40 research outputs found
Spontaneously spotting and applying shortcuts in arithmeticĂąâŹâa primary school perspective on expertise
The role of relational reasoning in children's addition concepts
The study addresses the relational reasoning of different-aged children and how addition reasoning is related to problem-solving skills within addition and to reasoning skills outside addition. Ninety-two 5- to 8-year-olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all self-reported strategies were used to monitor their addition performance. Children were also given a series of general relational reasoning tasks to assess their ability to solve problems based on thematic, causal and visual relations. The results revealed that, while children were able to reason about commutativity relations, recognition of relations based on additive composition was rare. Furthermore, children's ability to reason about addition concepts increased with age and problem-solving proficiency. Reasoning about addition concepts was related to performance on the thematic, causal and visual reasoning tasks for older children but not for younger children. Overall, the findings suggest that while children's early knowledge of addition relations is domain specific, as children develop in their broader reasoning abilities these developments enhance their addition reasoning
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Children's patterns of reasoning about reading and addition concepts
Children's reasoning was examined within two educational contexts (word reading and addition) so as to understand the factors that contribute to relational reasoning in the two domains. Sixty-seven 5- to 7-year-olds were given a series of related words to read or single-digit addition items to solve (interspersed with unrelated items). The frequency, accuracy, and response times of children's self-reports on the conceptually related items provided a measure of relational reasoning, while performance on the unrelated addition and reading items provided a measure of procedural skill. The results indicated that the children's ability to use conceptual relations to solve both reading and addition problems enhanced speed and accuracy levels, increased with age, and was related to procedural skill. However, regression analyses revealed that domain-specific competencies can best explain the use of conceptual relations in both reading and addition. Moreover, a cluster analysis revealed that children differ according to the academic domain in which they first apply conceptual relations and these differences are related to individual variation in their procedural skills within these particular domains. These results highlight the developmental significance of relational reasoning in the context of reading and addition and underscore the importance of concept-procedure links in explaining children's literacy and arithmetical development
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Patterns of analogical reasoning among beginning readers
Despite compelling evidence that analogy skills are available to beginning readers, few studies have actually explored the possibility of identifying individual differences in young children's analogy skills in early reading. The present study examined individual differences in children's use of orthographic and phonological relations between words as they learn to read. Specifically, the study addressed whether general analogical reasoning, short-term memory and domain-specific reading skills explain 5- to 6-year-olds' reading analogies (n=51). The findings revealed an orthographic analogy effect accompanied by high levels of phonological priming. Single-word reading and use of visual analogies predicted young children's orthographic and phonological analogies in the regression analyses. However, different findings emerged from exploring profiles based on individual differences in reasoning skill. Indeed, when individual differences in composite scores of orthographic and phonological analogy were examined, group membership was predicted by word reading and early phonological knowledge, rather than general analogical reasoning skills. The findings highlight the usefulness of exploring individual differences in children's analogy development in the early stages of learning to read