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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.

Socioeconomic status (SES) has been shown to be associated with children's arithmetic knowledge as early as kindergarten, which is an important issue, given that early numeracy knowledge and skills usually correlate to later academic achievement in arithmetic. In line with recent research, it is argued that the regular practice of exercises involving cardinality, ordinality and arithmetic transformations during class time could accelerate the progress of children, particularly among low-SES children. Participants were 118 kindergarteners (M[subscript age] = 3.87). Teachers were randomly assigned to the intervention group (immediate implementation of the intervention; N = 64) or the control group (intervention delayed, N = 54). This intervention consisted of playful exercises involving quantities and numerical transformations. The results indicated that the intervention tended to accelerate progress on the verbal numerical sequence, particularly among lower-SES children. In addition, the intervention tended to accelerate progress on cardinality and arithmetic. These results provide preliminary evidence of the effectiveness of the intervention to help children acquire basic mathematical skills.

Two longitudinal studies of word reading, spelling, and reading comprehension identified commonalities and differences in morphophonemic orthographies--French (Study 1, n = 1,313) 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 Grades 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.

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.

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. (Contains 2 tables.)

In a first experiment, adults were asked to solve one-digit additions, subtractions and multiplications. When the sign appeared 150 ms before the operands, addition and subtraction were solved faster than when the sign and the operands appeared simultaneously on screen. This priming effect was not observed for multiplication problems. A second experiment replicates these results on addition and multiplication and, moreover, shows that the priming effect in addition is observed for all problems, including very small ones such as 4 + 3. In fact, the only problems that were not primed by the addition sign were tie problems, which confirms that they have a special status in memory. Taken together, these results suggest that abstract procedures are pre-activated by the addition and subtraction signs and that these procedures are consequently used by adults to solve the problems. No such procedures would be pre-activated for multiplication, which are then most probably solved by retrieval of the result from memory. Moreover, while obviously two different strategies were used by individuals in order to solve addition and multiplication, solution times were similar when the problems were presented in their whole. These results, which question most of the conclusions of the current literature, support Anderson's model (1982) and Baroody's assumptions (1983) on the existence of compacted procedures that could be as fast as retrievals. (Contains 4 tables and 2 figures.)

The authors used the operand-recognition paradigm (C. Thevenot, M. Fanget, & M. Fayol, 2007) in order to study the strategies used by adults to solve subtraction problems. This paradigm capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. Therefore, greater difficulty in recognizing them is expected when calculations have been solved by reconstructive strategies rather than by retrieval of number facts from long-term memory. The present results suggest that low- and high-skilled individuals differ in their strategy when they solve problems involving minuends from 11 to 18. Whereas high-skilled individuals retrieve the results of such subtractions from long-term memory, lower skilled individuals have to resort to reconstructive strategies. Moreover, the authors directly confront the results obtained with the operand-recognition paradigm and those obtained with the more classical method of verbal report collection and show clearly that this second method of investigation fails to reveal this differential pattern. The rationale behind the operand-recognition paradigm is then discussed. (Contains 2 tables, 5 figures, and 2 footnotes.)

Longitudinal structural equation modeling was used to evaluate longitudinal relationships across adjacent grade levels 1 to 7 for levels of language in writing (Model 1, subword letter writing, word spelling, and text composing) or writing and reading (Model 2, subword letter writing and word spelling and reading; Model 3, word spelling and reading and text composing and comprehending). Significant longitudinal relationships were observed within and across levels of language: spelling to spelling and spelling to composing (Grades 1 to 7), Models 1 and 3, and composing to spelling (Grades 3 to 6, Model 1; Grades 4 to 6, Model 3); spelling to word reading and word reading to spelling (Grades 2 to 7), Models 2 and 3; spelling to word reading (Grade 1), Model 2, and word reading to spelling (Grade 1), Model 3; composition to comprehension (Grades 3 to 5), Model 3; comprehension to composition (Grades 2 to 6), Model 3; and comprehension to word reading (Grades 1 to 6), Model 3. Results are discussed in reference to the levels of language in translating ideas into written language and integrating writing and reading. (Contains 6 tables, 3 figures, and 2 footnotes.)

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. (Contains 2 figures.)

"The Number Race" is an adaptive game designed to improve number sense. We tested its effectiveness using a cross-over design in 53 low socioeconomic status kindergarteners in France. Children showed improvements in tasks traditionally used to assess number sense (numerical comparison of digits and words). However, there was no improvement on non-symbolic measures of number sense, suggesting that rather than being in number sense per se, the improvement was in number sense access; or links between symbolic and non-symbolic representations of number. Focused adaptive interventions such as this may contribute to reducing the socioeconomic gap in math achievement.

In the linguistics field, liaison in French is interpreted as an indicator of interactions between the various levels of language organization. The current study examines the same issue while adopting a developmental perspective. Five experiments involving children aged two to six years provide evidence for a developmental scenario which interrelates a number of different issues: the acquisition of phonological alternations, the segmentation of new words, the long-term stabilization of the word form in the lexicon and the formation of item-based constructions. According to this scenario, children favour the presence of initial CV syllables when segmenting stored chunks of speech of the type word1-liaison-word2 ("les arbres" "the trees" is segmented as /le/+/zarbr/). They cope with the variation of the liaison in the input by memorizing multiple exemplars of the same word2 (/zarbr/, /narbr/). They learn the correct relations between the word1s and the word2 exemplars through exposure to the well-formed sequence ("un"+"/narbr/", "deux+/zarbr/). They generalize the relation between a word1 and a class of word2 exemplars beginning with a specific liaison consonant by integrating this information into an item-based schema (e.g. "un"+/nX/, "deux"+/zX/). This model is based on the idea that the segmentation of new words and the development of syntactic schemas are two aspects of the same process.

