These prototypes, which are tasks to be done in time spans ranging from one to three class periods, represent only one of many important forms of assessment. Other forms of assessment are essential for a balanced program, including projects (extended pieces of mathematical investigation designed to take a substantial block of time), portfolios (structured collections of student work gathered over a long time period), and tests (time-limited responses to shorter tasks). Some of the references at the end of this volume (e.g., Pandey [1991]; Stenmark [1989]) describe these alternative approaches.
The Audience
Whom we are trying to reach
Many readers of Measuring Up will be persons who are professionally concerned with mathematics education, particularly developers of tests and other assessment instruments. For such people, both those who work within commercial test development companies as well as those in educational settings at the state or local levels, Measuring Up should stimulate development of new approaches to assessment that reflect the broad goals of the nation's standards for mathematics education.
If mandated assessments evolve to resemble more closely the ones suggested in this book, it is clear that different approaches to instruction and testing will be needed. Hence school administrators and educational policy makers will also be affected by the changes implicit in these prototypes. The tasks will convey to the audience of policy makers and education leaders what mathematics educators mean by assessment reform.
A third audience for Measuring Up consists of classroom teachers, and not just those at the fourth-grade level. It is only natural that many practicing elementary school teachers may find some of these tasks to be somewhat daunting, especially if their students have not had the mathematical preparation that the tasks assume. Teachers should look at the prototypes not as current expectations, but rather as goals to aim for. The prototypes can be viewed both as examples of what tomorrow's assessment in
