As described in Appendix A, quality assessments depend on three things: (1) clarity about the competencies that the assessment should measure, (2) tasks and observations that effectively capture those competencies, and (3) appropriate qualitative and quantitative techniques to give interpretive power to the test results. Clarity about the competencies to be measured requires a theoretical understanding (that is empirically supported) of mathematics learning. Unlike many other areas of the curriculum, early mathematics has the theoretical and conceptual models, as well as supporting empirical data, on which to build quality assessments. Substantial work has already been done to specify critical concepts and skills in this domain, providing assessment developers with substantial resources on which to draw in drafting the elements of a measurement strategy.
Even with a strong foundation on which to build in early mathematics, much work remains in designing and testing assessment items to ensure that inferences can accurately be drawn about student knowledge and competencies. And this work must be carefully crafted for the specific purpose and use of the assessment. This includes formative assessment for use in the classroom to assist learning. These assessments can, for example, provide feedback to the teacher on whether a particular skill or concept is mastered adequately, or whether some individual students need more time and practice before moving on. Summative assessments are also used in the classroom, but they come at the end of a unit, giving a teacher feedback on how well the students have mastered and brought together the set of concepts and skills taught in the unit. These may be helpful to the teacher in redesigning instruction for the next year, providing valuable data on students’ strengths and weakness that can inform instruction at the next level. School- or district-level assessments have a separate purpose. Rather than provide information on individual students, their purpose is to determine attainment levels for students as a group in order to evaluate the effectiveness of the school’s or the district’s instructional program and, in some cases, to hold schools accountable for the performance of their students.
Currently the different types of assessment are loosely con-