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Measuring Up: Prototypes for Mathematics Assessment
Too often test questions and assessment tasks are presented solely in written form, which may be a burden for poor readers and for children whose first language is not English. Such children might not be able to respond to the tasks in a way that shows their true level of mathematical knowledge or skills. Many alternative presentations are possible: videotaped introduction; teacher-taught introduction; computer-based presentation; and presentation using manipulative materials. The prototypes illustrate each of these alternative modes of presentation, and two of the tasks are written in Spanish as well as in English.
Notwithstanding the possible variety in presentation, the prototypes in Measuring Up adhere to a certain uniformity of structure. Most are organized as a sequence of questions, often of increasing difficulty. On the one hand, this provides a structure around which the child's problem solving must be organized. On the other hand, this sequence of questions may suggest that the problem-poser, rather than the problem-solver, is in charge of the problem-solving process. Although other forms of organization are certainly possible, these prototypes provide sufficient imposed structure to help the mathematically less sophisticated student get started and show what he or she can do, while allowing plenty of open-ended space at the top to challenge the more advanced student. Even though the questions within a task often grow in difficulty, many of the tasks involve problem solving, reasoning, and communication right from the beginning. These are important aspects of mathematics for all children.
Just as the tasks are presented in several formats, so they are also designed to give children a chance to respond in a variety of modes — perhaps by constructing an object or by creating a pattern on a computer screen. One important response mode