Creating Mathematics Performance Assessments That Address Multiple Student Levels‪.‬

In recent times there has been considerable commentary regarding the need to enhance mathematical assessment as evidenced by Numeracy, A Priority for All: Challenges for Australian Schools (2000). This emphasis on assessment is timely because although the mathematical reform movement has produced much-needed improvements in both curriculum and instruction, changes in assessment have not kept pace (Firestone & Schorr, 2004; Morgan, 1998). As Ridgway (1998, p. 2) states, "As an issue of policy, the implementation of standards-based curricula should always be accompanied by the implementation of standards-based assessment. In fact, incremental change in assessment systems will foster concurrent improvement in professional and curriculum development." There is a need to assess a much wider range of mathematical abilities than has been the case heretofore, including problem solving and posing, representing, and understanding. This broadened view of mathematical assessment is supported by curriculum guides from numerous nations. For example, Australian frameworks suggest that numeracy not only includes the ability to perform basic calculations, but also a thorough, connected understanding of number and operation (Leonelli & Schmitt, 2001). Traditional mathematics assessments tend to communicate that mathematics is an endeavor that involves determining a quick answer using a preexisting, memorized method (Bell, 1995; Clarke, Clarke & Lovitt, 1990), thus failing to represent the true complexity of mathematics (Galbraith, 1993). The measurement of decontextualized technical skills should be replaced with measures that reflect what is known about what it means to understand and do mathematics (AAMT, 2002; NCTM, 2000). Both the Assessment Standards for School Mathematics (NCTM, 1995) and the Principles and Standards for School Mathematics (NCTM, 2000) state that assessment tasks communicate what type of mathematical knowledge and performance are valued. Therefore, standards-based instruction is complemented by standards-based assessment (Dunbar & Witt, 1993).