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OCR for page 247
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BACKGROUND PAPER FOR THE CONVOCATION
What Is Bth Oracle Mathematics: A Look from NAEP
John Dossey
Mathematics Department, Illinois State University
One of the few sources that math-
ematics educators, or policy makers,
have upon which to base judgments
about Sth grade is the data from the
National Assessment of Educational
Progress in Mathematics (NAEP). This
federal large-scale assessment has been
collecting data about the mathematical
experiences of the eight graders (or 13-
year olds), as well as data on fourth
graders (or 9-year-olds) and twelfth-
graders (or 17-year olds), since 1973.
These random samples of the nation's
students at these grade/age levels are
taken to provide a picture of the status
of mathematics education at critical
junctures in their schooling.
The national NAEP assessment, has
been given in 1973, 197S, 1983, 1986,
1990, 1992, and 1996. There is a NAEP
Trend assessment that employs forms
of the 1973 examination to provide a
trend knowledge relative to basic skills
and knowledge in school mathematics
over time since 1973. This test was
given in the same years as NAEP, as
well as in 1994.
ACHIEVEMENT RESULTS
National NAEP Achievement
Results
What kind of picture do the results of
these assessments paint? First, they
show that our eighth grade students
have ma(le consistent progress over
time in mathematics. The achievement
trend on national NAEP is split into two
sections, as the nature of the NAEP
assessment was change(1 in 1990 by the
National Assessment Governing Board
to renect more open-en(le(1 problem
solving anti to narrow the number of
(lifferent content areas in mathematics
that were to be assessed. Since that
time, the assessment has focused on
student work in Number anti Opera-
tions, Measurement, Geometry, Alge-
bra, anti Data Analysis/Statistics/
OCR for page 248
Probability. The mean student scores
on the NAEP assessment from 1978
through 1986 were developed on ran-
dom samples of the nation's 9-, 13-, and
17-year olds. The results for 13-year-
olds showed a consistent picture, with
improvement for students in the last two
assessments given under the framework
(I)ossey, Mullis, I~in(lquist, & Cham-
bers, 19881. The scores for these
assessments are shown in Table 1.
Table 2 shows the scores for the new
NAEP scale for Sth graders initiated in
1990 with the first assessment to be
given under the new NAEP framework.
Note that the scores shown in Table
should not be compared with those
Table ~ . NAEP Trencl Scores for ~ 3-year-olcls for
National NAEP: ~ 973-] 986
Assessment Year
National Mean
1 973 1 978 1 983 1 986
266 26A 269*t 269*t
*t indicates that the score is significantly greater than the score in
1978 at the 0.05 level.
Table 2. NAEP Trencl Scores for ~ 3-year-olcls for
National NAEP: ~ 990-] 996
Assessment Year
National Mean
1990 1992
263 268*
1996
272*t
* indicates that the score is significantly greater than the score in
1990.
*t indicates that the score is significantly greater than the score in
1992.
APPE N DIX 6
shown in Table 2 as they are from two
different scales, representing different
content and different formats of exami-
nations. These results show a steady
and consistent improvement from 1990
through 1996.
An analysis of the scores in Table 2
indicate a strong and significant in-
crease in scores over the six year period
of time. Comparing the increases to the
benchmark of 10 NAEP score scale
points equals one gra(le-placement level
of progress, the (lata suggest that the
nation's eighth gra(lers' achievement
has increase(1 essentially one gra(le
placement since 1990! This is an indica-
tion of goo(1 things happening in the
school classroom (Reese, Miller,
Mazzeo, & Dossey, 19971.
NAEP TREND ASSESSMENT
RESULTS
One might look at the above results
anti have a feeling that the improve-
ment in achievement is really only
since 1990, as there was a dip in 1978 in
the (lata anti that we essentially ma(le
up in 1983 and 1986. Besides this.
critics of school reform anti change in
mathematics education might also
in(licate concern over the change
nature of the test anti fee} that the
"basics" have been left out of the new
NAEP assessment starting in 1990
OCR for page 249
Table 3. NAEP Trencl Assessment Scores for] 3-year-olcls for Trencl NAEP: ~ 973-] 996
Assessment Year 1973 1978 1983 1986 1990 1992 199A 1996
National Mean 266 26A 269 269 270*t 273*t 27~*t 27~*t
*I indicates that the score is significantly greater than the score in 1973 at the 0.05 level.
since it has been somewhat loosely
based on the NCTM Standards.
