One of the disappointments associated with the mathematical reform movement is the increasing mismatch between the improvements made in curriculum and instruction and prevalent assessment modes (Firestone & Schorr, 2004; Niss, 1993). Despite early calls for change in assessment practice, such as the 1989 Curriculum and Evaluation Standards (NCTM), recent research into the teaching and learning of mathematics that has provided detiled consideration of its "socially situated nature," has not focused to the same degree on mathematics assessment (Morgan, 1998). Therefore interest has increased in matching assessment methods to developments in curriculum.
There is a pressing need to assess a much wider range of abilities than has been the case heretofore, including problem posing and solving, representing, and understanding. Traditional mathematical assessment has frequently relied upon the ability of students to display behavior that matches their assessor's expectations rather than on any underlying understanding (Morgan, 1998). These traditional assessments communicate that mathematics is an endeavor that involves determining a quick answer using a preexisting, memorized method (Bell, 1995; Clarke, Clarke & Lovitt, 1990; Hancock & Kilpatrick, 1993) thus failing to represent the true complexity of mathematics (Galbraith, 1993; Izard, 1993; Wheeler, 1993). In contrast, assessment data that provide direct information about improving the learning experience increase legitimate mathematical learning that is thorough and connected (Black & William, 1998; NCTM, 1995). The measurement of de-contextualized technical skills should be replaced with measures that reflect what is known about what it means to know and do mathematics, i.e., that capture the degree of acquisition of both conceptual and procedural knowledge and the connections between them, and that assess the solving of worthwhile problems, the communication and justification of conjecture, and the representation of mathematical thinking in multiple ways (NCTM, 2000). As Ridgeway (1998) 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" (p. 2). The 1989 Standards states, "As the curriculum changes, so must the tests. Tests also must change because they are one way of communicating what is important for students to know.... In this way tests can effect change" (pp. 189, 190). Both the Assessment Standards (NCTM, 1995) and the Principles and Standards (NCTM, 2000) state that assessment tasks communicate what type of mathematical knowledge and performance are valued (p. 22). Therefore, standards-based assessment complements standards-based instruction (Dunbar & Witt, 1993).
Paralleling reform in mathematics curriculum and instruction have been calls to authenticate student assessment in all subject areas. Terms such as "Authentic Assessment," "Alternative Assessment," and "Performance Assessment" have become banners to rally focused efforts to change paradigms about the nature and purpose of assessment. According to McMillan (2004), a performance assessment is "... one in which the teacher observes and makes a judgment about the student's demonstration of a skill or competency in creating a product, constructing a response, or making a presentation. They possess several important characteristics:
1. Students perform, create, construct, or produce something
2. Deep understanding and/or reasoning skills are assessed.
3. They involve sustained work.
4. They call on students to explain, justify, and defend.
5. Performance is directly observable.
6. They involve engaging ideas of importance and substance.
7. There is a reliance on trained assessor's judgments for scoring.
8. Multiple criteria and standards are pre-specified and public. …