Strengthening Tomorrow's Education in Measurement: STEM

这个提议的项目是解决一个引人注目的问题的第一步，这个问题在数学教育中没有得到足够的研究关注：为什么与其他内容领域和其他发达国家的学生相比，美国学生的表现和对测量的理解如此之差？这个问题有据可查，但没有提出全面的、有经验根据的解释。如果没有这样的解释，通过改变课程、专业发展或教师教育来解决问题的努力将仍然是不集中和无效的。研究文献（例如，Clements, 1999; Lehrer, 2003; Strom, Kemeny, Lehrer, & Forman, 2001）表明，四个因素直接或相互作用地形成了这个问题：(1)出版的中小学课程的缺陷；(2)教师制定这些课程的问题；(3)课堂上关于测量的话语特征的问题；(4)教师自身的测量知识。认识到这种相互作用的复杂性，该项目将评估中小学课程的能力，以支持学生学习长度、面积和体积的测量。根据现有的研究文献，该项目将(a)评估中小学课程的不足和优势，(b)描述这些课程中的关键主题是如何由教师在课堂上制定的。根据市场份额、设计差异（出版商开发vs. nsf资助）和当地采用模式，选择了四门小学课程和三门中学课程。他们的完整内容的长度，面积和体积将使用一个框架进行评估，该框架建立在研究基础上，详细说明了稳健理解的要素。该内容包括(1)基本方法，(2)明确的内容陈述，例如，区域的定义，以及(3)与目标措施相关的所有问题、任务和活动。每一次评估都会产生一份课程简介，该简介将传达给每个作者团队，并根据他们的反馈进行适当的修改。教师在关键主题领域（长度介绍、复杂长度介绍、面积介绍、周长和面积介绍、表面积和体积介绍）的课程序列演示将使用相同的框架进行分析。主要目的是估计书面课程在多大程度上导致了学生学习能力低下的问题；第二个目标是跟踪教师如何在课堂上制定这些测量主题，作为对上述所有主要因素的贡献建模的一步。知识价值。该项目将提供一份详细的、以研究为基础的分析，分析当前出版的课程支持学生扎实学习核心测量内容的能力。对教师制定的课程的分析将描述书面材料如何与其他因素结合起来塑造学生的学习，无论是否有效。概念框架和课程概况将支持对其他书面课程（例如，高绩效国家的课程）、教师制定的课程和学生学习情况的分析。广泛的影响。长度、面积和体积在所有的小学和初中都教过，但教学往往是无效的。不了解测量的概念基础会破坏后续STEM学习的广泛内容。该项目将扩展和丰富目前由美国国家科学基金会资助的数学课程研究中心的工作，该中心的分析主要集中在数字、代数和推理上。

The proposed project is an initial step toward solving a compelling problem that has received insufficient research attention in mathematics education: Why do U.S. students perform and understand measurement so poorly, in contrast to other content domains and students' in other developed countries? The problem is well-documented, but no comprehensive, empirically-grounded explanation has been advanced. Absent such an explanation, efforts to redress the problem via changes in curricula, professional development, or teacher education will remain unfocused and ineffective. The research literature (e.g., Clements, 1999; Lehrer, 2003, Strom, Kemeny, Lehrer, & Forman, 2001) suggests that four factors shape the problem, directly and in interaction: (1) deficits in published elementary and middle school curricula, (2) problems in teachers' enactments of those curricula, (3) problems in the character of classroom discourse about measurement, and (4) teachers' own knowledge of measurement. Recognizing this interactive complexity, this project will assess the capacity of elementary and middle school curricula to support robust student learning of measurement of length, area, and volume. Drawing on the existing research literature, the project will (a) assess the deficits and strengths of elementary and middle school curricula, and (b) characterize how key topics in these curricula are enacted by teachers in their classrooms. Four elementary and three middle school curricula were selected based on market-share, differences in design (publisher-developed vs. NSF-funded) and local adoption patterns. Their complete content for length, area, and volume will be evaluated using a framework, built from research, that details the elements of robust understanding. That content includes (1) basic approach, (2) explicit content statements, e.g., definition of area, and (3) all problems, tasks, and activities linked to the target measures. Each evaluation will yield a curriculum profile that will be communicated to each author team and revised, if appropriate, from their feedback. Teachers' presentation of lesson sequences in key topic areas (introduction to length, complex lengths, introduction to area, perimeter & area, and surface area & volume) will then be analyzed using the same framework. The primary objective is to estimate the extent to which written curricula contribute to the problem of weak student learning; a secondary objective is to trace how teachers enact these measurement topics in their classrooms, as a step toward modeling the contributions of all major factors listed above. Intellectual Merit. This project will provide a detailed, research-based analysis of the capacity of current published curricula to support robust student learning of core measurement content. Analyses of teachers' enacted curricula will characterize how written materials combine with other factors to shape students' learning, productively or not. The conceptual frame and the curricular profiles will support analyses of other written curricula (e.g., those in high-performing countries), teachers' enacted curricula, and students' learning. Broad Impact. Length, area, and volume are taught in all elementary and middle grades, but too often instruction is ineffective. Failing to learn the conceptual foundations of measurement undermines subsequent STEM learning across a wide spectrum of content. The project will expand and enrich the work of the current NSF-funded Center for the Study of Mathematics Curriculum where analyses have primarily focused on number, algebra, and reasoning.