CAREER: Noticing and Using Students' Prior Knowledge in Problem-Based Instruction

问题导向型教学的支持者认为，这种方法可以帮助学生加深对数学的理解，获得对数学更积极的态度，并获得更真实的数学应用经验。然而，让学生参与基于问题的教学增加了教师的挑战，他们必须注意学生先前知识的影响并相应地调整教学。该项目将开发和研究一个专业发展框架，旨在帮助高中几何教师更仔细地关注学生的先验知识，解释学生先验知识的学习含义，并相应地调整教学实践。参与的教师将通过参与学习小组来分析生产性教学实践的动画来学习执行这些复杂的任务；合作规划、实施和分析几何课程；并评论他们自己的课堂教学视频。先前的研究表明，集体检查视频可以帮助教师增加对学生思维的关注，这是注意和适应学生先前知识的关键。本研究的专业发展框架的一个关键创新特征是使用课堂教学的动画小片段，让教师准备好检查他们自己的实践视频。使用基于卡通的课堂实践动画的优点是，它们可以被设计成描绘特定的教学动作，同时排除视频中常见的干扰，如身体特征、服装或个人习惯。此外，教师可以培养对相关互动的批判性眼光，而不必在讨论卡通人物描绘的虚构场景时过于礼貌。这种初步的实践还将使教师在评论自己课堂实践的视频之前，能够发展一种关于注意和回应学生先验知识的共同语言。这个项目促进了专业发展经验的知识，帮助教师注意到并考虑到学生带到课堂上的先验知识。将课堂实践的动画片段与课堂实践中的评论视频进行耦合分析的研究结果有可能显著提高数学教师以及一般教师的专业发展实践。项目成果将通过会议演讲、各种媒体的文章和项目网站广泛传播，该网站将提供项目产品，成为媒体和公众获取项目信息的场所，并成为促进教师与教师交流的工具。本研究的结果，以及在研究项目中制定的协议和工具，将为研究人员更好地理解和改善教师学习提供信息和支持。研究者的教育计划侧重于通过更明确地将教学决策与学生学习研究联系起来，将本研究的成果转化为职前教师教育的实践，从而促进基于学习轨迹的教学。

Advocates of problem-based instruction argue that the approach can help students develop a deeper understanding of mathematics, acquire more positive attitudes toward mathematics, and gain experience with more authentic applications of mathematics. Engaging students in problem-based instruction, however, increases challenges to teachers who must attend to the influence of student prior knowledge and adjust instruction accordingly. The proposed project will develop and study a professional development framework that is designed to help high school geometry teachers attend more carefully to student prior knowledge, interpret the learning implications of student prior knowledge, and adjust teaching practices accordingly. Participating teachers will learn to perform these complex tasks by participating in study groups to analyze animations of productive teaching practices; to collaborate in planning, implementing, and analyzing geometry lessons; and to critique videos of their own classroom instruction. Prior research has shown that collective examination of videos can help teachers increase attention on student thinking, a key to noticing and accommodating student prior knowledge.A key, innovative feature of the professional development framework for this study is the use of animated vignettes of classroom instruction to prepare teachers to examine videos of their own practice. The advantage of using cartoon-based animations of classroom practices is that they can be designed to depict specific teaching actions while excluding the usual distractions in videos, such as physical features, clothing, or individual mannerisms. Also, teachers can develop a critical eye for relevant interactions without feeling the need to be overly polite when discussing fictional scenarios portrayed by cartoon characters. This preliminary practice will also enable teachers to develop a common language about noticing and responding to student prior knowledge before critiquing videos of their own classroom practices.This project advances knowledge of professional development experiences that help teachers notice and take into account the prior knowledge that students bring to the classroom. Results from studying the effects of coupling analysis of animated vignettes of classroom practices with critiquing videos on one's own classroom practices have the potential to significantly enhance professional development practices among mathematics teachers, as well as teachers in general. Results from the project will be broadly disseminated via conference presentations, articles in diverse media outlets, and a project website that will make project products available, be a location for information about the project for the press and the public, and be a tool to foster teacher-to-teacher communication. The results of this study, as well as the protocols and instruments developed during the research project, will inform and support the researcher's own efforts to better understand and improve teacher learning. The education plan of the researcher focuses on translating the outcomes of this study to the practices of preservice teacher education by connecting instructional decision-making more explicitly to research on student learning, thereby promoting learning trajectory based instruction.