Exploring Relationships Among Use of Standards-Based Instructional Materials in Mathematics, Cognitive Demand, Alignment, and Student Achievement in an Urban District

• In Event: Roundtable Session 118
  In Roundtable Session: Instructional Materials-Based Mathematics Education Reform in Urban Districts

Abstract

Objectives. While districts adopt Standards-based instructional materials in mathematics as part of the mathematics education reform strategies, in studies that have explored how teachers use these materials, there is a wide variety of actual use in classrooms that is difficult to document (Chval, Chavez, Reys, & Tarr, 2009; Remillard, 2005). This paper builds on our prior work, which found that there is a relationship between teachers’ use of Connected Mathematics Project (CMP), Standards-based instructional materials adopted by the district, and increased students’ achievement on state standardized tests. However, there is also a relationship between teachers’ greater than average adaptation of CMP to increased student achievement (King, et al., in review). The proposed presentation explores the relationship among the teacher-reported cognitive demand of cognitive demand and alignment with instructional materials, standards, and assessment relate to students’ achievement on the state standardized tests.
Theoretical Framework. We take the view that the instructional materials represent cultural tools for teachers to use as they deem appropriate for their students’ learning needs (Cole, 1996; Wertsch, 1985). As a cultural tool, the textbook is not an intervention itself, but a tool that teachers use to work with students to enact a lesson leading to student learning (Remillard, 2005). From this perspective, we seek to understand when teachers use and adapt this tool for their purposes, and the impact of this use and adaptation on the desired outcome, student learning of mathematics.
Data Sources and Methods. Using the Surveys of Enacted Curriculum (SEC) and a project designed survey of CMP Implementation, in the spring of 2009 we surveyed all 159 middle grades mathematics teachers in the Newark (NJ) Public Schools on their use of CMP, the content of their instruction, and their instructional practice. We also had coded the NJ state standards, the 2009 NJ state assessments and the CMP materials for content coverage and cognitive demand using the SEC coding system and trained coders (Porter, 2002; Porter, 2011). Finally, we draw on student achievement scores on the 2008 and 2009 NJ Assessment of Skills and Knowledge, and demographic data for students in these teachers’ first mathematics class of the week. Using hierarchical linear modeling, we analyzed the effects of teachers’ instruction on students’ achievement.
Results. Preliminary results suggest that teachers’ adaptations that decrease the cognitive demand of the tasks used with students are related to higher scores on student achievement measures. At the same time, the alignment between the state standards and assessment is not optimal, with the assessment focusing on less cognitively demanding tasks.
Significance. These preliminary results suggest complex relationships between alignment of assessments, standards, and instructional materials and the ways in which alignment, or lack thereof, is related to teachers’ instructional choices, particularly in decreasing the cognitive demand of tasks for students. In particular, the alignment of materials, standards, and assessment must be considered in examining the fidelity of teachers’ implementation of inquiry-based instructional materials.

Authors

• Karen D. King, National Council of Teachers of Mathematics

• Monica B. Mitchell, MERAssociates

• Jessica Tybursky, New York University

• Robert J. Tobias, New York University

• Ognjen Simic, New York University

• Candace Barriteau Phaire, New York University