In several cases the problems suggested here for fourth grade could also be asked in the eighth or even the twelfth grade, although naturally the expected sophistication and completeness of the responses would be very different. If a mathematical task is genuinely interesting and worthwhile for fourth graders, there is no reason why it should not be worthwhile for older children, or even for adults.

The Tryouts

What we learned from children

Each prototype was tested on several score fourth-grade students in a number of different locales. These "tryouts" were not designed to be either representative or comprehensive, but to aid in improving the tasks. This they did, but they did much more as well. By observing how students react to the prototypes, we learned much about the gulf that separates current students from the goals of the Standards. We also learned that we are novices on how these new forms of assessment will work in the classroom.

Three examples can illustrate the types of surprises that all teachers will encounter as they begin to explore and extend these prototypes:

  • In a few cases the tasks as originally presented seemed not to be sufficiently challenging. One example is the "Lightning" task in which a fairly large proportion of the students could easily handle the map-reading requirements. So a question dealing with locating a lightning bolt that is a given distance from two observers was added.

  • Sometimes a proposed task yielded no information of any interest at all. In "Bridges," there was originally a more open-ended question in which students were to create their own bridges. Nobody created anything that went even a little bit beyond the two-support, single-span examples. This may have been due to the wording of the question, to the backgrounds of the particular students, or to some other factor. This lack of inventiveness and perseverance is something worth pursuing since creativity is



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Measuring Up: Prototypes for Mathematics Assessment In several cases the problems suggested here for fourth grade could also be asked in the eighth or even the twelfth grade, although naturally the expected sophistication and completeness of the responses would be very different. If a mathematical task is genuinely interesting and worthwhile for fourth graders, there is no reason why it should not be worthwhile for older children, or even for adults. The Tryouts What we learned from children Each prototype was tested on several score fourth-grade students in a number of different locales. These "tryouts" were not designed to be either representative or comprehensive, but to aid in improving the tasks. This they did, but they did much more as well. By observing how students react to the prototypes, we learned much about the gulf that separates current students from the goals of the Standards. We also learned that we are novices on how these new forms of assessment will work in the classroom. Three examples can illustrate the types of surprises that all teachers will encounter as they begin to explore and extend these prototypes: In a few cases the tasks as originally presented seemed not to be sufficiently challenging. One example is the "Lightning" task in which a fairly large proportion of the students could easily handle the map-reading requirements. So a question dealing with locating a lightning bolt that is a given distance from two observers was added. Sometimes a proposed task yielded no information of any interest at all. In "Bridges," there was originally a more open-ended question in which students were to create their own bridges. Nobody created anything that went even a little bit beyond the two-support, single-span examples. This may have been due to the wording of the question, to the backgrounds of the particular students, or to some other factor. This lack of inventiveness and perseverance is something worth pursuing since creativity is