|Two important premises undergird the framework. The first is that no single measure is used to make high-stakes decisions. Therefore, reference is made to both assessments and assessment systems. The intent is to draw attention to the importance of making use of data from a variety of assessment instruments, since it is not possible for one test or instrument to adequately measure the entire range of mathematical activity that is typically described in a set of content standards.
An assessment system is made up of many components:
- Content standards describing the mathematics that students should know and be able to do, including the mathematical activities that are taught and learned.
- Performance standards describing what students are expected to know about each of the content standards at specific times.
- One or more testing instruments. Each test or assessment instrument will be able to measure only a subset of the content standards; a framework should describe what is measured by each instrument.
- Materials that accompany each instrument, such as scoring guides and reports of assessment results.
Each component has a framework and accompanying materials and reports. All components of a high-quality assessment system are aligned, meaning that they describe the same expectations for the mathematics that students should know and be able to do.
The second premise of this framework is that a well-aligned assessment system is not necessarily a high-quality system. A system could have a high degree of alignment between assessments and content standards, but the content standards may be of poor quality. This can result in invalid inferences being made about students’ achievement and negative consequences for stakeholders. An assessment aligned with poor-quality content standards may not be a valid measure of students’ knowledge of important mathematics. The results of the assessment may be of little use to teachers, parents, students, or other potential constituencies. For example:
- If the content standards are vague, the results will not furnish useful suggestions on how to differentiate instruction.
- If the standards do not include mathematical processes, such as reasoning or problem solving, these processes are not likely to be emphasized in the classroom.
- If the standards are too narrowly conceived, the results of the assessment may encourage poor judgments, such as retaining students until their arithmetic fluency meets an established level, denying those students access to broader mathematical skills and concepts.