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مفاهیم مفید ریاضی کودکان دبستانی: ارتباط با تصورات والدین، پیشرفت ریاضی، و مشارکت در ریاضیات خانگی
Elementary School Children's Math Utility Conceptions: Associations with Parents' Conceptions, Math Achievement, and Home Math Engagement
This dissertation was made up of three studies, with the overall goal of examining first through fourth grade children’s math utility conceptions—knowledge and beliefs about the usefulness of math—and how those conceptions relate to their parents’ conceptions and children’s math achievement. All three studies used the Math Utility Conceptions conceptual model, an expansion of multiple theoretical models, to investigate children’s math utility conceptions.
The first paper examined children’s math utility conceptions and grade-level differences in math utility conceptions and home math engagement. Most children viewed math as heavily focused on low-level math operations and as learned and used primarily in school. Older children had more awareness of math in daily activities, but had a more school-based view than younger children. The second paper primarily investigated the associations between parents’ and children’s math utility conceptions and children’s home math engagement. Parents’ math utility conceptions positively predicted children’s math utility conceptions; this relation was moderated by the frequency with which children engaged in math activities at home and how often children see their parents using math. Results suggest that children develop their knowledge and beliefs about math utility from their parents as well as through engagement in math-related activities. The third paper explored the relation between children’s math utility conceptions and their math achievement. Overall math utility conceptions predicted math reasoning skills. Children’s productive disposition significantly predicted their math achievement. The associations between math applicability, math utility, and math achievement were different for older and younger children. Results suggest that the relation between children’s math utility conceptions is complex, but the extent to which elementary-age children view math as useful and worthwhile is associated with children’s math achievement.
Overall, these results may guide math curriculum development for elementary-aged children to more intentionally use real-world applications to teach math concepts and, in doing so, improve children’s understanding of the importance of math in their daily lives. By increasing young children’s knowledge of applications of math outside the school context and beliefs about the usefulness of math, parents and educators could help to increase children’s math proficiency.
درک تجربیات یادگیری دانش آموزان ریاضی رشدی
Understanding the Learning Experiences of Developmental Math Students
Developmental math education is designed to offer a pathway to college-level subject readiness. Existing research in developmental math education has evidenced success stories while also revealing opportunities for improvement. Prior studies have focused on issues of self-efficacy and have also contended with not only what helps students learn better, but also how this learning should be measured in the first place. Increasing external pressures from politicians and business interests underscore the need for greater understanding of how developmental math students can learn more effectively.
The research question for this study is: How do developmental math students experience learning in their developmental math coursework? Rather than beginning with an existing theory of how these students learn, this study used a grounded theory methodology to develop a framework from the students’ descriptions of their experiences. Data was collected over two phases. The first phase was a brief online survey that served as a baseline for discovering relevant themes. These formed the basis for questions in the extended individual interviews for the second phase of data collection. In vivo, axial, and focused coding were used to create the emergent framework for how developmental math students learn.
The survey identified themes of course engagement, affective teacher qualities, course structure, and student positionality as meaningful for the students. Analysis of the interviews led to the resultant theory that the students’ experiences were fundamentally influenced by the students’ ability to receive one-on-one help, their perception of their instructors’ willingness to help, and the extent to which their courses provided a supportive structure to organize the learning. Implications, limitations, and opportunities for further research are discussed as well.