Knowing Mathematics for Teaching Algebra

对美国K-12学生数学成绩质量的担忧继续主导着学术和大众媒体的全国性对话。学生在代数方面的表现尤其令人担忧，这可能部分是由于缺乏适当的教师知识。RAND数学研究小组（2003）指出，需要：澄清教学的知识需求，评估跨年级和数学领域教学的数学知识的工具，以及更深入地了解未来和实践教师有机会获得这类知识的方式；他们还把代数作为一个关键领域。因此，拟议的研究项目有三个主要目标：1。工具设计：开发项目并设计可靠有效的工具，以测量在职前和在职中学数学教师代数教学中的知识。2. 框架验证：为代数教学提供一个经经验验证的、全面的知识框架。3. 教师知识现状研究。目的：研究全国职前教师和在职教师代数学教学知识的现状及变化。在全国各地的研究合作者、国家顾问委员会和项目编写者的支持下，一个以密歇根州立大学为基础的跨学科研究团队将领导这个项目，他们在数学、数学教育、研究设计、心理测量分析和中学数学教学和课程方面拥有集体专业知识。拟议活动的智力价值：该研究将为中学水平的代数教学提供经验验证和全面的知识框架，以及在大规模环境中测量这些知识的项目和评估工具。结果将是澄清和描述教师知识在K-12数学课程的一个关键和有问题的领域。提议的活动产生的更广泛的影响：这里开发的项目和评估工具将对教师教育者、培养教师的数学家、专业发展的设计者和对代数领域的教师学习感兴趣的评估者有价值。最终，这项工作将对中学代数教学的改善产生实质性的影响。

Concerns about the quality of the mathematics achievement of K-12 students in the United States continue to dominate national dialogue in the academic and popular press. Students' performance in algebra is particularly worrisome, and this may be due in part to lack of appropriate teacher knowledge. The RAND Mathematics Study Panel (2003) notes the need for: clarification of the knowledge demands of teaching, tools for assessing mathematical knowledge for teaching across grade levels and mathematical domains, and deeper understanding of the ways in which prospective and practicing teachers have opportunities to acquire this kind of knowledge; they also single out algebra as a key area. Consequently, the proposed research project has three main objectives: 1. Instrument Design: To develop items and design reliable and valid instruments to measure knowledge in large scale settings for teaching algebra among pre-service and in-service secondary school mathematics teachers. 2. Framework Validation: To produce an empirically validated and comprehensive framework for knowledge for teaching algebra. 3. Status Study of Teacher Knowledge. To study the status and variation of knowledge for teaching algebra among pre-service and in-service teachers drawn from across the nation. An interdisciplinary MSU-based research team with collective expertise in mathematics, mathematics education, research design, psychometric analysis, and secondary school mathematics teaching and curriculum will lead the project, with the support of research collaborators around the country, a national advisory board, and item writers. Intellectual merit of the proposed activity: The study will contribute an empirically validated and comprehensive framework for knowledge for teaching algebra at the secondary school level, together with items and assessment instruments to measure this knowledge in large-scale settings. The result will be clarification and description of teacher knowledge in a crucial and problematic area of the K-12 mathematics curriculum. Broader impacts resulting from proposed activity: The items and assessment tools developed here will be of value for teacher educators, mathematicians who prepare teachers, designers of professional development, and evaluators interested in teacher learning in the area of algebra. Ultimately this work could have substantial impact on the improvement of secondary school algebra teaching and learning.