School Policies and Practices Affecting
Instruction in Mathematics:
Findings from the
National Assessment of Educational Progress

August 1998

Authors: Evelyn F. Hawkins and Frances B. Stancavage (American
Institutes for Research), and
John A. Dossey (Illinois State University)

Introduction

The teaching and learning of mathematics in our nation's schools
continue to generate tremendous attention, both among those who
support recent innovations and, more recently, among those who
question the wisdom of the promulgated reforms. [1] In order to
bring an empirical basis to this debate, it is important to gather
information on the policies and practices that are actually being
implemented, and this report provides one source for such
information. Written for policy makers and school administrators,
this report is the second of a series that discusses results from
the National Assessment of Educational Progress (NAEP) 1996
mathematics assessment.

This report describes the educational policies and practices that
prevailed during this period of sustained increases in mathematics
achievement, with particular attention to the relationship between
these policies and practices and student performance on the NAEP
mathematics assessment. More specifically, this report provides
information on the status of mathematics education in 1996 and
chronicles the changes that had taken place from the time of earlier
NAEP assessments...

This report is organized around three central questions:

• Who is teaching mathematics to our students?
• What emphasis does mathematics instruction receive?
• What are the resources in schools that support mathematics
  learning?

MAJOR FINDINGS

The major findings reported below include information about the
status of teachers and mathematics instruction in our nation's
schools as well as the relationships between student achievement in
mathematics and teacher characteristics and school policies and
practices in mathematics education. In general, we have highlighted
positive relationships. However, the reader should keep in mind the
limitations of survey data of the kind collected by NAEP.
Statistically significant associations between particular policies
or practices and achievement can provide an interesting starting
point for analysis or deliberation, but they cannot demonstrate a
causal relationship. Additionally, the lack of significant changes
or relationships to achievement with respect to variables reported
from the NAEP survey is not necessarily evidence that our nation has
remained static with regard to reforming policies and practices that
positively impact mathematics education. Perhaps an appropriate
conclusion from this report is that factors that impact teaching and
learning of mathematics in our nation's classrooms rarely, if ever,
work in isolation. The following are major findings from this
report.

Who is teaching mathematics to our students?

* Teachers of the large majority of fourth-grade students (83
percent) had college majors in education rather than
mathematics or mathematics education, while teachers of over
half of eighth-grade students had majors in mathematics or
mathematics education.

* Teachers' college majors appear to have some relationship to
students' mathematics performance; however, there are grade-
level differences. At grade 4, students whose teachers had a
college major in mathematics education or education
outperformed those students whose teachers had a major in a
field other than education, mathematics education, or
mathematics. At grade 8, it was the students of teachers with
a college major in mathematics who outperformed students
whose teachers had a college major in education or a field
other than education, mathematics education, or mathematics.

* Thirteen percent of fourth-grade students were being taught
mathematics by a teacher with a college major in mathematics
or mathematics education. However, nearly one-third of
fourth-grade students were being taught by teachers who had a
mathematics teaching certificate. This pattern was also
evident at the eighth-grade level: 62 percent had teachers
with a college major in mathematics or mathematics education;
81 percent of eighth-grade students had teachers with a
mathematics teaching certificate.

* Eighth-grade students whose teachers had a teaching
certificate in mathematics performed better than other
eighth-grade students.

* While teachers of fourth- and eighth-grade mathematics span
the range of years of mathematics teaching experience,
students taught mathematics by teachers with more than five
years of teaching experience were more likely to perform
better on the NAEP mathematics assessment than students
taught by teachers with five or fewer years of experience.

* Eighth-grade teachers appear to participate in more hours of
professional development in mathematics or mathematics
education than fourth-grade teachers, but the level of hours
of professional development was not related to students'
performance in mathematics at either grade level.

* Teachers of eighth-grade students reported having more
knowledge of NCTM curriculum and evaluation standards than
teachers of fourth-grade students.

* The more knowledge eighth-grade teachers reported of NCTM
curriculum and evaluation standards, the higher their
students' performance tended to be on the NAEP mathematics
assessment.

* Eighth-grade students enrolled in different mathematics
courses -- eighth-grade mathematics, pre-algebra, or algebra
-- appear to have had similar access to resources and
opportunities to learn as evidenced by the teacher factors
examined in this report.

What emphasis does mathematics instruction receive?

* In 1996, 54 percent of our nation's twelfth-grade students
were attending schools that required three or more years of
mathematics in grades 9-12 for high school graduation.

* High school graduation requirements in mathematics appear to
be related to student course-taking. Specifically, in schools
that required three or more years, the percentage of students
who reported having taken geometry was significantly higher
than the percentage of students in schools that required two
or fewer years (85 percent compared to 76 percent).

* Between 1990 and 1996, the percentage of eighth-grade
students attending schools that offered algebra for high
school credit or placement at that grade level remained
stable (76-80 percent). In 1996, 28 percent of the students
in such schools reported being enrolled in algebra. [6]

* Fourth-grade students were likely to receive more hours of
mathematics instruction per week than eighth-grade students.
In 1996, teachers of 68 percent of fourth-grade students
reported that they spent 4 or more hours on mathematics
instruction per week, while teachers of 33 percent of eighth-
grade students reported that they spent 4 or more hours of
mathematics instruction per week.

What are the resources in schools that support mathematics learning?

* Teachers of the majority of fourth- and eighth-grade students
reported that they got "most" or "all" of the instructional
materials and other resources they needed to teach their
class. For grade 8, higher levels of resources were found to
be related to higher levels of student performance.

* Many teachers reported that they get "some or none" of the
resources they need to teach their class (i.e., teachers of
34 percent of fourth-grade students and 21 percent of eighth-
grade students).

* Teachers of just less than half of fourth- and eighth-grade
students reported access to a curriculum specialist to help
or advise them in mathematics.

* Substantial proportions of students (71 percent of fourth-
grade students and 88 percent of eighth-grade students) were
being taught mathematics by teachers who reported having 3 or
more hours per week of designated preparation time.

* Students' access to calculators to do schoolwork increased
from 1992 to 1996. The percentage of fourth-grade students
whose teachers reported that their students had access to
school-owned calculators to do schoolwork increased from 59
percent in 1992 to 84 percent in 1996. Correspondingly, the
percentage of twelfth-grade students taking mathematics who
reported having access to calculators increased from 92
percent in 1992 to 95 percent in 1996. Data were not
available for eighth-grade students in 1992, but the reported
percentage with access was 80 percent in 1996.