It was just this concern that the
Department of Education and NAGB
had in deciding at the inception of
NAEP to continually give the 1973
examination to random samples of 13-
year-olds over time as a measure of
change from a baseline examination.
This examination was, and is, heavily
grounded in paper-and-pencil skills and
knowledge that was considered basic in
1973, a period marked by "back-to-the-
basics" following the New Mathematics
of the 1960s. Table 3 shows student
performance on this examination over
time. Again note, one should not
compare the scale numbers for this
assessment with the previous two, as it
is a third different assessment.
However, the data here, together with
the two previous sets of assessment
data, suggest that the mathematics
achievement, be it on new content, or on
traditional content, is improving over
time (Campbell, VoelkI, & Donahue,
19971. None of the assessment results
suggests that the "baby has been
thrown out with the bathwater" in the
move to reform school mathematics.
BACKGROUND PAPER ON NAEP
OTHER NAEP RESULTS
In addition to the achievement infor-
mation, the National NAEP program
collects information from the students
relative to their beliefs anti (1emographic
backgrounds, from their teachers
relative to their instruction and their
education, and from their schools about
the organization and curriculum of the
school program. These (lata permit the
description of the context in which
these students encounter mathematics
and the resources that they have as they
approach the study of mathematics.
Course Taking
Data from the 1996 NAEP assessment
indicated that 81 percent of the nation's
eighth graders attended a school that
offered the stu(ly of Algebra ~ as an option
in the eighth gra(le curriculum. Further,
the data indicated that 25 percent of the
nation's eighth graders actually enrolled
in Algebra ~ as their eighth grade math-
ematics course. The remaining students
either participated in a classroom where
mathematics was taught from an eighth
grade text from a basal K-S curriculum
series (43°/O), participated in a preaIgebra
OCR for page 250
class (26%), or were in some other form of
mathematics instruction (6%) (Hawkins,
Stancavage, & Dossey, 19981.
Calculator Usage
Data from the 1996 assessment
indicated that 80 percent of the nation's
eighth graders have access to school-
owned calculators. This percentage was
the same whether students were in
Algebra i, preaIgebra, or eighth-gra(le
mathematics. No significant difference
was noted between the performance of
the students having and not having
access to school-owned calculators
(Hawkins, Stancavage, & Dossey, 19981.
Teacher Backgrounds
The teaching of eighth-grade math-
ematics falls between elementary and
secondary preparation in many states, as
few states have a special middle school/
junior high school certification level.
Data from the teachers of the students in
the 1996 NAEP sample indicated that 62%
of these teachers either had degrees in
mathematics (49°/0) or mathematics
education (13%~. The remaining teach-
ers either had degrees in education but
not mathematics or mathematics e(luca-
tion (32%), or had degrees in some other
discipline (7°/01. Analysis of the student
achievement of the students of these four
groups of teachers by collegiate major
in(licate(1 that the students whose teach-
ers hall (1egrees in mathematics outper
APPE N DIX 6
formed the students of teachers whose
degrees were either in education abut not
mathematics education or in another
discipline. The students whose teachers
had degrees in mathematics education
had achievement scores that were not
significantly (lifferent from the achieve-
ment of students whose teachers had
degrees in either mathematics or educa-
tion/other (liscipline (Hawkins,
Stancavage, & Dossey, 19981.
Professional Development arc!
KnowIecIge of the NCTM
StancIarcIs
Eighth-grade teachers reported that
on average 26% of them ha(1 ha(1 less
than 6 hours of professional (levelop-
ment in mathematics during the past
year, 29% had from 6 to 15 hours of
professional development in mathemat-
ics during the past year, and 45% had
over 15 hours of professional develop-
ment in mathematics during the past
year. When one considers that 15 hours
of professional development is less than
two working days' time, one recognizes
that over half of the nation's eighth-
grade students are being taught by
teachers who are receiving precious
little opportunity for growth in their
major teaching field.
Teachers were also asked about the
level of knowledge they felt they had of
the NCTM Curriculum and Evaluation
Standards for School Mathematics
OCR for page 251
(NCTM, 19891. The teachers of 16% of
the students said that they felt they were
very knowledgeable, 32% were knowl-
edgeable,33% somewhat knowledgeable,
and 19% reported having little or no
knowledge of the Standards. Analysis of
the mean achievement scores of students
related to these four groups of teachers
indicated that students of teachers who
reported being knowledgeable or very
knowledgeable of the Standards per-
formed significantly higher than those of
teachers reporting little or no knowledge
of the Standards. However, one is unable
to determine the cause for this difference.
