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

该项目的目标是了解中学数学专业教师的知识，以便教授指数函数。特别是，这项研究考察了教师在教学生的过程中如何使用用于教学的数学知识，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教授指数函数单元的情况。他们将在本单元的整个教学过程中进行课堂观察，并在每个单元前后对教师进行访谈。该项目建立在为教学理解数学知识的其他框架的基础上。其他研究更多地集中在小学或中学教师身上。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话题，也是学生学习代数和微积分的基础话题。ECR计划强调基础STEM教育研究，以产生该领域的基础知识。在关键领域的投资是基本的、广泛的和持久的：STEM学习和STEM学习环境，扩大STEM的参与，以及STEM劳动力发展。研究的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依据的决策，他们用来做出决策的教学数学知识，以及影响这些决策质量的因素和学生进行数学推理的机会。他们正在招聘教授这些课程至少两年并被公认为高素质教师的专家教师。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。访谈中的问题集中在教师的决策上，并将探索他们的数学知识用于教学。用于教学的数学知识包括教师的知识如何支持他们对学生数学推理的计划、指导和评估。本研究还提供了一种研究方法，可用于学习数学知识，用于其他中学数学课题的教学。

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.