ERIC ED377073: Mathematics Assessment and Evaluation: Imperatives for Mathematics Educators.

378 Pages·1992·4.5 MB·English

by  ERIC

DOCUMENT RESUME
ED 377 073
SE 055 578
AUTHOR
Romberg, Thomas A., Ed.
TITLE
Mathematics Assessment and Evaluation: Imperatives
for Mathematics Educators.
SPONS AGENCY
Office of Educational Research and Improvement (ED),
Washington, DC.; Wisconsin Center for Education
Research, Madison.
REPORT NO
ISBN-0-7914-0900-7
PUB DATE
92
CONTRACT
R117G10002
NOTE
378p.
AVAILABLE FROM
State University of New York Press, State University
Plaza, Albany, NY 12246 (paperback:
ISBN-0-7914-0900-7; clothbound:
ISBN-0-7914-0899-X).
PUB TYPE
Books (010)
Viewpoints (Opinion/Position Papers,
Essays, etc.)
(120)
EDRS PRICE
MFO1 /PC16 Plus Postage.
DESCRIPTORS
*Calculators; Criticism; Educational Assessment;
Elementary Secondary Education; *Evaluation Methods;
Mathematics Achievement; Mathematics Education;
*Mathematics Tests; *Sex Differences; State Programs;
*Student Evaluation; Testing
IDENTIFIERS
*Alternative Assessment; NCTM Curriculum and
Evaluation Standards; Reform Efforts; *State
Mathematics Assessments
ABSTRACT
This books contains papers written on issues related
to externally mandated mathematics tests and their influence
on
school mathematics. Chapter 1 presents an overview of the book,
including brief abstracts of each chapter. Chapter 2 presents
a
summary of the overall problems associated with the need for valid
information. Remaining chapte...-s include: (3) Implications of the
National Council of Teachers of Mathematics (NCTM) Standards
for
Mathematics Assessment (Norman Webb & Thomas A. Romberg);
(4)
Curriculum and Test Alignment (Thomas A. Romberg, and others);
(5)
State Assessment Test Development Procedures (James Braswell);
(6)
Test Development Profile of a State-Mariated Large-Scale Assessment
Instrument in Mathematics (Tej Pandey);
(7) Assessing Students'
Learning in Courses Using Graphics Tools: A Preliminary Research
Agenda (Sharon L. Senk); (8) Mathematics Testing with Calculators;
Ransoming the Hostages (John G. Harvey);
(9) Gender Differences in
Test Taking: A Review (Margaret R. Meyer); (10) Communication and
the
Learning of Mathematics (David Clarke, and others);
(11) Measuring
Levels of Mathematical Understanding (Mark Wilson);
(12) A Framework
for the California Assessment Program to Report Students' Achievement
in Mathematics (E. Anne Zarinnia & Thomas A. Romberg); (13)
Evaluation--S.me Other Perspectives (Phillip C. Clarkson).
A
reference list organized by chapter contains 300 citations.
Appendices include the NCTM Evaluation Standards,
a classification
matrix, illustrative questions, history and rationale for
student
mathematics journals, SMP Project student log sample
pages, and the
report of Vermoner Mathematics Portfolio Assessment Program.
(MKR)
.1
U' ".."
I.
MATHEMATICS ASSESSMENT
AND
EVALUATION
3
K
SUNY Series. Reform in Mathematics Education
Judith Sowder, editor
The preparation of this book was supported by the Office for
Educational Research and Improvement, United States Depart-
ment of Education (Grant Number R117G10002) and by the
Wisconsin Center for Education Research, School of Education.
University of Wisconsin-Madison. The opinions expressed in
this publication do not necessarily reflect the views of the Of-
fice of Educational Research and Improvement or the Wiscon-
sin Center for Education Research.
4
MATHEMATICS ASSESSMENT
AND
EVALUATION
Imperatives for Mathematics Educators
Edited by
Thomas A. Romberg
STATE UNIVERSITY OE NEW YORK PRESS
5
Published by
State Univesity of New York Press, Albany
© 1992 State University cf New York
All rights reserved
Printed in the United States of America
No part of this book may be used or reproduced
in any mariner whatsoever without written permission
except in the case of brief quotations embodied in
critical articles and reviews.
For information, address the State University of New York Press,
State University Plaza, Albany, NY 12246
Production by Christine M. Lynch
Marketing by Fran Keneston
Library of Congress Cataloging-in-Publication Data
Mathematics assessment and evaluation
: imperatives for
mathematics educators / edited by Thomas A. Romberg
(SUNY series, reform in mathematics
cm.
p.
education)
Includes bibliographical references and index.
ISBN 0-7914-0899-X (CH : acid-free).
ISBN 0 -7914-
0900 -7 (PB : acid-free)
1. Mathematical abilityTesting. 2. Mathematics
Study and teachingUnited States. I. Romberg, Thomas
A. II. Series. 510'.71dc20
91-11157
CIP
5 4 3 2
10 9 8 7
6
1
CONTENTS
Overview of the Book
1.
Thomas A. Romberg
1
Evaluation: A Coat of Many Colors
2.
Thomas A. Romberg
10
