded in another proposition corresponding to “it is not true.” Thus, the propositional account predicts (a) that comprehension of negated sentences should take longer than comprehension of the corresponding positive sentence (because of the time needed to construct the embedding), but (b) that the resulting embedded propositions are informationally equivalent (but of opposite valence) to the simple proposition underlying the positive sentence. Contrary to these predictions, Experiment 1 demonstrates that negated sentences out of context are interpreted as situationally ambiguous, that is, as conveying less specific information than positive sentences. Furthermore, Experiment 2 demonstrates that when negated sentences are used in an appropriate context, readers do not take longer to understand them. Thus, difficulty with negation is demonstrated to be an artifact of presentation out of context. After discussing other serious problems with the use of abstract symbols, we describe the Indexical Hypothesis. This embodied account of meaning does not depend on abstract symbols, and hence it provides a more satisfactory account of meaning.     

Communication and Strong Compositionality

Ordinary semantic compositionality (meaning of whole determined from meanings of parts plus composition) can serve to explain how a hearer manages to assign an appropriate meaning to a new sentence. But it does not serve to explain how the speaker manages to find an appropriate sentence for expressing a new thought. For this we would need a principle of inverse compositionality, by which the expression of a complex content is determined by the expressions of it parts and the mode of composition. But this presupposes that contents have constituent structure, and this cannot be taken for granted. However, it can be proved that if a certain principle of substitutivity is valid for a particular language, then the meanings expressed by its sentences can justifiably be treated as structured. In its simplest form, this principle says that if in a complex expression a constituent is replaced by another constituent with a different meaning, the new complexhas a meaning different from the original. This principle is again inversely related to the normal compositional principle of substitutivity. The combination of ordinary and inverse compositionality is here called strong compositionality. The proof is carried out in the algebraic framework developed by Wilfrid Hodges and Dag Westerståhl.     

Exploring the forgetting mechanisms in working memory: Evidence from a reasoning span test

In working memory (WM) span tests participants have to maintain to-be-remembered information while processing other, potentially distracting, information. Previous studies have shown that WM span scores are greater when span lists start with a long processing task and end with a short processing task than when these processing tasks are presented in the reverse order (e.g., Towse, Hitch, & Hutton, 2000). In Experiment 1, we obtained a similar stimulus order effect in a reasoning span test, using reasoning sentences that were equated for length in terms of the number of constituent words, but which differed in processing complexity; span scores were greater when lists began with a complex sentence and ended with a simple sentence than when this stimulus order was reversed. In Experiment 2, the stimulus order effect was not found when processing duration was held constant while sentence complexity was varied using a computer-paced moving window presentation paradigm. These results suggest that duration-based constraints can affect degree of forgetting independently of the load generated during processing phases in WM span performance and therefore imply that time-related forgetting can occur in WM span tests, particularly when the difficulty of the processing component blocks active maintenance of to-be-remembered material.     

How do rhesus monkeys (<Emphasis Type="Italic">Macaca mulatta</Emphasis>) scan faces in a visual paired comparison task?

When novel and familiar faces are viewed simultaneously, humans and monkeys show a preference for looking at the novel face. The facial features attended to in familiar and novel faces, were determined by analyzing the visual exploration patterns, or scanpaths, of four monkeys performing a visual paired comparison task. In this task, the viewer was first familiarized with an image and then it was presented simultaneously with a novel and the familiar image. A looking preference for the novel image indicated that the viewer recognized the familiar image and hence differentiates between the familiar and the novel images. Scanpaths and relative looking preference were compared for four types of images: (1) familiar and novel objects, (2) familiar and novel monkey faces with neutral expressions, (3) familiar and novel inverted monkey faces, and (4) faces from the same monkey with different facial expressions. Looking time was significantly longer for the novel face, whether it was neutral, expressing an emotion, or inverted. Monkeys did not show a preference, or an aversion, for looking at aggressive or affiliative facial expressions. The analysis of scanpaths indicated that the eyes were the most explored facial feature in all faces. When faces expressed emotions such as a fear grimace, then monkeys scanned features of the face, which contributed to the uniqueness of the expression. Inverted facial images were scanned similarly to upright images. Precise measurement of eye movements during the visual paired comparison task, allowed a novel and more quantitative assessment of the perceptual processes involved the spontaneous visual exploration of faces and facial expressions. These studies indicate that non-human primates carry out the visual analysis of complex images such as faces in a characteristic and quantifiable manner.     

The active use of grammar in speech perception

Judgments of the location of short bursts of noise in sentences were used to reveal perceptual segmentation of sentences. It was assumed that segmentation would correspond to major constituent boundaries. In order to control for correlated variables of pitch and intonation, identical acoustic material was provided with alternate constituent structures. It was found that differences in response to identical strings were predicted by the points of variation in constituent structure.     

