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Measuring Up: Prototypes for Mathematics Assessment (1993) Mathematical Sciences Education Board (MSEB)

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. "The Standards." Measuring Up: Prototypes for Mathematics Assessment. Washington, DC: The National Academies Press, 1993.

 Page 16

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Measuring Up: Prototypes for Mathematics Assessment

additional steps required to turn these outlines into fully detailed scoring rubrics and to refine the levels of response to each task.

One important purpose of creating a scoring rubric is to communicate to the students exactly what is expected of them. Embedded in our assumption that the students have had an exemplary mathematics education is an implication that appropriate standards have already been communicated to the students. Thus, for example, when a protorubric mentions a "clear explanation" or an "appropriate drawing," it is assumed that the children and the assessor share a common understanding of what these terms mean.

Another purpose to is to help the teacher interpret students' responses by specifying or clarifying the mathematical essence of the task — which aspects of the task are critical mathematically and which are not. These clarifications will be improved as tasks such as these are tested with larger numbers of students, particularly with those who have studied in a Standards-based curriculum.

The Standards

Are we measuring the right things?

Since this entire project has been undertaken in a context of mathematics education reform, an important question that naturally arises is the extent to which these prototypes reflect the spirit of the NCTM's Curriculum and Evaluation Standards for School Mathematics. Figure 1 suggests how these particular tasks relate to the content that the Standards calls for in grades K-4.

Having constructed this figure, we must emphasize how potentially dangerous such tables can be because they promote a "check-off" approach that conflicts with a truly integrated view of mathematics. Each "x" within the body of the table is merely shorthand for a detailed account of how the particular task exemplifies, or illustrates, or even extends the ideas within that particular standard.

In some cases, the "x" means only that the idea is possibly, but not necessarily, involved in the task. For example, an "x"

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 Front Matter (R1-R10) Introduction (1-3) The Challenge (4-4) The Criteria (5-6) The Caveats (7-7) The Audience (8-8) The Prototypes (9-11) The Tryouts (12-12) The Format (13-13) The Protorubrics (14-15) The Standards (16-18) The Future (19-20) The Prototypes (21-22) Mystery Graphs (23-30) The Checkers Tournament (31-42) Bridges (43-52) Hexarights (53-64) Bowl-A-Fact (65-74) Point of View (75-84) The Quilt Designer (85-94) How Many Buttons? (95-100) The Taxman (101-114) Lightning Strikes Again (115-124) Comparing Grizzly Bears and Black Bears (125-132) The Towers Problem (133-140) The Hog Game (141-156) Resources (157-160) Mathematical Sciences Education Board (161-164) Credits (165-166)

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