**ERIC Identifier:** ED478348

**Publication Date:** 2003-08-00

**Author: **Howley, Craig B.

**Source: **ERIC Clearinghouse on
Rural Education and Small Schools Charleston WV.

## Mathematics Achievement in Rural Schools. ERIC Digest.

Rural communities need an infrastructure of good mathematics knowledge,
according to some observers. Moses and Cobb (2001), in particular, argue that
mathematical knowledge will, in the new century, figure as a path to political
and cultural power, much as the capacity to read and write served in the 19th
and 20th centuries.

What is the baseline of mathematical knowledge among students in the rural
United States? Poverty in nonmetropolitan areas exceeds that in metropolitan
areas (Jolliffe, 2002), and, for this reason, one might reasonably suspect that
mathematics achievement in rural schools is depressed as compared to the
national average. Is this really the case? This Digest assesses the best
evidence available and concludes with recommendations for further action, based
in part on conclusions reached by a national effort to develop new research
about mathematics education in rural places.

### NAEP REPORTS OF RURAL MATHEMATICS ACHIEVEMENT

In both 1996
and 2000, the National Assessment of Educational Progress (NAEP) mathematics
scores of students in rural and small-town schools exhibited some statistically
nonsignificant negative differences from the national average at all grade
levels tested. Although nonsignificant differences are sometimes interpreted as
harboring practical significance, absent a consistent pattern in the
directionality of such differences (i.e., positive or negative), such inferences
are unwarranted.

Two inferences about NAEP trends do seem warranted, however. First, across 25
years of testing and regardless of locale definition, there has been little
change--increase or decrease--in the mathematics performance of rural students.
Second, with rare exceptions, the recent performance of rural students at all
NAEP grade levels barely differed from the national average (see Howley, 2002,
Table 3). The observed, nonsignificant differences are small, they sometimes
favor rural and small-town schools, and they harbor no practical implications.

### CURRENT RESEARCH ON MATH ACHIEVEMENT IN RURAL AREAS

NAEP
reports consist largely of descriptive data; seldom do they test hypotheses or
develop fine-grained explanations of the accurate descriptions they provide.
Only empirical studies with an explicit base in theory can offer such
explanations. The extant research literature is thin, but three recent
quantitative studies provide a surprisingly comprehensive picture of mathematics
achievement among rural students: Haller, Monk, and Tien (1993); Fan and Chen
(1999); and Lee and McIntire (2000).

Haller and colleagues (1993) examined the 1987-1989 mathematics scores of
10th-grade students on tests administered by the Longitudinal Study of American
Youth (LSAY). The Haller team sought to explain the lack of statistically
significant findings in previous inferential studies (not summarized in this
Digest) as a possible case of inappropriate testing: the result of using
norm-referenced tests with reputedly inauthentic items not deemed to represent
higher-order thinking. Rural schools, after all, offered fewer advanced courses
than other schools, and such a shortcoming might yield deficient higher-order
thinking among graduates of rural schools. The researchers characterized the
LSAY math test as more reflective of higher-order thinking.

Haller and colleagues (1993, p. 71) concluded, "While large schools offer
more advanced courses than do small ones, those offerings appear to have no
influence on average levels of student achievement." In other words, according
to these researchers, a more narrow rural curriculum in mathematics did "not"
depress higher-order mathematics thinking (as measured on the LSAY tests). The
researchers "did" find a positive relationship ("r" =+.38) between proportion of
students enrolled in more advanced courses and achievement levels.1

A problem with the Haller study is that national averages obscure a great
deal of variation--specifically regional and state achievement variation--in
mathematics test scores. State and regional variation require critical analysis
for several reasons. First, the ultimate authority for schooling rests with
states, and management of their school systems can differ sharply. Second,
regions of the nation exhibit sharp differences in economies, cultures,
ethnicities, and the structure of schooling. Third, despite an average
exhibiting parity of mathematics achievement, rural areas exhibit overall
differences from the national norm that are still important to policy and
administration (e.g., differences in school and district size). Without
attention to these sources of variation, educational research cannot inform
improvement efforts. Fortunately, within this small literature, Fan and Chen
(1999) examined the issue of "regional" variation in mathematics achievement,
whereas Lee and McIntire (2000) addressed "state" variation in their study.

