Collaborative Research: Cognitive Processes - Classroom Practices that Lead to Student Proficiency with Word Problems in Algebra

这项为期三年的研究对数学课堂实践进行了详细的描述和分析，这些实践导致了代数1学生在代数应用题解决方面的熟练程度的发展。预期研究性研究将：(A)加深对数学课程核心重要领域数学能力教学机制的了解；(B)开发研究工具，支持对促进数学学习的教学机制进行更深入的研究；以及(C)开发可大规模使用的实用工具，用于确定基准和改进教学实践。讨论了以下两个研究问题：(1)教师经常使用哪些教学实践来帮助学生提高解决应用题的熟练程度？(2)哪些分析方法可以被开发并用于表征这些有希望的教学实践，并且成本足够低，从而可以在大量课堂上检验教与学之间的联系？我们将仔细研究精心挑选的大师教师的教学实践，试图找出能给学生带来强大学习效果的实践。在第一年，将征集和审查一系列教师的录像带，这些录像带是被选中的，因为他们成功地帮助了许多学生在数学上取得了良好的成绩。将进行不同层次的多种分析，从建立课堂社会数学规范到学生访谈，以确定数学上富有成效的课堂实践和相关的学生理解。在第一年，研究将开发和改进与社会数学规范和有效课堂教学相关的编码和分析方案，以解决应用问题。这些将在第二年的一个小规模项目的基础上进一步完善，该项目的目标是对一系列教室中的教学和学生学习进行分析，力求将教学实践与学生的成果联系起来。第三年将把研究扩展到更大的样本，对结果进行编码，并产生可供研究社区和实践者使用的分析工具。研究重点是开发和测试有效地向代数1学生教授典型和非常规应用问题解决的方法。这方面的有效数学教学的课堂录像带将在一年级进行分析和编码。这些代码将提供由于课堂社会数学规范的有效内部化而产生的学生创造性行为的特征。这些规范侧重于诸如什么构成不同的、有效的和复杂的数学解释、理由，以及更广泛的推理等问题。在第二年，这些代码将通过一小部分教室样本进行测试和改进。在第三年，前两年的结果将在更大的代数1教室样本中进行测试。本研究对希望更有效地教授解题教学的教师具有一定的现实意义。在研究层面上，本研究试图将社会数学规范的使用扩展到代数1字问题的解决。研究人员(和教师)还将获得分析这一内容领域有效课堂实践的工具。这项研究在这个时候尤其需要，因为全国各地的代数1课堂上都有学生，他们带来了不同的观点和背景知识。

This three-year study provides a detailed description and analysis of mathematics classroom practices that result in Algebra 1 students' development of proficiency in word problem solving in algebra. The research study is expected to: (a) provide an enhanced understanding of the mechanisms of teaching for mathematical proficiency in a centrally important area of the mathematics curriculum, (b) develop research tools that support deeper investigation into the mechanisms of teaching for robust mathematics learning, and (c) develop practical tools that can be used on a large scale for benchmarking and improving teaching practice. The following two research questions are addressed: (1) What instructional practices are frequently used by teachers judged to be doing an exceptional job of helping students to develop proficiency in solving word problems? (2) What analytic procedures can be developed and used to characterize these promising teaching practices, with low enough cost so that connections between teaching and learning can be examined for a large number of classrooms? The instructional practices of carefully selected master teachers will be examined in an attempt to identify practices that result in powerful student learning. In year 1 videotapes of a range of teachers selected for demonstrated success in helping a wide range of students perform well in mathematics will be solicited and examined. Multiple analyses at varied levels of grain size from the establishment of classroom sociomathematical norms and student interviews to identify mathematically productive classroom practices and related student understandings will be performed. In year 1, the research will develop and refine coding and analytic schemes relevant to sociomathematical norms and effective classroom instruction in word problem solving. These will be further refined in year 2 on the basis of a small scale project that targets the analyses of teaching and student learning in a range of classrooms, seeking to link instructional practices with student outcomes. Year 3 will extend the study to a larger sample, codifying the results and producing analytic tools that can be used by the research community and by practitioners.The study focuses on developing and testing ways to teach typical and nonroutine word problem solving to Algebra 1 students in an effective manner. Classroom videotapes of effective mathematics instruction in this content area will be analyzed and coded in year 1. The codes will provide characteristics of productive student behavior as a result of effective internalization of classroom sociomathematical norms. These norms focus on issues such as what constitutes different, effective, and sophisticated mathematical explanations, justifications, and more generally, reasoning. In year 2, the codes will be tested and refined with a small sample of classrooms. In year 3, results from the prior two years will be tested over a larger sample of Algebra 1 classrooms. The study has practical significance for teachers who want to learn to teach word problem solving in a more effective manner. At the research level, the study seeks to expand the use of sociomathematical norms to Algebra 1 word problem solving. Researchers (and teachers) will also be provided with tools for analyzing effective classroom practices in this content area. The research is especially needed at this time because Algebra 1 classrooms around the country consist of students who bring with them a diversity of perspectives and background knowledge.