certain ideas from algebra and discrete mathematics are indeed appropriate in the lower grades.

The third, proof, appears in several of the tasks. Even in fourth grade, children should be given opportunities to formulate simple but convincing arguments. Statements that begin like these:

Johann could not *possibly* have gotten a 6 because. …

There are *exactly* eight different three-block towers that can be made from two colors because. …

You *can't* make a hexaright with an area of 36 cm^{2} and a perimeter of 24 cm because. …

can be completed in ways that amount to informal proofs.

These prototypes reveal just one aspect of the unfolding picture of reform in mathematics assessment. Both the NCTM and the MSEB are currently engaged in further efforts to promote standards-based assessment. NCTM is preparing assessment standards to complement earlier standards for curriculum and instruction. MSEB, in a parallel effort, is examining measurement and policy issues involved in various forms of assessment. In addition, advances in mathematics assessment are being made in many states across the nation.

The messages conveyed by the prototypes in *Measuring Up* are consonant with the national goal of standards-based educational reform. In no way, however, do these prototypes provide definitive answers to the very deep and difficult issues surrounding assessment in mathematics education. The goal of *Measuring Up* is more modest: to further reform by providing rich examples that can be discussed and debated, refined, and improved. Through these prototypes we can glimpse the future of assessment in America.

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OCR for page 19

Measuring Up: Prototypes for Mathematics Assessment
certain ideas from algebra and discrete mathematics are indeed appropriate in the lower grades.
The third, proof, appears in several of the tasks. Even in fourth grade, children should be given opportunities to formulate simple but convincing arguments. Statements that begin like these:
Johann could not possibly have gotten a 6 because. …
There are exactly eight different three-block towers that can be made from two colors because. …
You can't make a hexaright with an area of 36 cm2 and a perimeter of 24 cm because. …
can be completed in ways that amount to informal proofs.
The Future
Where do we go from here?
These prototypes reveal just one aspect of the unfolding picture of reform in mathematics assessment. Both the NCTM and the MSEB are currently engaged in further efforts to promote standards-based assessment. NCTM is preparing assessment standards to complement earlier standards for curriculum and instruction. MSEB, in a parallel effort, is examining measurement and policy issues involved in various forms of assessment. In addition, advances in mathematics assessment are being made in many states across the nation.
The messages conveyed by the prototypes in Measuring Up are consonant with the national goal of standards-based educational reform. In no way, however, do these prototypes provide definitive answers to the very deep and difficult issues surrounding assessment in mathematics education. The goal of Measuring Up is more modest: to further reform by providing rich examples that can be discussed and debated, refined, and improved. Through these prototypes we can glimpse the future of assessment in America.

OCR for page 19

Measuring Up: Prototypes for Mathematics Assessment
This page in the original is blank.