Fan and Chen (1999) examined test scores from the National Educational
Longitudinal Survey (NELS:88) data set. Separate analyses were conducted for
8th-, 10th-, and 12th-grade students. These researchers were concerned primarily
to provide a "systematic" test of the hypothesis of rural deficiency. That is,
they were particularly concerned to overcome five methodological shortcomings of
previous studies (i.e., sampling issues; inconsistent definitions of locale; and
the influences of socioeconomic status, ethnicity, and school sector [private
vs. public] as potentially confounding variables). Their analyses were carefully
executed and comparatively sophisticated. The results are very simply stated:
with careful controls in place, no practically significant differences between
mathematics test scores existed by locale (rural, suburban, and urban).2

Lee and McIntire (2000) used NAEP 8th-grade data for 1992 and 1996 to
investigate state-level variability in rural versus nonrural mathematics
achievement, as well as to investigate the potential influences of six
"schooling conditions" on that variability. This study, among the three cited,
is notable for its exclusive consideration of "mathematics" achievement. (The
others had included other subjects as well as mathematics.) This more narrow
focus allowed the researchers to make hypotheses about, and to investigate the
variation in, the conditions of mathematics instruction that might influence
rural mathematics achievement at the state level as well as the national level.

The results were somewhat surprising. For the 1996 comparison, the rural mean
was 276 and the nonrural mean was 268. With standard errors of 1.92 and 1.80,
the implied standard error of the difference (5.26) indicates a statistically
significant difference in 1996, "favoring rural students." The difference, in
fact, equates to a respectable effect size of +.23. This "positive" difference
is equal in magnitude to the largest pre-1986 "negative" difference between
disadvantaged "extreme rural" and the national average (see Howley, 2002, Table
3). The 1992 differences were not statistically different (265 rural, 267
nonrural).

A great deal of variation, however, was evident at the state level. In fact,
in 7 (of 35) states, and contrary to the national average, "nonrural" student
aggregate scores were "higher" than those of rural students (Georgia, Kentucky,
Maryland, North Carolina, South Carolina, Virginia, and West Virginia).

To account for such variation, Lee and McIntire assessed the influence of six
policy-related "schooling conditions" prospectively evident at the state level.
Across the 35 state cases, these six conditions, in regression analysis, account
for an impressive 84% of the variation in state-level, NAEP 8th-grade
mathematics achievement among the rural portions of the respective states'
populations and 69% for the nonrural portions (still high). Focusing on three of
the conditions, the researchers reported

"Rural students" in states where they have access to instructional support,
safe/orderly climate, and collective support [collegiality] tend to perform
better than their counterparts in states where they don't. (emphasis added) (Lee
& McIntire, 2000, p. 171)

The analysis, although comparatively fine-grained, is not sufficient to
generalize the conclusion to future years. Instead, it provides substantial
material to inform hypotheses in subsequent research. In particular, Lee and
McIntire's work strongly suggests that the most interesting and useful work to
be done lies below the national level, and can profitably address issues of
state and local context.

### CONCLUSIONS AND RECOMMENDATIONS

Although the studies
reported here use different definitions of rural, it seems likely that
mathematics achievement in rural and small-town schools has converged with
national averages--whether or not scores are statistically controlled for the
effects of poverty and other influences. Key conclusions from this assessment
follow:

*
Currently, a national rural versus nonrural mathematics achievement gap does not
exist.

*
Currently, neither a national rural versus suburban, nor a national rural versus
urban mathematics achievement gap exists.

*
Currently, at the state level, a rural-nonrural achievement gap exists in 40% of
the states--half favoring rural students.

