What's Behind a "+" Sign? Perceiving an Arithmetic Operator Recruits Brain Circuits for Spatial Orienting.

Do mathematical symbols evoke spatial representations? Although behavioral studies have long demonstrated interactions between space and the processing of Arabic digits, how to interpret these results remains controversial. Here, we tested whether activity in regions supporting spatial processing contributes to the processing of symbols conveying fundamental arithmetic concepts-such as operation signs-even in the absence of associated digits. Using functional magnetic resonance imaging, we show that merely perceiving a "+" sign triggers activity in brain regions that support the orienting of spatial attention in adults. Activity in these regions was greater for "+" than for "×" signs, indicating that it is modulated by whether an operator reflects an operation that evokes numerical manipulation (rather than rote memorization). Finally, the degree to which subjects activated a spatial region in response to a "+" sign was correlated with the degree to which subjects benefited from being briefly presented with that sign before having to calculate a single-digit addition problem, an effect termed operator-priming. Therefore, not only are some arithmetic operators linked to spatial intuitions, but such intuitions might also have an important role during arithmetic calculation. More generally, our findings support the view that mathematical symbols inherently evoke spatial representations.

Substituted-letter and transposed-letter effects in a masked priming paradigm with French developing readers and dyslexics.

The aim of the study was to undertake a behavioral investigation of the development of automatic orthographic processing during reading acquisition in French. Following Castles and colleagues' 2007 study (Journal of Experimental Child Psychology, 97, 165-182) and their lexical tuning hypothesis framework, substituted-letter and transposed-letter primes were used in a masked priming paradigm with third graders, fifth graders, adults, and phonological dyslexics matched on reading level with the third graders. No priming effect was found in third graders. In adults, only a transposed-letter priming effect was found; there was no substituted-letter priming effect. Finally, fifth graders and dyslexics showed both substituted-letter and transposed-letter priming effects. Priming effects between the two groups were of the same magnitude after response time (RT) z-score transformation. Taken together, our results show that the pattern of priming effects found by Castles and colleagues in English normal readers emerges later in French normal readers. In other words, language orthographies seem to constrain the tuning of the orthographic system, with an opaque orthography producing faster tuning of orthographic processing than more transparent orthographies because of the high level of reliance on phonological decoding while learning to read.

Acquisition of new arithmetic skills based on prior arithmetic skills: A cross-sectional study in primary school from grade 2 to grade 5.

BACKGROUND: In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations. AIM: In order to address this question, our goal was to determine the predictive power of previously taught operations on newly taught ones above general cognitive skills and basic numerical skills. SAMPLES: More than one hundred children in each school level from Grades 2 to 5 from various socio-cultural environments (N = 435, 229 girls) were tested. METHODS: Children were assessed on their abilities to solve the four basic arithmetic operations. They were also tested on their general cognitive abilities, including working memory, executive functions (i.e., inhibition and flexibility), visual attention and language. Finally, their basic numerical skills were measured through a matching task between symbolic and nonsymbolic numerosity representations. Additions and subtractions were presented to children from Grade 2, multiplications from Grade 3 and divisions from Grade 4. RESULTS AND CONCLUSIONS: We show that addition predicts subtraction and multiplication performance in all grades. Moreover, multiplication predicts division performance in both Grades 4 and 5. Finally, addition predicts division in Grade 4 but not in Grade 5 and subtraction and division are not related whatever the school grade. These results are examined considering the existing literature, and their implications in terms of instruction are discussed.

Facilitating Text Production in Fourth Graders: Effects of Script-Based Knowledge and Writing Prompts.

This study aimed at providing evidence that prior knowledge (semantic relatedness) and its organization (scripted versus not related) prompted either through pictures alone, pictures and associated words, words only have different impacts on several components of text produced by fourth graders. The results showed that the semantic relatedness affected three dependent measures: prompt words recalled, coherence and quality of texts. The nature of the prompts impacted on planning (number of ideas) and translating (number of propositions and length of texts) processes. Findings, instructional applications, limitations, and proposals for future research are discussed.

Rapid automatized naming skills of children with intellectual disability.

BACKGROUND: A deficit in Rapid Automatized Naming (RAN), acknowledged to be linked to dyslexia, has rarely been investigated as a potential explanation of the reading difficulties that children with intellectual disability (ID) often face. The existing studies mainly focused on adolescent or adults with ID matched to typically developing (TD) children on verbal mental age, or used a single RAN task. AIMS: The aim of this study was to compare the RAN pattern and skills of children with ID and low reading skills to the ones of TD children with matched reading skills. METHOD: 30 children with mild to moderate ID with mixed etiology (M = 9.4 years-old) were pair-matched to 30 TD children (M = 4.3 years-old) on phonological awareness- and reading-level. They were all administered color, object, finger, and vowel RAN tasks. OUTCOMES AND RESULTS: Results showed that children with ID had more domain-specific RAN skills and were largely slower in most of the RAN tasks than their younger TD peers. CONCLUSIONS AND IMPLICATIONS: This suggests that a deficit in RAN should be added to the explanations of their frequent reading difficulties, which might open new remediation possibilities.

