Consensus or Confusion?

Abstract

While most states have developed well-articulated mathematics standards, including specific expectations, Ms. Reys and Ms. Lappan found no consensus--and the potential for much confusion--when they conducted a national study of state mathematics standards. ********** AMONG its many provisions, No Child Left Behind (NCLB) requires that states adopt challenging academic content in mathematics, reading/language arts, and science. These standards must specify what children are expected to know and be able to do, must contain coherent and rigorous content, and must encourage the teaching of advanced skills. What's more, the states are required to measure the achievement of students against the state standards in grades 3 through 8. Since 2002, 38 states have developed or revised their mathematics curriculum standards, some of which are intended to serve as models for local districts, while others are mandatory and specify the mathematics all students in the state are expected to learn at particular grades. The state curriculum standards serve as guidelines for shaping each state's annual assessments. All of that is old news to most Kappan readers. What might be new news is that the new state standards do not reflect anything like a consensus of opinion regarding when students should learn particular topics in mathematics. In fact, the variation in grade placement of topics across the state standards is quite likely to contribute to the continued development of textbooks that are repetitive and provide superficial treatment of a range of topics. AUTHORITY OF STANDARDS DOCUMENTS The newest iterations of state mathematics standards specify learning expectations. For many states, these documents are far more specific with regard to grade placement of topics than previous state standards or frameworks. For example, prior to NCLB, most state departments of education provided school districts with a broad set of standards (generally organized by grade band, such as K-4, 5-8, and 9-12). The states then monitored student learning at particular grades (e.g., grades 4, 8, and 10). School districts were encouraged to use these broad guidelines to create more detailed learning goals for each grade. But because of the mandates of NCLB, states that had not previously provided much detail have now created grade-by-grade learning goals for mathematics. The relationship of these standards to high-stakes assessments in the states has given the documents new authority and made them far more relevant than they had been before. According to respondents to a recent survey of state-level mathematics curriculum supervisors, most teachers and school administrators today are paying closer attention to the curriculum standards provided by state education agencies than they did in the past. In fact, more than two-thirds of respondents perceived the new state-level curriculum standards to be significantly influencing classroom instruction, textbook selection, and professional development for teachers. (1) In an effort to understand the nature of the new standards and the level of consensus across states, we reviewed all state mathematics standards that outline grade-specific learning goals for at least grades 3-8 (41 states in all, plus the Department of Defense Education Agency). Findings from this study confirm that mathematics learning expectations vary across the states along several dimensions, including level of specificity, language used to convey learning goals, and grade placement of specific learning expectations. We summarize our findings on each of these dimensions below. VARIATION ACROSS STATES Specificity and complexity. We noted two major areas of variation in the structure of learning expectations (GLEs) within state standards. The first is the level of specificity of the GLEs. For example, the Arizona standards on functions include the same GLE in each of grades 4-8, using the words grade-level appropriate to differentiate between the specific expectations at each level. …