Building Understanding and Measurement of Secondary Mathematical Knowledge for Teaching (MKT)

2013年，国家研究委员会发布了一份报告《监控K-12 STEM教育成功的进展：一个进步的国家？》，其中概述了14项指标以及创建一个监测国家STEM教育质量的系统所需的研发。本项目是应亲爱的同事来信的要求而资助的，该信要求对促进测量和评估创新计划进行研究，该计划专注于开发研究和工具，以提高国家衡量这些指标的能力。该项目的研究人员将处理指标6：教师的教学科学和数学内容知识。本研究建立在一个成功的项目--制定有效的教师数学知识教学测量(MKT)计划的基础上，表明教师成功利用学生所需要的数学知识不同于传统的数学知识。本研究将检验两个假设：1)。初级MKT测评项目的测评设计理论扩展到二级MKT测评项目的设计；扎实的传统数学知识，重点是高等数学知识，对中学MKT比初级MKT更重要。该项目将包括召集专家，以确定研究结果对未来围绕数学指标6进行研究和开发的影响。该项目将使用在先前NSF资助的研究中开发的用于中学教师MKT的项目。研究人员将进行认知访谈，以确定教师在多大程度上正确地回答了问题，以及他们的反应理由在多大程度上与教学所需的数学专业知识或传统的数学推理相一致。这项研究的结果将是一个专家论坛的重点，研究结果将构成为研究和发展议程制定建议所需的建议，以制定有效和可靠的中学教师对教学数学知识的理解指标。

The National Research Council in 2013 released the report Monitoring Progress toward Successful K-12 STEM Education: A Nation Advancing?, which outlined 14 Indicators as well as the needed research and development to create a system to monitor the quality of STEM education in the nation. This project is funded in response to a Dear Colleague Letter request for research in the Promoting Innovation in Measurement and Evaluation program focused on developing research and tools to advance the nation's capability to measure these indicators. The researchers in this project will address Indicator 6: Teachers' science and mathematics content knowledge for teaching. This research builds on a successful program that is developing valid measures of teachers' Mathematical Knowledge for Teaching (MKT), which indicates that the mathematical knowledge teachers need to be successful with students is different than conventional mathematical knowledge. The research will test two hypotheses as follows: 1). the assessment design theory for elementary MKT assessment items extends to secondary MKT item design; and 2). Strong conventional mathematical knowledge, with a focus on knowledge of advanced mathematics, is more integral to secondary MKT than to elementary MKT. The project will include a convening of experts to identify the implications of the findings for future research and development around Indicator 6 in mathematics. The project will use items for secondary teacher MKT that have been developed in prior NSF-funded research. The researchers will conduct cognitive interviews to determine the extent to which the teachers correctly respond to the items and the extent to which their rationale for their response is in alignment with the reasoning around specialized knowledge of mathematics for teaching or with conventional mathematical reasoning. The findings of the study will be the focus of an expert forum in which the findings from the study will structure the development of recommendations for the research and development agenda needed to develop valid and reliable indicators of secondary teachers' understanding of mathematical knowledge for teaching.