Collaborative Research: Assessing Secondary Teachers' Algebraic Habits of Mind

波士顿大学、教育发展中心公司和圣奥拉夫学院正在合作评估中学教师的代数思维习惯（ASTAHM），以开发评估中学教师数学思维习惯（mhm）的工具。这些习惯为教师的数学思维带来了节俭、专注和连贯，反过来，也为他们与学生的合作带来了便利。数学数学模型是中学数学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如何成为教师有效性的指标，该伙伴关系正在研究以下问题：在数学教学中运用数学数学理论的教师如何将数学数学理论运用到教学实践中？教师对MHoM的参与和他们在教学中使用这些习惯与学生的理解和成就有什么关系？为了调查这些问题，ASTAHM正在开发两种工具：纸笔（P&amp；P）评估和观察协议，分别衡量教师对mhm的知识和课堂使用。这项工作分两个阶段进行：(1)仪器改进和学习阶段，(2)仪器测试和研究阶段。第一阶段的目标是收集数据，以完善项目现有的工具，并了解影响教师知识和课堂使用mhm之间关系的桥梁因素。具体的研究活动包括：对40名教师进行试点P&amp；P评估，对8名教师的代数教学进行录像，对仪器进行初步测试和改进，并使用数据分析桥梁因素。第二阶段是一项大规模的研究，包括对200名教师进行P&amp；P评估的实地测试，对20名教师进行录像并使用观察协议进行研究，收集3000名学生的成绩数据，并与200名数学家一起检查P&amp；P内容的有效性。有了这些经过验证的工具，该项目将对上述研究问题进行调查。莱斯利大学的项目评估和研究小组（PERG）是外部评估机构。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与课堂实践以及学生成绩之间存在的关系程度。评价人员还在调查这两种仪器的用户编码指南是否能使现场测试人员有效地使用它们并对它们进行充分评分。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数学教学知识与中学生的数学理解和成绩之间的联系。mhm结构与共同核心国家数学标准（CCSS-M）密切相关；特别是《数学实践标准》。例如，两者都重视寻找和使用数学结构。因此，本项目生产的工具可以作为专业发展计划在准备教师实施CCSS-M方面有效性的事前和事后措施。中学阶段的数学教师知识是一个未被充分研究的领域。通过分析教师在工作中的思维习惯和实践，ASTAHM正在开发一种工具，可以用来阐明有效的中学教学。

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.