Narrative Composition of Boys and Girls with Learning Disabilities by Brynheld Martinez

            Educational research has indicated that boys and girls differ in learning behavior, which may result in academic achievement disparity (Hansen, 2001). Researchers have found that boys tend to underperform in narrative composition (Berninger & Fuller, 1992), but little attention has been given to gender differences in specific components of story coherence. Further, a small number of investigations have been conducted to examine the influence of gender in the students with learning disabilities.           

           Writing is a complex process that necessitates the activation and coordination of several linguistic skills including, semantic, syntax, spelling and writing convention (Bereiter & Scardamalia, 1987). Producing coherent narratives are essential for developing language and writing skills (Marjanovic-Umek, Krancj, & Fekonja, 2002). Moreover, studies have indicated a relationship between story coherence and quality of writing (Fitzgerald & Speigel, 1986; McCulley, 1985), as well as associations between story cohesion and story coherence (McCulley, 1985; Fitzgerald & Speigel, 1986). However, the complexity of the writing process may result in the failure of many students to achieve grade level competencies. While comparative analysis in story coherence has been explored at different grade levels and languages, modest consideration has been given to gender differences in children’s narratives.           

           The purpose of this study is to examine gender differences in story coherence, as well as independent constructs of story coherence, in the narratives of children with learning difficulties. The study’s sample included students diagnosed with learning disabilities in the fifth and sixth grades, between the ages of 10 and 12, from an elementary school in a suburb of Montreal, Quebec. The sample consisted of 26 girls and 31 boys in the fifth grade, and 39 girls and 35 boys in the sixth grade. The participants were asked to write a folktale in class. Written narrative performance was analyzed at two levels, namely macrostructure and microstructure. Microstructure analysis included: (a) length - the total number of words; (b) T-units – defined as one main clause with all the subordinate clauses attached to; and (c) syntax - the number of words/T-units. Microstructure analysis looked at the Total Episode Score based on story grammar analysis (Strong, 1998). In addition, two raters independently evaluated the narratives using a rubric for total story coherence, in addition to the four following subscales: (a) causality, (b) discourse, (c) elaboration, and (d) organization. Inter-rater reliability was calculated using 50% of randomly selected the data. Cronbach's Alpha obtained was α = .930 with p< .001. 

          A one-way ANOVA was used to test for mean score differences in the independent coherence variables and overall story coherence between male and female students. Statistically significant interactions between students' story coherence and all four subscales were found for gender. Girls were found to have statistically higher mean scores for total story coherence, causality, discourse, elaboration, and organization.           

         This study contributes to the understanding of children’s writing development and narrative composition through emphasizing the importance of gender in the narrative coherence of elementary school-aged children. With the growing concerns of boys’ academic difficulties, these findings have implications for educators, researchers, and parents to improve the writing achievements of boys and girls, particularly children with learning disabilities.

Using Invariant Manifolds To Solve An Anti-Competitive System of Difference Equations

By Chris D Lynd

           In this paper, we analyze the global character of the solutions of an anti-competitive system of rational difference equations. We prove that the solutions of the system can have four types of global behavior, corresponding to different regions of the parameter space. We also show that, in a range of the parameter space, there is a curve of period-2 points. These period-2 points are fixed points of the 2$^\text{nd}$ iterate of the map corresponding to the system; and each fixed point has a linear global stable manifold. Given an initial point $(x_0,y_0)$, we use the equations of the invariant manifolds to calculate the limit points of the solution of the system of difference equations.