Project Aspire: Defining and Assessing Mathematical Knowledge For Teaching Secondary Mathematics

本项目重点关注中学数学知识教学，在现有小学数学工作的基础上进行扩展。该项目正在开发两种相关的评估工具：一种用于评估中学数学教学教师的数学知识（MKTsm），另一种用于评估中学数学教学质量（IQAsm）。同时使用，这些工具能够将中学教师的数学知识与他们的教学联系起来。第一个工具借鉴了先前对教师和学生对关键数学概念的理解的研究。第二部分扩展了现有的侧重于中小学数学质量的教学质量评估（IQA），使其更明确地关注中学数学和教师教学所培养的数学思想的质量。这些仪器的建造、验证和测试分三个重叠的阶段进行。MKTsm评估的开发借鉴了现有的关于教师和学生对代数和微积分基础概念理解的研究。IQAsm的扩展借鉴了现有的IQA验证研究、合作pi最近关于转变中学教师课堂数学实践的研究，以及在设计MKTsm工具的开发过程中所学到的东西。MKTsm和IQAsm仪器正在数学与科学伙伴关系（MSP）计划的三个项目中试用，以确保这些仪器对MSP项目和一般数学教育具有广泛的价值。这些工具正在网上分发，并且正在采取措施确保其他研究人员或可能将这些工具用于包括评价在内的目的的管理人员有效和适当地使用这些工具。除了这些仪器之外，该项目还在编制培训录象、评分准则和供管理人员使用的概览，并正在制订一个程序，使出版商在这些仪器商业化时要求获得使用这些仪器的专业发展证明。

This project focuses on mathematical knowledge for teaching at the secondary level, building upon and extending existing work for elementary mathematics. The project is developing two related assessment instruments: one for assessing teachers' mathematical knowledge for teaching secondary mathematics (MKTsm) and one for assessing the quality of secondary mathematics instruction (IQAsm). Used simultaneously, these instruments are capable of linking secondary teachers' mathematical knowledge with their instruction. The first instrument draws from prior research on teachers' and students' understanding of key mathematical ideas. The second extends the Instructional Quality Assessment (IQA), an existing assessment that focuses on the quality of elementary and middle school mathematics, so that it has a clearer focus on secondary mathematics and on the quality of mathematical ideas that a teacher's instruction fosters. The instruments are being constructed, validated, and tested in three overlapping phases. Development of the MKTsm assessment draws on existing research on teachers' and students' understandings of foundational ideas in algebra and precalculus. The IQAsm extension draws from existing IQA validation studies, from the co-PIs' recent research on transforming secondary teachers' classroom mathematical practices, and from what is learned through the development process in designing the MKTsm instrument. The MKTsm and IQAsm instruments are being piloted in three projects of the Math and Science Partnership (MSP) program, to ensure that the instruments are broadly valuable to MSP projects and mathematics education in general. The instruments are being distributed online, and measures are being taken to ensure valid and appropriate usage by other researchers, or by administrators who might use the instruments for purposes that could include evaluation. In addition to the instruments, the project is developing training videos, scoring guidelines, and an overview for administrators, and also is creating a process by which the publisher will require certification of professional development for use of the instruments when they become commercialized.