CAREER: Leveraging Contrasting Cases to Investigate Integer Understanding

目前，大多数学生在学习正数很久之后才学会负数，他们很少有时间或机会通过对比这两个概念来建立他们先前的理解。因此，他们很难理解负整数的概念，因为这似乎与他们目前的理解相冲突。这个职业项目的目的是确定有助于提高小学生对涉及负整数的加减法问题的理解的语言因素和教学顺序。第二个目标是确定小学教师如何解释他们学生的整体理解，并使用研究结果来支持他们对这些概念的教学。这个项目期望对发展整数理解的理论做出贡献，以及在学习新的相关概念时如何形成有用的对比案例。此外，这个项目的结果可以帮助我们理解如何在学生的基础上发展？首席调查员将进行一系列四项实验研究，涉及学习准备部分，学生被随机分配到处理组或对照组。研究一将涉及二年级和四年级学生，并将测试支持学生理解整数的语言因素。研究2-4将涉及二年级和五年级学生，并将测试整数加法和减法问题相互对比和顺序不对比的最佳顺序。使用测量学生的项目？在理解整数和整数运算的基础上，PI将比较学生在小组之间的前测和后测的成绩。此外，调查员将对学生进行定性编码？基于后续访谈和书面工作的解决方案战略，以获得有关小组之间差异的更多信息。在实验研究之后，PI将与小学教师合作进行三个课程研究周期，在此期间，教师将在先前研究的基础上实施教学？结果。PI将比较参加课程学习单元的学生和对照教室的学生的表现，以衡量该单元的影响。课程学习单元的视频以及负整数教案将提供给其他教师和教师教育工作者使用。此外，研究人员将把研究成果纳入本科生的数学方法课程。为了确保这项研究的结果接触到更广泛的受众，调查者将创建一个整数游戏和故事书，说明通过研究确定的关键概念，父母可以在家庭数学之夜和家里与孩子一起探索。在更广泛的范围内，这个项目有可能说明如何在数学主题的排序中发展更多的连贯性，以更有效地建立在学生？目前的理解是。

DRL #1350281PI: Laura BofferdingAbstractCurrently, most students learn about negative numbers long after they have learned about positive numbers, and they have little time or opportunity to build on their prior understanding by contrasting the two concepts. Therefore, they struggle to make sense of negative integer concepts, which appear to conflict with their current understanding. The purpose of this CAREER project is to identify language factors and instructional sequences that contribute to improving elementary students' understanding of addition and subtraction problems involving negative integers. A second objective is to identify how elementary teachers interpret their students' integer understanding and use research findings to support their teaching of these concepts. This project is expected to contribute to theories regarding the development of integer understanding as well as what makes a useful contrasting case when learning new, related concepts. Moreover, the results of this project can contribute to our understanding of how to build on students? prior number knowledge rather than contradict it.The principal investigator will conduct a series of four experimental studies involving a preparation for learning component with students randomly assigned to treatment or control groups. Study 1 will involve second and fourth graders and will test the language factors that support students' understanding of integers. Studies 2-4 will involve second and fifth graders and will test the optimal order in which integer addition and subtraction problems are presented in contrast with each other versus sequentially without contrasts. Using items that measure students? understanding of integers and integer operations, the PI will compare students' gains from pre-tests to post-tests between groups. Further, the investigator will qualitatively code students? solution strategies based on follow-up interviews and written work for additional information on the differences between groups. Following the experimental studies, the PI will work with elementary teachers over three lesson study cycles, during which teachers will implement instruction based on the prior studies? results. The PI will compare the performance of students who participate in the lesson study unit versus control classrooms to measure impact of the unit. Videos of the lesson study unit, as well as the negative integer lesson plans will be made available for other teachers and teacher educators to use. Further, the investigator will incorporate the research results into an undergraduate mathematics methods course. To ensure that the results of this research reach a wider audience, the investigator will create an integer game and storybook, illustrating key concepts identified through the research, that parents can explore together with their children during family math nights and at home. On a broader scale, this project has the potential to illuminate ways to develop more coherence in the sequencing of mathematics topics to more effectively build on students? current understanding.