Assessing the Structure of Knowledge in Teaching Mathematics

了解小学教师的数学教学知识是如何发展的，以及它如何影响教学和学生的学习，一直是数学教育中的一个长期挑战。几乎没有什么措施可以让研究人员可靠地评估教师数学知识的性质。本研究的目的是为新入门的和有经验的小学教师制定数学知识的测量方法，以便更有效地评估教师知识及其与学生学习的关系。这项研究将利用最新的心理测量学和方法论的进步来开发更复杂和敏感的教师数学知识的教学测量方法。该提案包括一套四项研究。第一项研究将考察新手和有经验的教师在教学方面的数学知识有何不同。第二项研究将考察教师数学教学知识的发展及其与该领域教学课题经验的关系。第三项研究将考察学生对特定数学概念的学习与教师对这些概念的了解之间的关系。第四项研究将包括课堂观察，以考察用于教学的数学知识与数学教学的相应方面是如何联系的。该方法利用诊断性分类模型来表征教师在特定数学领域--分数和小数--的知识。该项目得到了NSF的EHR核心研究(ECR)计划的支持。ECR计划强调基础STEM教育研究，以产生该领域的基础知识。在基本、广泛和持久的关键领域进行投资：STEM学习和STEM学习环境，扩大STEM的参与，以及STEM劳动力发展。该计划支持积累强有力的证据，为理解、构建解释理论和建议干预和创新提供信息，以应对STEM兴趣、教育、学习和参与方面的持续挑战。

Understanding how elementary teachers' mathematical knowledge for teaching develops and how it influences instruction and student learning has been a persistent challenge in mathematics education. Very few measures exist that allow researchers to reliably assess the nature of teachers' mathematical knowledge. The purpose of this study is develop measures of mathematical knowledge for teaching in both novice and experienced elementary teachers to more effectively assess teacher knowledge and its relationship to student learning. This study will take advantage of recent psychometric and methodological advances to develop more sophisticated and sensitive measures of teachers' mathematical knowledge for teaching. The proposal includes a set of four studies. The first study will examine how mathematical knowledge for teaching differs for novice vs. experienced teachers. The second study will examine the development of teacher mathematical knowledge for teaching and its relationship to the experience of teaching topics in that area. The third study will examine how student learning of specific mathematics concepts is related to teacher knowledge of those concepts. The fourth study will involve classroom observations to examine how mathematical knowledge for teaching is related to corresponding aspects of mathematics instruction. The methodology makes use of diagnostic classification models to characterize teacher knowledge in particular domains of mathematics--fractions and decimals. This project is supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development. The program supports the accumulation of robust evidence to inform efforts to understand, build theory to explain, and suggest intervention and innovations to address persistent challenges in STEM interest, education, learning and participation.