French children program the words they write syllable by syllable. We examined whether the syllable the children use to segment words is determined phonologically (i.e., is derived from speech production processes) or orthographically. Third, 4th and 5th graders wrote on a digitiser words that were mono-syllables phonologically (e.g. "barque" = [baRk]) but bi-syllables orthographically (e.g. "barque" = "bar.que"). These words were matched to words that were bi-syllables both phonologically and orthographically (e.g. "balcon" = [bal.ko] and "bal.con"). The results on letter stroke duration and fluency yielded significant peaks at the syllable boundary for both types of words, indicating that the children use orthographic rather than phonological syllables as processing units to program the words they write. (Contains 2 tables.)

Four experiments examined whether motor programming in handwriting production can be modulated by the syllable structure of the word to be written. This study manipulated the number of syllables. The items, words and pseudo-words, had 2, 3 or 4 syllables. French adults copied them three times. We measured the latencies between the visual presentation and the first production (L1), the first and second production (L2), and the second and third production (L3). The results show an effect of the number of syllables in L1 for pseudo-words but not for words and on L2 and L3 for all the items (Experiments 1 and 2). Experiment 3 ruled out an interpretation of the latencies for pseudo-words in terms of reading time with a delayed copying task. Experiment 4 replicated the previous results and assessed the effect of varying the temporal interval between the second and third trials. The results of the four experiments confirm the role of the syllable in word writing. The number of syllables of a word modulates the time course of handwriting production.

We describe a large-scale regression study that examines the influence of lexical (word frequency, lexical neighborhood) and sublexical (feedforward and feedback consistency) variables on spelling accuracy among first, second, and third- to fifth-graders. The wordset analyzed contained 3430 French words. Predictors in the stepwise regression analyses were grade-level-based and compiled from child-directed written materials. In all grades, feedforward consistency and word frequency had independent effects. However, whereas the feedforward-consistency contribution remained high and did not vary across grades, the impact of word frequency exhibited a massive jump between first and second grade. Interaction analyses showed that the feedforward-consistency effect was significantly lower for monosyllabic words than for polysyllabic ones, and significantly higher for low-frequency words. The effect of feedback consistency was difficult to clarify. Finally, the feedforward-consistency effects obtained at two different grain sizes suggest that children use more contextual information to spell words as orthographic knowledge develops. The findings are discussed in relation to models of spelling and to the developmental aspects of learning to spell.

Two processes, serial and hierarchical, are generally opposed to account for grammatical encoding in language production. In a developmental perspective, the question addressed here is whether the subject-verb agreement during writing is computed serially, once the words are linearly ordered in the sentence, or hierarchically, as soon as the number features are determined in a hierarchical frame. Adults and children from 3rd to 5th grades were requested to listen to sentences with built-in prepositional phrases or relative clauses and to transcribe them as quickly as possible. A serial hypothesis assumes that subject-verb agreement errors should be equally frequent with both preambles because each has the same length separating the subject head noun and the main verb. Conversely, according to a hierarchical view, errors should be more frequent with a prepositional phrase because the syntactic distance between the subject and the verb is greater than with a relative clause. The results revealed a main effect of the preamble manipulated in 5th graders and adults, but not in 3rd graders. These data were in favor of a hierarchical processing in older writers and a serial one in younger children. However, in 3rd grade, we assumed that the potential serial account was a result of the resource constraint on writing more than of a real serial processing of the agreement.

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.

This study examined how French third (36) and fifth (36) graders used the morphosyntactic context when they spell morphologically complex words with homophonous suffixes (/a/). Participants had to spell adverbs (/a/ transcribed ent) and present participles (/a/ transcribed ant), contrasted on the basis of their frequency, in isolation or embedded within a sentence. Spelling performances were better when the words were dictated in the context of a sentence than in a condition of isolated word dictation. This was the case even in Grade 3, despite the fact that explicit teaching about the transcription of the suffixes /a/ had been provided only to the fifth graders. The frequency of target words was an important determinant of spelling success even when a sentence context was provided. Thus, even though children benefited from the morphosyntactic information provided by the sentence, they did not rely (systematically) on a morphological rule such as "words ending with /a/ are always given the ant spelling after the preposition en (e.g., en regardant "in looking")."

This study tested 5- and 8-year-olds and adults in a bisection task with a sequence of stimuli in which time and number co-varied. Findings indicated that the number of stimuli interfered with 5-year-olds' performance on the temporal bisection task. Number interference decreased both with age and counting strategy. In the numerical bisection task, task duration did not interfere with numerical discrimination for any age group. (Author/KB)

Tested in three experiments hypothesis that coordinating saying number-words and pointing to each object to count requires use of the central executive and that cost of coordination decreases with age. Found that for 5- and 9-year-olds and adults, manipulating difficulty of each component affected counting performance but did not make coordination more difficult. (Author/KB)

Tests the hypothesis that the use of the written mode increases the working memory load. Finds that participants recalled more words in the oral condition than in either the written mode or the "oral and categorization" conditions and that second graders performed better in the oral mode than in the "oral and drawing" condition. (SC)