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

该项目的目的是了解中学数学专家教师在指数函数教学中的知识。特别是，该研究调查了教师在教授学生时如何使用教学数学知识，以及影响他们与学生互动的因素。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的指数函数单元的教学。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。该项目建立在理解数学教学知识的其他框架的基础上。其他研究更多地关注小学或中学教师。这项工作的贡献是了解高中教师在与学生的工作中使用的数学内容。指数函数是高中三门课程中常见的主题，也是学生学习代数和微积分的基础主题。ECR项目强调在该领域产生基础知识的基础STEM教育研究。投资在至关重要、广泛和持久的关键领域：STEM学习和STEM学习环境，扩大STEM参与，以及STEM劳动力发展。本研究的研究问题集中在专家教师在与指数函数教学相关的决策中所做的决策，他们用于决策的教学数学知识，以及影响决策质量和学生数学推理机会的因素。他们正在招募教授课程至少两年并被公认为高质量教师的专家教师。收集的数据包括课堂观察和观察前和观察后访谈的视频数据。访谈中要问的问题侧重于教师的决策，并将探讨他们的数学知识的教学。教学中的数学知识包括教师如何利用这些知识来支持他们对学生数学推理的规划、指导和评估。本研究也为其他中学数学学科的数学知识教学提供了研究方法。

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.