Collaborative Research: Initiating a Foundational Research Model for Secondary Mathematical Knowledge for Teaching (INFORMS MKT)

本研究的目的是了解专家型中学数学教师对指数函数教学的认识。特别是，本研究探讨了如何教学的数学知识是由教师使用，因为他们是教学生的和影响他们与学生的互动因素。该项目正在招募教师，以观察他们在高中代数II，微积分预科和大学代数课程中教授指数函数单元。他们将在整个单元的教学过程中进行课堂观察，并在每个单元之前和之后与教师进行访谈。该项目建立在其他理解教学数学知识的框架之上。其他研究更频繁地关注小学或中学教师。这项工作的贡献是了解数学内容的教师在高中使用他们的工作与学生。指数函数是高中三门课程中的一个常见课题，也是学生学习代数和微积分的基础课题。ECR计划强调基础STEM教育研究，产生该领域的基础知识。 在重要、广泛和持久的关键领域进行投资：STEM学习和STEM学习环境，扩大STEM参与，STEM劳动力发展。研究的研究问题集中在专家教师在做出与教学指数函数相关的决策时所借鉴的决策，他们用来做出决策的教学数学知识，以及影响这些决定的质量和学生数学推理机会的因素。他们正在招聘教授课程至少两年的专家教师，并被公认为高素质教师。收集的数据包括课堂观察的视频数据以及观察前和观察后的访谈。访谈中的问题主要集中在教师的决策上，并将探讨他们的数学知识用于教学。数学教学知识包括教师如何支持他们的计划，教学和评估学生的数学推理的知识。本研究亦提供了一个研究方法，可供其他中学数学学科的教学参考。

The goal of the project is to understand expert secondary mathematics teachers' knowledge for teaching exponential functions. In particular, the study examines how mathematics knowledge for teaching is used by teachers as they are teaching students' and the factors that influence their interactions with students. The project is recruiting teachers in order to observe their teaching of exponential functions units in Algebra II, Pre-Calculus, and College Algebra courses in high schools. They will conduct classroom observations throughout the teaching of the unit and conduct interviews with the teachers before and after each unit. The project builds on other frameworks for understanding mathematics knowledge for teaching. Other studies have focused more frequently on elementary or middle school teachers. The contribution of this work is to understand the mathematics content teachers are using in high school in their work with students. Exponential functions are a common topic in the three high school courses and a foundational topic for students' learning of algebra and calculus. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development.The research questions for the study focus on the decisions expert teachers draw on while making decisions related to teaching exponential functions, the mathematics knowledge for teaching they use to make decision, and the factors that influence the quality of those decisions and students' opportunity to reason mathematically. They are recruiting expert teachers who have taught the courses for at least two years and are recognized as high quality teachers. The data collected include video data from classroom observations and pre-observation and post-observation interviews. The questions to be asked in interviews focus on teachers' decision-making and will probe for their mathematics knowledge for teaching. Mathematics knowledge for teaching includes how teachers' knowledge that supports their planning, instruction, and assessment of students' mathematical reasoning. The study also provides a research methodology that could be used to study mathematics knowledge for teaching in other secondary mathematics topics.