The task development experience that underpins both the model for balanced assessment in Chapter 2 and the discussion of opportunity-to-perform issues in Chapter 3 was not conducted behind the closed doors of assessment designers' offices. Instead, much of this experience has been obtained in mathematics classrooms across the country, because each assessment task is put through several rounds of systematic classroom trials, including initial task trials implemented in two or three mathematics classrooms, and also large-scale field tests where the tasks are put through trials with a large stratified sample of students.

Each classroom trial is observed by at least one of the following:

  • a full-time assessment developer,

  • a full-time mathematics teacher who is participating as a co-developer in the assessment development process,

  • a classroom teacher who is responsible for providing written evaluations of the task in action, or

  • a teacher who is participating in a professional development program focusing on assessment.

This chapter draws upon this extensive body of classroom-generated experience to present a series of recommendations and conclusions based on observations of assessment tasks in the social context of the classroom. Many of the sections of this chapter highlight barriers to opportunity to learn, such as tight sequencing of teaching and testing, inappropriate emphasis on skills acquisition activities, inappropriate task modification, the need to cover the curriculum, preconceptions of teachers, and gaps in the curriculum. Each of these discussions is framed by locating it within the context of relevant and recent research. Where appropriate, larger implications for the teaching and learning of mathematics are identified. Other sections discuss how complex tasks may be used to enhance learning opportunities in the classroom. While working through such a task, for example, misconceptions and mistakes may be viewed as opportunities to learn rather than as complications to be avoided. Furthermore, class work on complex tasks is necessary to develop problem-solving tenacity and the ability to communicate about mathematics. The purpose of this chapter is to identify how efforts to improve assessment might be used to improve mathematics instruction and learning. Therefore, the primary concern in this chapter is not just finding better ways to assess students but finding ways to enable students to perform better on worthwhile assessments. The chapter closes with a list of recommendations based upon these issues and informed by Black and Wiliam's (1998) contention that learning is driven by what teachers do in classrooms.



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