National Academies Press: OpenBook
« Previous: The Challenge
Suggested Citation:"The Criteria." National Research Council. 1993. Measuring Up: Prototypes for Mathematics Assessment. Washington, DC: The National Academies Press. doi: 10.17226/2071.
×

example, the type of assessment exercises that would be appropriate to measure our nation's progress toward the goals of mathematics education.

To create the prototypes, the MSEB subsequently convened a small writing group of mathematics educators, teachers, and mathematicians. Taking up Governor Romer's challenge, the writing group created a sampler of tasks to encompass many of the goals for mathematics instruction that are expressed in the NCTM Standards. These tasks, which illustrate what a standards-based education really means, have been pilot tested on a limited basis in four states. Many have been revised, often more than once, but all can benefit from continued improvement and adaptations.

Readers who skip ahead will see that these prototypes are not only innovative and challenging but also just plain fun. Teachers, children, and even parents should find these tasks both engaging and surprising. We invite readers to try them, either before or after reading the surrounding analysis.

The Criteria

What we are trying to do

Not surprisingly, the MSEB writing group debated extensively the criteria for prototypical assessment tasks. They faced the pioneer's challenge — to use incomplete information as a basis for decisions whose consequences are difficult to foresee. From these discussions emerged several criteria that helped shape the nature and selection of prototypes in this volume:

  • Mathematical content: The tasks should reflect the ''spirit" of the reform movement, but not necessarily be limited by particular curricular content, present or planned. Many of the tasks should incorporate a variety of mathematics, particularly in areas such as statistics, geometry, and probability that are least often emphasized in traditional K-4 programs.

  • Mathematical connections: Everyone involved in the mathematics reform movement, from classroom teach-

Suggested Citation:"The Criteria." National Research Council. 1993. Measuring Up: Prototypes for Mathematics Assessment. Washington, DC: The National Academies Press. doi: 10.17226/2071.
×

ers to national policy makers, agrees on the importance of connecting mathematics — to science, to social science, to art, to everyday life, and to other parts of mathematics. Accordingly, the prototypes should develop links with science, with the visual arts, and with the language arts.

  • Thoughtful approaches: Insofar as possible, the tasks should promote "higher-order" thinking. Just as the verbs explore, justify, represent, solve, construct, discuss, use, investigate, describe, develop, and predict are used in the Standards to convey "active physical and mental involvement of children" in learning mathematics, they are appropriate to seek in assessment activities as well. Further, given a choice between cognitive complexity and simplicity, the focus of these tasks should be on the former.

  • Mathematical communication: The tasks should emphasize the importance of communicating results — not simply isolated answers, but mathematical representations and chains of reasoning. Children should have opportunities to work in groups to explain their thinking to others, and to write explanations of their approaches.

  • Rich opportunities: The tasks should let children solve problems via a variety of creative strategies; demonstrate talents (artistic, spatial, verbal) beyond those normally associated with numerical mathematics; invent mathematics that (to them) is new; recognize opportunities to use and apply mathematics; and show what they can do (as opposed to what they cannot do).

  • Improved instruction: The tasks should have the potential for influencing instruction positively, both in content and in pedagogy. Teachers who use these tasks should become better teachers as a result of the experience; children who participate should emerge with increased self-confidence and heightened expectations for future mathematics courses.

Suggested Citation:"The Criteria." National Research Council. 1993. Measuring Up: Prototypes for Mathematics Assessment. Washington, DC: The National Academies Press. doi: 10.17226/2071.
×
Page 5
Suggested Citation:"The Criteria." National Research Council. 1993. Measuring Up: Prototypes for Mathematics Assessment. Washington, DC: The National Academies Press. doi: 10.17226/2071.
×
Page 6
Next: The Caveats »
Measuring Up: Prototypes for Mathematics Assessment Get This Book
×
Buy Paperback | $45.00
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

Glimpse the future of mathematics assessment in Measuring Up This book features 13 classroom exercises for fourth grade students that demonstrate the dramatic meaning of inquiry, performance, communication, and problem solving as standards for mathematics education.

Policymakers, education leaders, classroom teachers, university-based educators, and parents can learn from the use of these genuine mathematics problems to challenge and prepare students for the future.

single copy, $10.95; 2-9 copies, $8.50 each; 10 or more copies, $6.95 each (no other discounts apply)

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    Switch between the Original Pages, where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

    « Back Next »
  6. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  7. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  8. ×

    View our suggested citation for this chapter.

    « Back Next »
  9. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!