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

该项目侧重于中学数学知识教学，建立和扩展现有的小学数学工作。该项目正在开发两个相关的评估工具：一个用于评估教师教授中学数学的数学知识（MKTsm），另一个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关于教师和学生对关键数学思想的理解的研究。第二个扩展教学质量评估（IQA），现有的评估，重点是小学和中学数学的质量，使它有一个更明确的重点是中学数学和数学思想的质量，教师的教学培养。这些工具正分三个相互重叠的阶段进行建造、验证和测试。MKTsm评估的发展借鉴了教师和学生对代数和微积分基础思想的理解的现有研究。IQAsm扩展借鉴了现有的IQA验证研究，从co-PI最近的研究转变中学教师的课堂数学实践，并从什么是通过设计MKTsm工具的开发过程中学到的。MKTsm和IQAsm工具正在数学和科学伙伴关系（MSP）计划的三个项目中进行试点，以确保这些工具对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，并正在采取措施确保其他研究人员或可能将这些工具用于评价等目的的管理人员有效和适当地使用这些工具。除了这些工具外，该项目还在为管理人员制作培训视频、评分指南和概述，并正在创建一个程序，以便出版商在这些工具商业化时要求获得使用这些工具的专业发展认证。

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.