Evidence for knowledge of the syntax of large numbers in preschoolers.

The aim of this study was to provide evidence for knowledge of the syntax governing the verbal form of large numbers in preschoolers long before they are able to count up to these numbers. We reasoned that if such knowledge exists, it should facilitate the maintenance in short-term memory of lists of lexical primitives that constitute a number (e.g., three hundred forty five) compared with lists containing the same primitives but in a scrambled order (e.g., five three forty hundred). The two types of lists were given to 5-year-olds in an immediate serial recall task. As we predicted, the lists in syntactic order were easier to recall, suggesting that they match some knowledge of the way lexical primitives must be ordered to express large numerosities.

When one-two-three beats two-one-three: Tracking the acquisition of the verbal number sequence.

Learning how to count is a crucial step in cognitive development, which progressively allows for more elaborate numerical processing. The existing body of research consistently reports how children associate the verbal code with exact quantity. However, the early acquisition of this code, when the verbal numbers are encoded in long-term memory as a sequence of words, has rarely been examined. Using an incidental assessment method based on serial recall of number words presented in ordered versus non-ordered sequences (e.g., one-two-three vs. two-one-three), we tracked the progressive acquisition of the verbal number sequence in children aged 3-6 years. Results revealed evidence for verbal number sequence knowledge in the youngest children even before counting is fully mastered. Verbal numerical knowledge thus starts to be organized as a sequence in long-term memory already at the age of 3 years, and this numerical sequence knowledge is assessed in a sensitive manner by incidental rather than explicit measures of number knowledge.

The use of automated procedures by older adults with high arithmetic skills during addition problem solving.

In contrast to other cognitive abilities, arithmetic skills are known to be preserved in healthy elderly adults. In fact, they would even outperform young adults because they more often retrieve arithmetic facts from long-term memory. Nevertheless, we suggest here that the superiority of older over younger adults could also stem from the use of more efficient automated and unconscious counting procedures. We tested 35 older participants using the sign priming paradigm and selected the 18 most efficient ones, aged from 60 to 77. Sign priming is interpreted as the indicator of the preactivation of an abstract procedure as soon as the arithmetic sign is presented. We showed that expert elderly arithmeticians behaved exactly as 26 young participants presenting the same level of arithmetic proficiency. More precisely, we showed that presenting the "+" sign 150 ms before the operands speeds up the solving process compared to a situation wherein the problem is classically presented in its whole on the screen. Only tie problems and problems involving 0 were not subjected to these priming effects, and we concluded that only these problems were solved by retrieval, either of the answer for tie problems or of a rule for + 0 problems. These results could provide new insights for the conception of training programs aiming at preserving older individuals' arithmetical skills and, in a longer-term perspective, at maintaining their financial autonomy, which is decisive for keeping them in charge of their daily life. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Usage-based account of the acquisition of liaison: evidence from sensitivity to the singular/plural orientation of nouns.

This study investigates whether children's production and recognition of obligatory liaison sequences in French depend on the singular/plural orientation of nouns. Certain nouns occur more frequently in the plural (e.g., arbre "tree"), whereas others are found more often in the singular (e.g., arc-en-ciel "rainbow"). In the input, children more frequently encounter these plural-oriented nouns after determiners that indicate plurality (e.g., les,des "the", deux "two") and that are often associated with a /z/ liaison (e.g., deux arbres [døzarbr] "two trees"). In Experiment 1, 122 children (3 years 2 months to 6 years 3 months of age) were asked to produce nominal phrases with either /z/ liaisons (i.e., in plural contexts such as deux ours [døzurs] "two bears") or /n/ liaisons (i.e., in singular contexts such as un ours [oe nurs] "one bear"). We found correlations between the plural orientation of the nouns and (a) the probability that they will be preceded by an incorrect /z/ liaison in the singular context and (b) the probability that they will be preceded by a correct /z/ liaison in the plural context. This result was, however, restricted to the younger children. In Experiment 2, 20 children (5 years 5 months to 6 years 3 months of age) were asked to monitor target words in auditorily presented sentences. The results showed shorter reaction times for singular-oriented nouns when preceded by a singular determiner than when preceded by a plural determiner. Conversely, plural-oriented nouns were responded to faster when preceded by a plural determiner than when preceded by a singular determiner. Results are discussed within the framework of a two-stage model of liaison acquisition recently proposed by Chevrot, Chabanal, and Dugua (Journal of French Language Studies,17 [2007] 103-128) as well as by Chevrot, Dugua, and Fayol (Journal of Child Language [in press]).

