6A School District: A Case Study Correlating Content Standards to Teacher Practice
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In light of new legislation defining society’s newest standards for math learning, my research aims to observe how teachers are adapting to put these mandates into practice. Through a case study of one high school Algebra 1 teacher, I analyzed how differences in pedagogical practices affected student learning outcomes. In observing the shifts in teacher practices in the facilitation of math discourse and the building of procedural fluency from conceptual understanding, I have found a strong correlation between the change in teaching practices and the shifts from the McDougal & Littell (M&L) and College Preparatory Mathematics (CPM) textbooks. In this study, “Conceptual Understanding” is defined as the ability for a student to “understand why a mathematical ideal is important and the contexts for which it is useful”, and “Procedural Fluency” means that “students understand when to use certain procedures and how to perform them with both flexibility and precision.” (National Research Council, 2001, p. 118) By creating a more encouraging environment where students are unafraid to ask for help, and providing more opportunities for students to justify their reasoning, the changes in Cornelia’s teaching practices are a positive adaption to meet the Common Core State Standards for Mathematics (CCSSM) standards, and highly aligned to the shift in textbooks. As the CPM lesson specifically dictates that students work in groups, there is an explicit emphasis on student communication as members must check-in with each other to verify their solutions. Additionally, CPM provides a higher percentage of problems that do not have solutions to reinforce the idea that students must justify when they can use a procedure. Overall, the shifts between Chapter ten of McDougal & Littell textbook and Chapter eight of College Preparatory Mathematics textbook are moderately aligned to the change in content standards. While CPM presents students with more opportunities to justify their understanding in writing and via peer communication, many improvements to Chapter 8 of the CPM text can be made to fully align the text to the CCSSM standards regarding quadratic equations. These changes include limiting the use of Learning Logs, (notebooks where students explain their conceptual understanding), until students can fully prove a hypothesis, including more sections that begin with contextual problems like Sections 8.2.1 and 8.2.4, and better connecting the 8 Standards of Mathematical Practice (Practices students should use in the math classroom) to each lesson. Because the curriculum shifts are moderately aligned to the changes in content standards, we can conclude that the changes in student standards have made a moderate impact on teacher practices.