Young Children's Explorations of Chance and Probability

拟议的研究计划拨款的目标是建立一个实质性的为期三年的研究计划，研究幼儿对机会和概率的学习。我建议把重点放在偶然性和概率论上，因为这些概念本身很丰富，偶然性和概率论使数学和科学之间的联系成为可能，而且这种关注可以向幼儿传达数学的强大愿景。本研究从合作问题解决教学的角度探讨小学一年级儿童对机会与概率的探索。由于越来越多的人认识到背景对知识构建的影响，它还研究了在不同情况下学习这些概念的影响。研究规划补助金的活动包括完成文献审查、改进和扩大教学干预、实施两个试点研究周期、起草理论框架，以反映儿童在这一领域的概念发展的多个方面及其对解决问题的影响；以及准备完整的拨款提案。第一个试点研究周期的重点是让二年级学生成对参与一系列机会和概率任务，包括预测、实证调查、推断和解释。第二个试验周期将研究扩展到小组学习，并开始探索不同情况对儿童理解机会和概率的影响。所有的课程都有录像，以便对儿童的思维和活动顺序的有效性进行微观分析。该研究旨在构建和完善机会和概率领域的问题解决教学的强大模型，因为它使用这些作为工具来仔细检查幼儿的知识构建。

The goal of the proposed Research Planning Grant is to structure a substantial three-year program of research on young children's learning of chance and probability. I propose to focus on chance and probability because of the richness of the ideas themselves, the connections that chance and probability make possible between mathematics and science, and the powerful vision of mathematics that such a focus could convey to young children. The research program investigates primary grade children's explorations of chance and probability from the perspective of collaborative problem solving instruction. It also examines the effects of learning these concepts in different situations, because of the growing recognition of the influence of context on knowledge-construction. Activities of the Research Planning Grant include completion of literature reviews, refinement and extension of instructional interventions, implementation of two pilot research cycles, drafting of a theoretical framework to capture the multiple aspects of children's conceptual development in this domain and their effect on problem solving, and the preparation of the full grant proposal. The first pilot research cycle focuses on pairs of second graders engaged in a series of chance and probability tasks, involving prediction, empirical investigation, extrapolations and explanation. The second pilot cycle extends the research to small group learning and also begins to explore the entailments of different situations for children's understanding of chance and probability. All sessions are videotaped to enable microanalysis of children's thinking and the effectiveness of the activity sequence. The research aims to construct and refine powerful models of problem solving instruction in the domain of chance and probability, as it uses these as a vehicle to closely examine young children's knowledge- construction.