CAREER: Investigating Changes in Students' Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra

当学生学习新的数学概念时，教师需要确保先前的知识和先前的理解方式不会受到负面影响。该奖项探讨了“向后迁移”，即新的学习方式对先前建立的推理方式的影响。PI将观察和评估四个代数I教室的学生学习二次函数。PI将研究关于二次函数新概念的不同类型的教学如何帮助或阻碍学生先前对线性函数概念的数学知识。更一般地说，该奖项将通过扩大知识转移的应用，将其从只有向前关注的方向移动到包括向后关注的方向，从而为数学教育领域做出贡献。一个由在数学教育、评估、社会互动、定量推理和测量方面具有专长的学者组成的顾问委员会将支持该项目。这项研究将在不同的教室进行，并在国家组织的年度会议上发表报告，发表同行评议的出版物，并为教师建立一个网站，解释该项目的理论模型和研究结果。目前也正在为职前和在职教师编制利用该项目的录象数据的大学本科课程和专业发展讲习班。最终，研究结果将产生新的知识，并为小学教师提供指导，因为他们准备学生的代数。这项研究包括三个阶段。第一阶段包括四个代数I教室的观察和录音，并将测试学生在二次函数课程前后对线性函数的理解。这一阶段还将包括与学生的访谈，以更好地理解他们对线性函数问题的推理。课堂教学将根据他们所提倡的推理方式进行编码。该项目的第二阶段将涉及四个设计研究周期，以创建可用于教学干预的二次函数和线性函数活动。与此阶段相结合，职前教师将通过与设计研究同时提供的课程来观察教学过程。该项目的最后阶段将涉及试点应用研究，该研究将测试教学活动对课堂设置中学生线性函数推理的影响。这一阶段将包括实验组和对照组，并进一步测试在前两个阶段开发的假设和教学产品。探索研究K-12项目（DRK-12）旨在通过研究和开发创新资源、模型和工具（rmt），显著提高pre -12学生和教师对科学、技术、工程和数学（STEM）的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和实证依据

As students learn new mathematical concepts, teachers need to ensure that prior knowledge and prior ways understanding are not negatively affected. This award explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate students in four Algebra I classrooms as they learn quadratic functions. The PI will examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions. More generally, this award will contribute to the field of mathematics education by expanding the application of knowledge transfer, moving it from only a forward focused direction to include, also, a backward focused direction. An advisory board of scholars with expertise in mathematics education, assessment, social interactions, quantitative reasoning and measurement will support the project. The research will occur in diverse classrooms and result in presentations at the annual conferences of national organizations, peer-reviewed publications, as well as a website for teachers which will explain both the theoretical model and the findings from the project. An undergraduate university course and professional development workshops using video data from the project are also being developed for pre-service and in-service teachers. Ultimately, the research findings will generate new knowledge and offer guidance to elementary school teachers as they prepare their students for algebra. The research involves three phases. The first phase includes observations and recordings of four Algebra I classrooms and will test students' understanding of linear functions before and after the lessons on quadratic functions. This phase will also include interviews with students to better understand their reasoning about linear function problems. The class sessions will be coded for the kind of reasoning that they promote. The second phase of the project will involve four cycles of design research to create quadratic and linear function activities that can be used as instructional interventions. In conjunction with this phase, pre-service teachers will observe teaching sessions through a course that will be offered concurrently with the design research. The final phase of the project will involve pilot-applied research which will test the effects of the instructional activities on students' linear function reasoning in classroom settings. This phase will include treatment and control groups and further test the hypotheses and instructional products developed in the first two phases.The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects