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

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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.