[Acquisition of arithmetic knowledge]. / L'acquisition de l'arithmétique élémentaire.

The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3).

Hippocampal spatial mechanisms relate to the development of arithmetic symbol processing in children.

Understanding the meaning of abstract mathematical symbols is a cornerstone of arithmetic learning in children. Studies have long focused on the role of spatial intuitions in the processing of numerals. However, it has been argued that such intuitions may also underlie symbols that convey fundamental arithmetic concepts, such as arithmetic operators. In the present cross-sectional study, we used fMRI to investigate how and when associations between arithmetic operators and brain regions processing spatial information emerge in children from 3rd to 10th grade. We found that the mere perception of a '+' sign elicited grade-related increases of spatial activity in the right hippocampus. That is, merely perceiving '+' signs - without any operands - elicited enhanced hippocampal activity after around 7th grade (12-13 years old). In these children, hippocampal activity in response to a '+' sign was further correlated with the degree to which calculation performance was facilitated by the preview of that sign before an addition problem, an effect termed operator-priming. Grade-related increases of hippocampal spatial activity were operation-specific because they were not observed with '×' signs, which might evoke rote retrieval rather than numerical manipulation. Our study raises the possibility that hippocampal spatial mechanisms help build associations between some arithmetic operators and space throughout age and/or education.

General and Specific Contributions of RAN to Reading and Arithmetic Fluency in First Graders: A Longitudinal Latent Variable Approach.

In the present study, we opted for a longitudinal design and examined rapid automatized naming (RAN) performance from two perspectives. In a first step, we examined the structure of RAN performance from a general cognitive perspective. We investigated whether rapid naming measures (e.g., digit RAN and color RAN) reflect a mainly domain-general factor or domain-specific factors. In a second step, we examined how the best fitting RAN model was related to reading and arithmetic outcomes, assessed several months later. Finally in a third step we took a clinical perspective and investigated specific contributions of RAN measures to reading and arithmetic outcomes. While RAN has emerged as a promising predictor of reading, the relationship between RAN and arithmetic has been less examined in the past. Hundred and twenty-two first graders completed seven RAN tasks, each comprising visually familiar stimuli such as digits, vowels, consonants, dice, finger-numeral configurations, objects, and colors. Four months later the same children completed a range of reading and arithmetic tasks. From a general descriptive perspective, structural equation modeling supports a one-dimensional RAN factor in 6- to -7-year-old children. However, from a clinical perspective, our findings emphasize the specific contributions of RANs. Interestingly, alphanumeric RANs (i.e., vowel RAN) were most promising when predicting reading skills and number-specific RANs (i.e., finger-numeral configuration RAN) were most promising when predicting arithmetic fluency. The implications for clinical and educational practices will be discussed.

Relationships of French and English Morphophonemic Orthographies to Word Reading, Spelling, and Reading Comprehension during Early and Middle Childhood.

Two longitudinal studies of word reading, spelling, and reading comprehension identified commonalities and differences in morphophonemic orthographies-French (Study 1, n=1313) or English (Study 2, n=114) in early childhood (grade 2) and middle childhood (grade 5). For French and English, statistically significant concurrent relationships among these literacy skills occurred in grades 2 and 5, and longitudinal relationships for each skill with itself from grade 2 to 5; but concurrent relationships were more sizable and longitudinal relationships more variable for English than French especially for word reading to reading comprehension. Results show that, for both morphophonemic orthographies, assessment and instructional practices should be tailored to early or middle childhood, and early childhood reading comprehension may not be related to middle childhood spelling. Also discussed are findings applying only to English, for which word origin is primarily Anglo-Saxon in early childhood, but increasingly French in middle childhood.

Identifying strategies in arithmetic with the operand recognition paradigm: a matter of switch cost?

Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we developed the operand recognition paradigm (ORP). It capitalizes on the fact that, contrary to retrieval, calculation procedures degrade the memory traces of the operands involved in a problem. As a consequence, the use of calculation procedures is inferred from relatively long recognition times of the operands. However, it has been suggested that recognition times within the ORP do not reflect strategies but the difficulty of switching from a difficult task (calculation) to a simpler one (recognition). In order to examine this possibility, in a series of 3 experiments we equalized switch-cost variations in all conditions through the introduction of intermediate tasks between problem solving and recognition. Despite this neutralization, we still obtained the classical effects of the ORP, namely longer recognition times after addition than after comparison. We conclude that the largest part of the ORP effects is related to different strategy use and not to difficulty-related switch costs. The possible applications and promising outcomes of the ORP in and outside the field of numerical cognition are discussed.

Lexical orthographic knowledge develops from the beginning of literacy acquisition.

