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。 该奖项探索“向后迁移”，即新学习影响先前建立的推理方式的方式。 PI将观察和评估学生在四个代数I教室，因为他们学习二次函数。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对线性函数先前概念的先前数学知识。 更广泛地说，该奖项将通过扩大知识转移的应用，将其从仅向前集中的方向移动到包括向后集中的方向，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咨询委员会将支持该项目。 该研究将在不同的教室进行，并在国家组织的年度会议上进行介绍，同行评审的出版物，以及为教师建立的网站，解释理论模型和项目结果。 还正在利用该项目的录像数据为职前和在职教师编制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，并提供指导，小学教师，因为他们准备他们的学生代数。 研究分为三个阶段。 第一阶段包括四个代数I教室的观察和录音，并将在二次函数课程之前和之后测试学生对线性函数的理解。 这一阶段还将包括与学生的访谈，以更好地了解他们对线性函数问题的推理。 课程将根据他们所提倡的推理进行编码。 该项目的第二阶段将涉及四个设计研究周期，以创建可用作教学干预的二次和线性函数活动。 在这一阶段，职前教师将通过一个课程，将提供与设计研究同时观察教学会议。 计划的最后阶段将进行先导应用研究，以测试教学活动对学生在课堂上进行线性函数推理的影响。 这一阶段将包括治疗组和对照组，并进一步测试前两个阶段开发的假设和教学产品。发现研究K-12计划（DRK-12）旨在通过研究和开发创新资源，模型和工具（RMT），显着提高K-12学生和教师的科学，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，这些研究和开发工作为拟议项目提供了理论和经验依据

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