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

基于问题的教学的倡导者认为，这种方法可以帮助学生更深入地理解数学，获得更积极的数学态度，并获得更真实的数学应用经验。 然而，让学生参与以问题为基础的教学，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。 拟议的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参加学生的先验知识，解释学生先验知识的学习意义，并相应地调整教学实践。 参与教师将学习通过参加学习小组来执行这些复杂的任务，以分析富有成效的教学实践的动画;在规划，实施和分析几何课程方面进行合作;并评论自己的课堂教学视频。 以往的研究表明，集体检查的视频可以帮助教师提高对学生的思维，注意和容纳学生的先验知识的关键。本研究的专业发展框架的一个关键，创新的特点是使用动画的课堂教学的小插曲，教师准备检查自己的实践视频。 使用基于卡通的课堂实践动画的优点是，它们可以被设计为描述特定的教学动作，同时排除视频中通常的干扰，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。 这个初步的实践也将使教师发展一种共同的语言，关于注意和回应学生的先验知识之前，批评他们自己的课堂实践的视频。这个项目推进专业发展的经验，帮助教师注意到，并考虑到学生带到课堂上的先验知识的知识。 从研究结果耦合分析的动画小插曲的课堂实践与批评视频对自己的课堂实践的影响有可能显着提高数学教师的专业发展实践，以及教师的一般。 该项目的成果将通过会议发言、各种媒体的文章和一个项目网站广泛传播，该网站将提供项目产品，成为新闻界和公众了解项目信息的场所，并成为促进教师之间交流的工具。 本研究的结果，以及研究项目期间开发的协议和工具，将通知和支持研究人员自己的努力，以更好地理解和改善教师学习。 研究者的教育计划的重点是将本研究的结果转化为副教师教育的实践，通过更明确地将教学决策与学生学习研究联系起来，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.