An experimental approach to the design of cartographic symbols

Graphic designers and an experimental psychologist worked together to improve the design of two map symbols which are frequently confused: the symbols for cuttings and embankments on topographic maps. The problem was analysed in terms of the function of the symbols and their likely cognitive representations. Tests were developed to evaluate alternative designs, including an intervisibility task which requirred users to visualize the landform from the symbols viewed in the context of a map. Tests were given to schoolchildren and to experienced map users in order to compare the standard symbols with five alternative designs. Children's performance was strongly affected by the symbols they used, but experienced users were much less affected. After some refinement of the symbols a further experiment demonstrated the superiority of a number of alternative designs over the existing symbols on a range of test: scores were almost double on the intervisibility task. The paper makes recommendations to cartographers and argues for greater consideration of the inexperienced map user in the design process.     

Memory effects in syntactic ERP tasks

The study presented here investigated the role of memory in normal sentence processing by looking at ERP effects to normal sentences and sentences containing grammatical violations. Sentences where the critical word was in the middle of the sentence were compared to sentences where the critical word always occurred in sentence-final position. Grammaticality judgments were required at the end of the sentence. While the violations in both conditions result in the expected increase in the P600 component (reflecting the fact that the syntactic violation is being processed), the sentences with the sentence-medial critical word also result in a late frontal negativity effect. It is hypothesized that this effect is due to greater memory requirements that are needed to keep the violation in mind until a response can be made at the end of the sentence. The maintenance of the decision that a sentence is ungrammatical must be kept in memory longer for sentence-medial violations as opposed to when the violation occurs at the end of the sentence (immediately preceding the moment at which the judgment can be made).     

儿童句子错误记忆:发展性逆转现象及精加工推理效应

为探究文本背景下句子错误记忆的发展性逆转现象及精加工推理效应,95名有效被试学习3篇文本材料后,参与由学过句、内涵推理句、外延推理句和无关句组成的再认测验。结果发现：（1）高中二年级被试学过句的正确再认率和关键诱饵句的校正的错误再认率均显著高于小学五年级和初中二年级,后二者差异不显著;（2）内涵推理句错误再认率高于外延推理句,高中二年级被试尤甚。结论：（1）句子真实记忆随着年龄增长而增加;句子错误记忆存在发展性逆转现象,初中二年级到高中二年级是句子错误记忆发展相对迅速的阶段;（2）文本背景下,不同的精加工推理诱发了不同程度的句子错误记忆,这种精加工推理效应与一般世界知识的自上而下激活的程度有关。     

Priority Information Used for the Processing of Japanese Sentences: Thematic Roles,Case Particles or Grammatical Functions?

The present study investigated scrambling effects on the processing of Japanese sentences and priority information used among thematic roles, case particles and grammatical functions. Reaction times for correct sentence decisions were significantly prolonged for scrambled active sentences with transitive verbs in the first experiment and with ditransitive verbs in the second experiment. Errors were made with scrambled sentences more than canonical sentences in both experiments, which suggested that scrambling effects were apparent in active sentences. Passive sentences in the third experiment indicated that canonical order defined based on case particles, not thematic roles, was more quickly and accurately identified than scrambled order. Potential sentences in the fourth experiment and causative sentences in the fifth experiment indicated that the processing of scrambled sentences based on grammatical functions, but not on case particles, required longer reaction times and resulted in higher error rates than canonical sentences. Consequently, scrambling effects in the present study indicated that neither thematic roles nor case particles can provide fully-satisfactory information for canonical phrase order, and that only grammatical functions offer satisfactory information in all types of sentences.     

Seeing a phrase "time and again" matters: the role of phrasal frequency in the processing of multiword sequences

Are speakers sensitive to the frequency with which phrases occur in language? The authors report an eye-tracking study that investigates this by examining the processing of multiword sequences that differ in phrasal frequency by native and proficient nonnative English speakers. Participants read sentences containing 3-word binomial phrases (bride and groom) and their reversed forms (groom and bride), which are identical in syntax and meaning but that differ in phrasal frequency. Mixed-effects modeling revealed that native speakers and nonnative speakers, across a range of proficiencies, are sensitive to the frequency with which phrases occur in English. Results also indicate that native speakers and higher proficiency nonnatives are sensitive to whether a phrase occurs in a particular configuration (binomial vs. reversed) in English, highlighting the contribution of entrenchment of a particular phrase in memory.     

Word order and information status in child language

In expressing rich, multi-dimensional thought in language, speakers are influenced by a range of factors that influence the ordering of utterance constituents. A fundamental principle that guides constituent ordering in adults has to do with information status, the accessibility of referents in discourse. Typically, adults order previously mentioned referents ("old" or accessible information) first, before they introduce referents that have not yet been mentioned in the discourse ("new" or inaccessible information) at both sentential and phrasal levels. Here we ask whether a similar principle influences ordering patterns at the phrasal level in children who are in the early stages of combining words productively. Prior research shows that when conveying semantic relations, children reproduce language-specific ordering patterns in the input, suggesting that they do not have a bias for any particular order to describe "who did what to whom". But our findings show that when they label "old" versus "new" referents, 3- to 5-year-old children prefer an ordering pattern opposite to that of adults (Study 1). Children's ordering preference is not derived from input patterns, as "old-before-new" is also the preferred order in caregivers' speech directed to young children (Study 2). Our findings demonstrate that a key principle governing ordering preferences in adults does not originate in early childhood, but develops: from new-to-old to old-to-new.