From the NCSM President
Diane J. Briars
Selecting Instructional Materials: Much More Than "Aligned to Standards"
Selection of instructional materials is one of our very important activities as mathematics education leaders. While committees of teachers, administrators, and other stakeholders typically select the materials, our planning and facilitation of the process, along with related professional development, are critical components of the selection process. "Aligned to standards" has become the cornerstone of materials selection, with committees examining materials to determine whether grade-level standards are included in materials for that grade, and publishers providing extensive alignment documents to show that, yes, their materials cover all the standards for each grade or course. While alignment can provide important "opportunity to learn" information, too often alignment is now just a "Prego" checklist-"Is it in there?" with little consideration of how content is organized and presented in addition to other factors essential for effective mathematics instruction.
To select materials that best support students' learning, we need to go beyond alignment-the "Is it in there?" question-to analysis of the potential of materials to support students' attainment of the standards. Analysis involves careful examination of the content, instructional tasks, and teacher support the instructional materials provide. This shift is particularly important in light of the Common Core State Standards (CCSS), given the differences between the CCSS and previous state standards: (1) the progression of the CCSS across grades, which whenever possible reflects research on students' learning of mathematics content; and (2) the Standards for Mathematical Practice, which describe the thinking processes, habits of mind, and dispositions students need in order to develop a deep, flexible, and enduring understanding of mathematics and to be able to "do" mathematics.
MATHEMATICAL CONTENT: Analysis requires examinations of clarity, comprehensiveness, accuracy, and coherence of content presentation within and across grades and courses. For the CCSS, it is particularly important to examine the progression of content across grades and courses. Do the materials present content at the CCSS recommended grade levels? Do they address "key advances" in the CCSS-all the common addition, subtraction, multiplication and division situations, units and unitizing (e.g., unit fractions, unit rates), informal computation strategies based on place value and properties of operations, congruence, and similarity in terms of geometric transformations and modeling.
INSTRUCTIONAL TASKS: A second criterion for instructional materials is the nature of the instructional tasks they contain. Do the materials provide opportunities for all students to engage in cognitively challenging tasks? Are such tasks used regularly as the basis for instruction? A growing body of research links students' engagement in cognitively challenging tasks to increased achievement;1 engaging in such tasks is essential for developing proficiency in the CCSS for Mathematical Practice.
Teacher support for planning and enacting lessons and assessing student learning: How teachers implement challenging tasks influences what students learn from them. Maintaining the level of demand in implementation and orchestrating effective classroom discussions pose significant challenges for many teachers. Thus, a third review criterion is the instructional support provided to teachers. Do the materials help teachers anticipate possible student solutions and provide questions/suggestions for task set-up, for support of students' work on the task, and for the summary discussion? To what extent do the materials provide appropriate questions/tasks for formative as well as summative assessment? Analysis of the teacher and ancillary materials should focus on the content of these materials, not just their technology platforms.
To support this type of instructional materials analysis, NCSM is collaborating with Bill Bush of the University of Louisville and a team of mathematics educators and mathematicians to develop a tool/process for analyzing instructional materials in light of the CCSS. The team is also creating professional development activities on effective use of this tool. The target release date for both is Spring, 2011. Moving beyond the current view of "alignment" to a multi-dimensional comprehensive analysis of instructional materials will help teachers provide high quality, research-informed instruction to all students every day.
1 Resnick, L. (Ed.) (2006). Do the math: Cognitive demand makes a difference. American Education Research Association, 4(2), www.aera.net/uploadedFiles/Journals_and_Publications/Research_Points/RP_Fall06.pdf