Implications of the NCTM Standards for
3.
Mathematics Assessment
Norman Webb and Thomas A. Romberg
37
Curriculum and Test Alignment
4.
Thomas A. Romberg, Linda Wilson,
'Mamphono Khaketla, and Silvia Chavarria
61
State Assessment Test Development Procedures
5.
James Braswell
75
Test Development Profile of a State-Mandated
6.
Large-Scale Assessment Instrument in
Mathematics
Tej Pandey
100
Assessing Students' Learning in Courses
7.
Using Graphics Tools: A Preliminary
Research Agenda
Sharon L. Senk
128
Mathematics Testing with Calculators:
8.
Ransoming the Hostages
John G. Harvey
139
7
Gender Differences in Test Taking: A Review
9.
Margaret R. Meyer
169
Communication and the Learning
10.
of Mathematics
David Clarke, Max Stephens, and
184
Andrew Waywood
Measuring Levels of Mathematical
11.
Understanding
213
Mark Wilson
A Framework for the California
12.
Assessment Program to Report Students'
Achievement in Mathematics
242
E. Anne Zarinnia and Thomas A. Romberg
EvaluationSome Other Perspectives
13.
285
Philip C. Clarkson
301
Appendices
335
References
356
Contributors
357
Index
1
Overview of the Book
Thomas A. Romberg
The purpose of this book Is to share with mathematics educa-
tors a set of recent papers written on issues surrounding math-
ematics tests and their influence on school mathematics. The
impetus for the contributions grew from a conference, The
Influence of Testing on Mathematics Education," sponsored by
the Mathematical Sciences Education Board (MSEB) at UCLA
in June 1986. The purpose of the conference was to gather
informed input and advice on current testing practices. The
fact is that students in American schools are subjected to a
variety of tests, often standardized tests, from kindergarten to
graduate school. Such tests are, according to widely held per-
ception, inhibitors to change and improvement in education
and especially in mathematics education. Since MSEB was or-
;anized to coordinate the current reform movement in school
mathematics, the topic of the conference was deemed critical.
Two things became clear at the UCLA meeting: First, there
was agreement that tests need to change to reflect curriculum
changes, and second, many participants articulated their
beliefs about the inadequacy of current tests and provided rel-
evant anecdotes on problems to others at the conference. How-
ever, no one was sure how such changes could be accom-
plished, nor did participants even have substantive, reliable
information about the actual impact of testing on classroom
practices.
1
9
Mathematics Assessment and Evaluation
2
Following the conference, a three-person Testing Design Task
Force, consisting of Jeremy Kilpatrick, Tej Pandey, and Thomas
Romberg, was organized by MSEB. In September 1986, this
task force produced ''A Proposal for Studies of Mathematics
Tests and Testing" based on the following four assumptions:
Valid information about student mathematics is needed
by a variety of people (students, teachers, parents,
administrators, policy makers) for a variety of pur-
poses (monitoring progress, selection for and place-
ment in courses, program evaluation, accountability).
Both the curriculum and teaching practice in math-
ematics need to be directed toward strategies which
students could use to solve problems, the application
of mathematics to practical situations, and the devel-
opment of thinking skills. Consequently, testing should
reflect students' achievement in these directions.
Serious questions have arisen about the validity of
existing tests for the uses to which they are being
put. Standardized tests and state-mandated tests may
yield information that is invalid for certain purposes
and provide little or no information on several impor-
tant dimensions of achievement.
The continued use of existing tests appears likely to
impede the much-needed reform in curriculum and
instruction to which the mathematics education com-
munity is committed.
On the basis of these assumptions, a set of questions and
research studies was proposed. In particular, several literature
reviews were planned, each of which would explore one facet of
the validity of mathematics tests for various purposes. Topics
were to include surveys of testing practice, the alignment of
tests with curricula, test-preparation practices and effects, test-
taking skills, the student use of calculators during test taking,
teacher and student attitudes toward tests, time spent in test-
ing, alternatives to testing, and minority group and gender
group differences in risk taking and test performance.
In 1987, when the Wisconsin Center for Education Research
was awarded the grant to form the National Center for Re-
10