Thesis (EdD)-Open University.

Thesis (Ph.D.)--University of Iowa, 2009. / Thesis supervisor: J.B. Tomblin. Includes bibliographical references (leaves 126-133).

Purpose: This study examined the relationship between arithmetic word problem solving skill in first graders and 1) their oral language skill, 2) their nonverbal understanding of mathematical sets, and 3) rewording and gesture scaffolds designed to help the children access both the linguistic and the nonverbal content of Compare 6 word problems. Method: Two groups of first graders (15 with good oral language skill and 15 with low oral language skill) solved a matched set of verbal and nonverbal arithmetic problems, followed by three types of Compare word problems. Twenty first graders with low oral language skill (9 with low normal language (LN) and 11 with a diagnosis of language impairment (LI)) then solved orally-presented Compare 6 word problems under 4 scaffold conditions: 1) traditional wording, 2) traditional wording + gesture, 3) rewording, and 4) rewording + gesture. Results: Children with low oral language skill had greater difficulty solving orally-presented arithmetic word problems than their peers with good language skill, but performed comparably on a nonverbal arithmetic task. Using proportion of problems solved correctly, rewording Compare 6 word problems was facilitative for the LN group but not for the LI group. Changing the problem wording from a Compare 6 to a Compare 3, by using `more than' instead of `fewer than' and by eliminating pronoun anaphora, resulted in comparable performance to rewording that also included a rationale, optional verbs and placing the question first. The gesture scaffold was marginally significant for both groups. Conclusions: The LI group did not benefit from implicitly-presented rewording or gesture scaffolds; the LN group did benefit from the rewording scaffold. The gesture scaffold was marginally facilitative despite the finding that children with low oral language skill were able to access nonverbal information in a nonverbal arithmetic task. Empirical and anecdotal evidence suggested that, for a number of these children, rewording and gesture scaffolds altered their mental model of the word problem structure. This altered representation resulted in the use of different solution strategies. The new strategies, however, were not always correct. Implications for classroom intervention and suggestions for future research are discussed.

Cette recherche a pour objet la compréhension des énoncés de problèmes arithmétiques complexes et leur résolution. Les problèmes complexes choisis combinent des problèmes simples de types Changement et Combinaison. Ce travail s’appuie sur le modèle de la Construction-Intégration de Kintsch. Les résultats montrent qu’il existe une relation entre le niveau d’expertise en compréhension de textes narratifs et la résolution des problèmes arithmétiques complexes. Comprendre un texte narratif ou un énoncé de problème complexe exige de la part des lecteurs la construction d’un réseau propositionnel hiérarchisé et les résultats suggèrent, entre autres, une sensibilité des élèves aux propositions textuelles et aux ellipses contenues dans les textes. La formation des macropropositions est un processus fondamental et les résultats montrent une relation entre le nombre d’objets contenus dans les énoncés de problème et la procédure préférentiellement choisie par les élèves. Ils suggèrent d’une part, la mise en oeuvre du processus de catégorisation au cours du processus de compréhension et d’autre part, l’affaiblissement des liaisons entre les macropropositions élaborées et le schéma de problème Parties-Tout qui leur sont liés. D’un point de vue pédagogique, les résultats montrent que les questions relatives à l’activation d’une part des concepts superordonnés et d’autre part des schémas de problèmes Parties-Tout ne sont pas à privilégier pour aider les élèves. Finalement, les connaissances du lecteur sont essentielles à la compréhension. Cet élément est confirmé ici et la compréhension des problèmes complexes nécessite des connaissances solides relativement aux problèmes arithmétiques simples. / This research deals with text comprehension processes and complex arithmetic word problems resolution by 9-10 years old children in Reunion Island based upon the CI model of Kintsch. The complex word arithmetic problems used in this research are a combination of Change simple problems and Combine simple problems. The results show a relation between subject’s level of expertise in narrative texts comprehension and complex arithmetic word problems resolution. In order to understand a narrative text or to resolve a complex arithmetic word problem, subjects have to elaborate a coherent hierarchical propositional network : bridging inferences and macropropositions are involved to achieve complex arithmetic word problems resolution too. More precisely, the results suggest children are sensitive to the number of propositions and to the ellipsises. Macropropositions formation is an integral process of reading. The results show a relation between number of objects in complex arithmetic problems and procedure naturally used by children to solve them. They suggest on the one hand, categorization processes are an integral part of reading and on the other hand, some links between macropropositions and arithmetic hypothesis become weaker. Consequently, questions about superordinate concepts and arithmetic hypothesis attached to them are not helpul to resolve complex arithmetic word problems. Finally, reader’s knowlegde is a key element of comprehension processes and to achieve complex arithmetic word problems, problem schemata about simple arithmetic word problems are crucial. The results show a relation between subject’s level of expertise in simple arithmetic word problems and complex arithmetic word problems resolution.