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Measuring Up: Prototypes for Mathematics Assessment example, the type of assessment exercises that would be appropriate to measure our nation's progress toward the goals of mathematics education. To create the prototypes, the MSEB subsequently convened a small writing group of mathematics educators, teachers, and mathematicians. Taking up Governor Romer's challenge, the writing group created a sampler of tasks to encompass many of the goals for mathematics instruction that are expressed in the NCTM Standards. These tasks, which illustrate what a standards-based education really means, have been pilot tested on a limited basis in four states. Many have been revised, often more than once, but all can benefit from continued improvement and adaptations. Readers who skip ahead will see that these prototypes are not only innovative and challenging but also just plain fun. Teachers, children, and even parents should find these tasks both engaging and surprising. We invite readers to try them, either before or after reading the surrounding analysis. The Criteria What we are trying to do Not surprisingly, the MSEB writing group debated extensively the criteria for prototypical assessment tasks. They faced the pioneer's challenge — to use incomplete information as a basis for decisions whose consequences are difficult to foresee. From these discussions emerged several criteria that helped shape the nature and selection of prototypes in this volume: Mathematical content: The tasks should reflect the ''spirit" of the reform movement, but not necessarily be limited by particular curricular content, present or planned. Many of the tasks should incorporate a variety of mathematics, particularly in areas such as statistics, geometry, and probability that are least often emphasized in traditional K-4 programs. Mathematical connections: Everyone involved in the mathematics reform movement, from classroom teach-
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Measuring Up: Prototypes for Mathematics Assessment ers to national policy makers, agrees on the importance of connecting mathematics — to science, to social science, to art, to everyday life, and to other parts of mathematics. Accordingly, the prototypes should develop links with science, with the visual arts, and with the language arts. Thoughtful approaches: Insofar as possible, the tasks should promote "higher-order" thinking. Just as the verbs explore, justify, represent, solve, construct, discuss, use, investigate, describe, develop, and predict are used in the Standards to convey "active physical and mental involvement of children" in learning mathematics, they are appropriate to seek in assessment activities as well. Further, given a choice between cognitive complexity and simplicity, the focus of these tasks should be on the former. Mathematical communication: The tasks should emphasize the importance of communicating results — not simply isolated answers, but mathematical representations and chains of reasoning. Children should have opportunities to work in groups to explain their thinking to others, and to write explanations of their approaches. Rich opportunities: The tasks should let children solve problems via a variety of creative strategies; demonstrate talents (artistic, spatial, verbal) beyond those normally associated with numerical mathematics; invent mathematics that (to them) is new; recognize opportunities to use and apply mathematics; and show what they can do (as opposed to what they cannot do). Improved instruction: The tasks should have the potential for influencing instruction positively, both in content and in pedagogy. Teachers who use these tasks should become better teachers as a result of the experience; children who participate should emerge with increased self-confidence and heightened expectations for future mathematics courses.
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