*
Conditions of schooling account (variably and somewhat hypothetically) for a
large proportion of the variance associated with the rural-nonrural achievement
gap at the state level.

What do these findings "mean?" Do we need to pay any attention at all to
mathematics teaching and learning in rural places?

Skip Kifer (2001) quite rightly advises that comparisons of "variation"
rather than of "averages" constitute the most important work for researchers.
The advice is apt, but to challenge the charge of inferiority (which persists in
the case of rural culture, lifeways, and talents), the study of averages has
practical and theoretical merit. This Digest provides evidence that charges of
rural inferiority in comparison to national averages are weak.

Regardless of locale, meaningful variability exists at the district, school,
and classroom levels--as well as at the state level. Some of this variability
might be random, so that it harbors few practical implications. But much of it
is probably not random. Much of it may be related to features of locale over
which humans might exert some influence for the common good of more and better
mathematics learning (Howley, 2003), including:

*
structural features of the educational system (e.g., class size, school size,
district size, and the relationships among them)

*
equity of local resources (e.g., income distribution in the community, parity of
instructional resources among district schools, patterns of assignment of the
best teachers among a district's schools)

*
the local culture of schooling (e.g., "embeddedness" of the school in the
community and the community in the school, conceptions of educational purposes
and effects)

*
intentions of teachers and administrators (e.g., school climate, professional
collegiality, relationships among students and between students and educators)

*
adequacy of resources (e.g., school funding levels in view of challenges, tax
effort, staff turnover)

*
degree of collective purpose (e.g., student-centered focus, extent of tracking,
equity of educational outcomes)

A good deal of educational scholarship, of course, has considered such
issues, but very little attention has been directed at the influences present in
rural places that support mathematical learning or invoke resistance to
instruction in mathematics. Quantitative studies can and should be informed by
such meanings. But rather than seeking simple differences, future quantitative
studies should consider variation, interactions, dilemmas, and contradictions,
for these are the challenges that make practice and improvement difficult.

### NOTES

1. There are numerous explanations for such a result.
Indeed, the highest correlations by far with 12th-grade math achievement in this
study are those with prior achievement--a powerful control variable in this
study, and the only one to prove statistically significant in the regression
analyses (see authors' discussion on p. 70).

2. With very large sample sizes, some statistically significant differences
will always be found; effect sizes, however, interpret the degree of influence
exerted by such differences. The few such differences found in this study are
associated with very marginal effect sizes (e.g., a magnitude of about .01).

### REFERENCES

Fan, X., & Chen, M. J. (1999). Academic
achievement of rural school students: A multi-year comparison with their peers
in suburban and urban schools. Journal of Research in Rural Education, 15(1),
31-46.

Haller, E. J., Monk, D. H., & Tien, L. T. (1993). Small schools and
higher-order thinking skills. Journal of Research in Rural Education, (2),
66-73.

Howley, C. B. (2002). Research about mathematics achievement in the rural
circumstance (An ACCLAIM Working Paper). Athens, OH: The Appalachian
Collaborative Center for Learning, Assessment, and Instruction in Mathematics,
Research Initiative.

Howley, C. (2003). Understanding mathematics education in rural context. The
Educational Forum, 67(3), 215-224.

Jolliffe, D. (2002). Rural poverty at record low in 2000. Rural America,
17(4), 74-77.

Kifer, E. (2001). Why research on science and mathematics education in rural
schools is important or the mean is the wrong message. In S. A. Henderson (Ed.),
Understanding Achievement in Science and Mathematics in Rural Schools:
Conference Proceedings (pp. 44-48). Lexington, KY: Appalachian Rural Systemic
Initiative.

Lee, J., & McIntire, W. G. (2000). Interstate variation in the
mathematics achievement of rural and nonrural students. Journal of Research in
Rural Education, 16(3), 168-181.

Moses, R., & Cobb, C. (2001). Radical equations: Math literacy and civil
rights. Boston: Beacon Press.