This study reports two experiments assessing the spelling performance of French first graders after 3 months and after 9 months of literacy instruction. The participants were asked to spell high and low frequency irregular words (Experiment 1) and pseudowords, some of which had lexical neighbours (Experiment 2). The lexical database which children had been exposed to was strictly controlled. Both a frequency effect in word spelling accuracy and an analogy effect in pseudoword spelling were obtained after only 3 months of reading instruction. The results suggest that children establish specific orthographic knowledge from the very beginning of literacy acquisition.

Written but not oral verbal production is preserved in young schizophrenic patients.

The aim of this study is to discover whether the language capabilities of young schizophrenic patients are more affected in speaking than in writing or whether the disorders are equivalent in the two modes. To do this, we compared spoken and written descriptions of pictures obtained from 10 schizophrenic patients with those produced by 10 control subjects. These productions were analysed on the basis of objective indices. The syntax and coherence of the productions were evaluated by judges. The comparison of the performances of the controls and schizophrenic patients supports the hypothesis that the latter suffer from a language disorder affecting the oral mode but impacting less frequently and less severely on the written mode. These results are discussed in the light of the cognitive mechanisms which may provide an explanation of these language disorders.

The determinants of spoken and written picture naming latencies.

The influence of nine variables on the latencies to write down or to speak aloud the names of pictures taken from Snodgrass and Vanderwart (1980) was investigated in French adults. The major determinants of both written and spoken picture naming latencies were image variability, image agreement and age of acquisition. To a lesser extent, name agreement was also found to have an impact in both production modes. The implications of the findings for theoretical views of both spoken and written picture naming are discussed.

Interword and intraword pause threshold in writing.

Writing words in real life involves setting objectives, imagining a recipient, translating ideas into linguistic forms, managing grapho-motor gestures, etc. Understanding writing requires observation of the processes as they occur in real time. Analysis of pauses is one of the preferred methods for accessing the dynamics of writing and is based on the idea that pauses are behavioral correlates of cognitive processes. However, there is a need to clarify what we are observing when studying pause phenomena, as we will argue in the first section. This taken into account, the study of pause phenomena can be considered following two approaches. A first approach, driven by temporality, would define a threshold and observe where pauses, e.g., scriptural inactivity occurs. A second approach, linguistically driven, would define structural units and look for scriptural inactivity at the boundaries of these units or within these units. Taking a temporally driven approach, we present two methods which aim at the automatic identification of scriptural inactivity which is most likely not attributable to grapho-motor management in texts written by children and adolescents using digitizing tablets in association with Eye and Pen (©) (Chesnet and Alamargot, 2005). The first method is purely statistical and is based on the idea that the distribution of pauses exhibits different Gaussian components each of them corresponding to a different type of pause. After having reviewed the limits of this statistical method, we present a second method based on writing dynamics which attempts to identify breaking points in the writing dynamics rather than relying only on pause duration. This second method needs to be refined to overcome the fact that calculation is impossible when there is insufficient data which is often the case when working with young scriptors.

Learning to spell from reading: general knowledge about spelling patterns influences memory for specific words.

Adults often learn to spell words during the course of reading for meaning, without intending to do so. We used an incidental learning task in order to study this process. Spellings that contained double n, r and t which are common doublets in French, were learned more readily by French university students than spellings that contained less common but still legal doublets. When recalling or recognizing the latter, the students sometimes made transposition errors, doubling a consonant that often doubles in French rather than the consonant that was originally doubled (e.g., tiddunar recalled as tidunnar). The results, found in three experiments using different nonwords and different types of instructions, show that people use general knowledge about the graphotactic patterns of their writing system together with word-specific knowledge to reconstruct spellings that they learn from reading. These processes contribute to failures and successes in memory for spellings, as in other domains.

The use of the operand-recognition paradigm for the study of mental addition in older adults.

OBJECTIVES: Determining how individuals solve arithmetic problems is crucial for our understanding of human cognitive architecture. Elderly adults are supposed to use memory retrieval more often than younger ones. However, they might backup their retrieval by reconstructive strategies. In order to investigate this issue, we used the operand-recognition paradigm, which capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. METHOD: Twenty-three older adults (M = 70.4) and 23 younger adults (M = 20.0) solved easy, difficult, and medium-difficulty addition and comparison problems and were then presented with a recognition task of the operands. RESULTS: When one-digit numbers with sums larger than 10 were involved (medium-difficulty problem), it was more difficult for younger adults to recognize the operands after addition than comparison. In contrast, in older adults, recognition times of the operands were the same after addition and comparison. DISCUSSION: Older adults, in contrast with younger adults, are able to retrieve the results of addition problems of medium difficulty. Contrary to what was suggested, older participants do not seem to resort to backup strategies for such problems. Finally, older adults' reliance on the more efficient retrieval strategy allowed them to catch up to younger adults in terms of solution times.