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提供了数学课堂实践的详细描述和分析，这些实践导致代数1学生在代数中解决文字问题的熟练程度的发展。这项研究预计将：(a)在数学课程的一个核心重要领域提供对数学熟练程度教学机制的更好理解，(b)开发研究工具，支持对稳健数学学习的教学机制进行更深入的调查，以及(c)开发可大规模用于基准测试和改进教学实践的实用工具。以下两个研究问题被处理：(1)哪些教学实践被认为在帮助学生熟练地解决文字问题方面做得非常出色的教师经常使用？(2)在成本足够低的情况下，可以开发和使用哪些分析程序来描述这些有前途的教学实践，以便在大量的课堂上检查教与学之间的联系？精心挑选的大师教师的教学实践将被检查，以试图确定导致强大的学生学习的实践。在一年级，我们将征集和审查一系列教师的录像带，这些教师被挑选出来，以证明他们在帮助广泛的学生学好数学方面取得了成功。将从课堂社会数学规范的建立和学生访谈中进行不同粒度水平的多重分析，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，研究将开发和完善与社会数学规范和有效的课堂教学有关的编码和分析方案。在第2年，这些将在一个小规模项目的基础上进一步完善，该项目旨在分析一系列教室的教学和学生学习，寻求将教学实践与学生成果联系起来。第三年将把研究扩展到一个更大的样本，编纂结果并产生可供研究界和实践者使用的分析工具。本研究的重点是开发和测试如何有效地教授代数1学生解决典型和非常规的单词问题。这一内容领域的有效数学教学课堂录像将在一年级进行分析和编码。作为课堂社会数学规范有效内化的结果，这些规范将提供富有成效的学生行为特征。这些规范关注的问题是，什么构成了不同的、有效的、复杂的数学解释、论证，以及更普遍的推理。在第二年，守则将在一小部分教室样本中进行测试和完善。在第三年，前两年的成绩将在更大的代数1教室样本中进行测试。本研究对希望更有效地教授应用题教学的教师具有现实意义。在研究层面，本研究试图将社会数学规范的应用扩展到代数1的字题解决。研究人员（和教师）也将提供工具来分析有效的课堂实践在这个内容领域。这项研究在这个时候是特别需要的，因为全国各地的代数1教室由学生组成，他们带来了多样化的观点和背景知识。

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.