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

协作研究：认知过程 - 提高学生熟练掌握代数单词问题的课堂实践

• 批准号: 0909815
• 负责人: Alan Schoenfeld
• 金额: $ 49.3万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0909815&HistoricalAwards=false
• 关键词: Collaborative; Research; Cognitive; Processes; Classroom

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.

这项为期三年的研究提供了一个详细的描述和分析的数学课堂实践，导致代数1学生的发展熟练的代数应用题解决。这项研究预计将：（a）提供一个数学课程的核心重要领域的数学能力的教学机制的加深理解，（B）开发研究工具，支持深入调查的教学机制强大的数学学习，以及（c）开发实用的工具，可以在大规模上用于基准和改进教学实践。本研究提出以下两个问题：（1）教师在帮助学生提高应用题解决能力方面做得最好的是什么样的教学实践？(2)什么样的分析程序可以开发和使用，以表征这些有前途的教学实践，以足够低的成本，使教学和学习之间的联系，可以检查大量的教室？精心挑选的大师级教师的教学实践将被检查，试图确定的做法，导致强大的学生学习。在第一年，将征求和审查一系列教师的录像带，这些教师被选为成功帮助各种学生在数学方面表现良好的教师。从建立课堂社会数学规范和学生访谈，以确定数学生产力课堂实践和相关的学生理解的粒度在不同层次的多重分析将被执行。 在第一年，研究将开发和完善相关的社会数学规范和有效的课堂教学解决应用题的编码和分析方案。第二年将在一个小规模项目的基础上进一步完善这些标准，该项目的目标是分析一系列教室的教学和学生学习情况，寻求将教学实践与学生成果联系起来。第三年将研究扩展到一个更大的样本，编纂的结果和生产的分析工具，可以由研究界和从业者使用。研究的重点是开发和测试的方法来教典型的和非常规的文字问题解决代数1学生以有效的方式。在这一内容领域有效的数学教学课堂录像带将在第一年进行分析和编码。作为课堂社会数学规范有效内化的结果，这些守则将提供富有成效的学生行为的特征。这些规范关注的问题，如什么构成不同的，有效的，复杂的数学解释，理由，更普遍的是，推理。在第二年，将对这些守则进行测试，并以一小部分教室为样本加以完善。在第3年，前两年的结果将在代数1教室的更大样本进行测试。本研究对教师如何更有效地进行应用题解决教学具有一定的现实意义。 在研究层面上，本研究旨在将社会数学规范的使用扩展到代数1字问题解决。研究人员（和教师）也将提供工具，用于分析这一内容领域的有效课堂实践。这项研究是特别需要在这个时候，因为全国各地的代数1教室由学生谁带来了他们的观点和背景知识的多样性。