Examining Interactions Between Opportunities and Propensities for Learning Math in Homes and Classrooms in Early Elementary Grades

项目摘要/摘要 数学成绩是大学和职业成就、终身收入、 和健康结果。然而，构成后来数学成绩的很大一部分是由时间决定的 孩子们进入了学校。因此，更好地了解环境和认知决定因素是至关重要的 早期的数学技能，以弥补顽固的数学成就差距。考虑这些不同决定因素的一种方式是 在机会-倾向(O-P)模型中。这个模型表明特征可以被组织成 预测成绩的三个因素：前因变量代表影响情境的远端变量 哪个孩子出生(例如，社会经济地位)；机会代表学习环境的特征 (例如，教育和课外活动)；和倾向代表促进 学习(例如，执行职能)。该项目旨在更好地了解机会和 独立和互动的倾向有助于早期初级数学技能的发展。 儿童接触数学语言的个体差异预测儿童的数学技能。先前的研究 分别描述了家庭和课堂中数学语言输入和数学技能之间的关系， 但很少有研究探索这些投入的独特和/或互补影响。此外，还有一些 孩子比其他孩子更倾向于从机会中学习，这在一定程度上可能是 由执行功能(EF)的变化来解释，EF是为目标导向的认知和行为而招募的技能。 以前的研究已经证明了EF和数学之间的牢固关系，并表明EF可能会起到作用 作为一种补偿机制，为数学水平较低的入学儿童提供补偿。进一步的研究是 需要测试EF是否与数学语言相互作用以预测数学技能。 O-P模型为理解技能的发展提供了一个有用的框架，并为 发展干预措施。先行因素很难干预，而且往往需要系统性的政策变化， 而倾向可能更容易在儿童层面上受到影响。正如观测数据所显示的那样 倾向性在先行因素和机会因素与成就之间的关系中起完全中介作用， 倾向因素可能是干预的理想目标。因此，这项调查试图了解 改变倾向是否会影响成就和/或机会与成就之间的关系。 这项研究的主要目标是(1)检查学习机会之间的关系，通过 数学语言和儿童技能；(2)测试EF在数学语言和数学技能之间的关系中的作用；以及 (3)培养儿童的兴趣，以阐明导致数学进步的机制。调查结果将会有 对干预和学习科学、政策和实践的影响。这项拟议的研究是 更广泛的博士后培训计划，其目标是为申请人成为独立的职业生涯做好准备 研究人员重点关注了在一流研究型大学任教期间早期数学技能的发展。

PROJECT SUMMARY/ABSTRACT Math achievement is one of the strongest predictors of college and career attainment, lifetime earnings, and health outcomes. However, much of what comprises later math achievement is decided by the time children enter school. Thus, it is essential to better understand environmental and cognitive determinants of early math skills to close stubborn math achievement gaps. One way to consider these varied determinants is within the Opportunity-Propensity (O-P) model. This model suggests characteristics can be organized into three factors predicting achievement: antecedents represent distal variables which influence the context into which the child is born (e.g., socioeconomic status); opportunities represent features of learning environments (e.g., educational and extracurricular activities); and propensities represent proximal processes that facilitate learning (e.g., executive function). This project aims to better understand ways in which opportunities and propensities independently and interactively contribute to the development of early elementary math skills. Individual differences in children's exposure to math language predict children's math skills. Prior studies have described relations between math language input and math skills in homes and classrooms separately, but little research has explored unique and/or complementary influences of these inputs. Furthermore, some children have a greater propensity to learn from opportunities than do others and this might in part be explained by variations in executive function (EF), skills recruited for goal-directed cognitions and behaviors. Previous research has demonstrated robust relations between EF and math and suggests that EF might serve as a compensatory mechanism for children who enter school with low levels of math skills. Further research is needed to test whether EF interacts with math language to predict math skills. The O-P model provides a useful framework for understanding the development of skills and a basis for developing interventions. Antecedents are difficult to intervene upon and often require systemic policy change, whereas propensities might be more easily affected at the child level. As observational data have suggested propensities fully mediate relations between both antecedent and opportunity factors and achievement, propensity factors might be an ideal target for intervention. As such, this investigation seeks to understand whether modifying propensities affects achievement and/or relations between opportunities and achievement. The primary goals of this research are to (1) examine relations between learning opportunities indexed by math language and child skills; (2) test the role of EF in relations between math language and math skills; and (3) train child propensities to elucidate mechanisms that lead to improvements in math. Findings will have implications for intervention and learning science, policy, and practice. The proposed research is part of a broader post-doctoral training program whose goal is to prepare the applicant for a career as an independent researcher focused on the development of early math skills as faculty at a top-tier research university.