It may be in hiring practices of districts, or
that some districts have more resources,
give more professional development, or
pay higher salaries (Hawkins, Stancavage,
& Dossey, 19981.
Performance in Content Sub-
Areas
When students' achievement work is
examined by content sub-areas, their
performance in each area showed a
significant increase from 1992 to 1996.
The sub-areas and 1996 achievement
scores for each are as follows: Number
Sense, Properties, and Operations
(274), Measurement (270), Geometry
and Spatial Sense (269), Data Analysis/
Statistics/Probability (272), and Algebra
and Functions (2731. Like the results
from TIMSS, the lowest performance
areas were Geometry and Measurement
BACKGROUND PAPER ON NAEP
(Mitchell, Hawkins, Jakwerth,
Stancavage, & Dossey, 19991.
Item Types arc! Special StucIies
The items in the 1996 NAEP were
approximately distributed as follows:
55% multiple choice, 38% short student
constructed answer, and 7% extended
student constructed answer format.
Overall it was expected that students
would have spent about 40% of their
response time working on items that
called for student constructed re-
sponses of one type or another. Results
of the testing showed improvement on
students' abilities to construct answers
to questions in 1996 over prior years.
This was an in(lication that communica-
tion and reasoning are playing greater
roles in classroom assessment pro-
grams across the nation. However,
when one looks at the results of student
performance on extended student
constructed response items, graded by
a 5 point rubric, one sees that there is
still considerable room for improve-
ment, as few students achieved the
highest levels of score on these items.
As part of the 1996 assessment,
eighth-grade students were also given a
block of items where the context for the
block was common, although the actual
items were locally independent that is,
no item's answer depended on the
answer to another item. Student perfor-
mance on these items, including the
OCR for page 252
extended constructed response items
tended to be slightly higher than that on
similar format items in the regular
NAEP. This may indicate that the
changing of contexts within regular
NAEP from item to item may slightly
suppress student performance levels, or
alternatively, maintaining a context
helps students develop a positive focus
(Hawkins, Mitchell, Stancavage, &
Dossey, in press).
Summary
While this is but a brief overview of
teh eighth-grade results Tom 1996
NAEP, these data and results provide a
gestalt for the context and nature of
eighth-grade students' achievement
patterns at present. A thorough reading
of the NAEP reports wait provide an
even more complete picture of eighth-
grade mathematics in the United States
today.
APPE N DIX 6
References
Campbell, I.R, Voelkl, K.E., & Donahue, P.L
(1997~. NAEP 1996 Trends in Academic
Progress. Washington, DC: National Center for
Education Statistics.
Dossey, J.A., Mullis, I.V.S., Lindquist, M.M., &
Chambers, D.L. (1988~. The Mathematics
Report Card: Are We Measuring Up?
Princeton, NI: Educational Testing Service.
Hawkins, E.F., Mitchell, J.H., Stancavage, F.B., &
Dossey, J.A. (in press). Focused Studies in the
NAEP 1996 Mathematics Assessment: Findings
from the National Assessment of Educational
Progress. Washington, DC: National Center for
Education Statistics.
Hawkins, E.F., Stancavage, F.B., & Dossey, J.A.
(1998~. School Policies and Practices Affecting
Instruction in Mathematics: Findings from the
National Assessment of Ed ?Y cational Progress.
Washington, DC: National Center for Educa-
tion Statistics.
Mitchell, J.H., Hawkins, E.F., Jakwerth, P.M.,
Stancavage, F.B., & Dossey, J.A. (1999~.
Staidest Work and Teacher Practices in Math-
ematics. Washington, DC: National Center for
Education Statistics.
Nationa Council of Teachers of Mathematics.
(1989~. Cavrric?`l?`m and Evaluation Standards
for School Mathematics. Reston, VA Author.
Reese, C.M., Miller, KE., Mazzeo, J., & Dossey,
I.A. (1997~. NAEP 1996 Mathematics Report
Card for the Nation and the States. Washing-
ton, DC: National Center for Education
Statistics.
Representative terms from entire chapter:
naep assessment
