Collaborative Research: Assessing Secondary Teachers' Algebraic Habits of Mind

波士顿大学教育发展中心，和圣奥拉夫学院正在合作评估中学教师的数学思维习惯（ASTAHM），以开发工具来评估中学教师的数学思维习惯（MHoM）。这些习惯给教师的数学思维带来了简约、专注和连贯性，反过来，也影响了他们与学生的合作。MHoM是中学数学知识教学的重要组成部分。认识到需要一种科学的方法来调查MHoM是教师有效性的指标，该伙伴关系正在研究以下问题：1。如何从事MHoM教师为自己做数学时也带来MHoM到他们的教学实践？2.教师与MHoM的互动以及他们在教学中使用这些习惯与学生的理解和成就有何关系？为了调查这些问题，ASTAHM正在开发两种工具：纸笔（P P）评估和观察协议，分别衡量教师的知识和课堂使用，MHoM。这项工作正在进行两个阶段：（1）工具完善和学习阶段，（2）工具测试和研究阶段。第一阶段的目标是收集数据，以完善该项目的现有工具，并了解影响教师的知识和课堂使用MHoM之间的关系的桥梁因素。具体的研究活动包括：管理试点P P评估40名教师，录像代数指令的8名教师，进行初步测试和完善的仪器，并利用数据来分析桥梁的因素。第二阶段是一个大规模的研究，涉及现场测试的P P评估与200名教师，录像20名教师和研究他们使用的观察协议，收集成绩数据从3000名学生，并检查P P内容的有效性与200名数学家。有了这些经过验证的工具，本项目将对上述研究问题进行调查。莱斯利大学的计划评估和研究小组（PERG）是外部评估员。PERG正在评估ASTAHM在开发有效和可靠的工具方面的总体成功，以调查教师的MHoM与他们的课堂实践以及学生成绩之间的关系。评估人员还在调查这两种工具的用户编码指南是否能使实地测试人员有效地使用和适当地评分。这项工作符合一个更大的研究议程，其最终目标是了解中学教师的教学数学知识与中学生的数学理解和成就之间的联系。MHoM结构与共同核心国家标准-数学（CCSS-M）密切相关;特别是其数学实践标准。例如，两者都重视寻求和使用数学结构。因此，该项目产生的工具可以作为前和后的措施，专业发展计划的有效性，在准备教师实施CCSS-M。中学数学教师知识是一个研究不足的领域。通过分析教师在工作中的做法和思维习惯，ASTAHM正在开发可用于阐明有效中学教学的工具。

Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.