Accessibility of Primary Schools in Rural Areas and the Impact of Topography: A Case Study in Nanjiang County, China

Abstract

In recent years, many developing countries have consolidated rural primary schools, closed small community schools, and enlarged centralized schools, which can reduce the accessibility of education to many communities. Meanwhile, expanding road networks may enable people in far-flung communities to access schools more easily. To evaluate the impacts of both trends on spatial justice in access to education, it is important to examine spatial patterns of primary school accessibility and their predictors. How do the topographic features of villages and surrounding landscapes correlate with primary school accessibility in rural upland areas? Using a digital map route planning application, this study evaluates the primary school accessibility of each village in Nanjiang County, a mountainous county in southwest China. By evaluating relationships between primary school accessibility and village characteristics, this study provides evidence corroborating frequent claims that rural remote mountainous areas have poor primary school accessibility. Additionally, by analyzing the effects of elevation and ruggedness of villages and of the zone between villages and schools as well as the mechanisms driving these effects, we find that, contrary to expectations, with increasing village elevation, a village’s primary school accessibility first decreases and then increases. The ruggedness of the terrain upon which a village is built has no significant effect. The ruggedness of the zone between a village and its nearest school exerts significant effects. These findings demonstrate that the two policies have created a pattern of spatial injustice that disadvantages peripheral villages, illustrating the need to attend to topography in efforts to provide equitable school access in rural mountainous areas.

1. Introduction

Accessibility refers to the ease of moving from one place to another, based on the starting point, final destination, and the form of connection between them [1]. With regard to primary schools, accessibility is affected by the spatial distribution of primary schools, students’ dwellings, and the transportation system between them. Accessing primary school is a crucial activity for children and their families [2], through which economic and social sustainable development may be achieved regionally and globally [3]. As a universal call, Sustainable Development Goal (SDG) 4 aims to ensure inclusive and equitable quality education, and it also contributes to the overarching goals of eradicating poverty (SDG 1) and reducing inequities (SDG 10) [4,5]. Additionally, owing to the physical limitations of young children, as well as safety considerations, long-distance daily commuting is not suitable for primary school students. Consequently, it is of particular importance that policymakers make primary schools accessible.

The theory of spatial justice, elaborated by Soja, emphasizes the fact that justness and fairness differ in different locations depending on a range of factors, giving the theory of justice a spatial dimension [6]. Physical space has long been seen as a fixed background that supports and impacts the realization of social justice through its influence on social action [6], while with the increasing attention to space [7] and its effects on people’s activities, the physical environment is gradually realized by scholars as the production of social and economic processes [8]. Physical distance is one of the important factors affecting spatial justice. In Soja’s description, “the friction of distance” results in a “distance-minimizing behavior” and those human activities “tend to cluster” [6]. Uneven access to school is a means of spatial injustice in education [9], spatial patterns of primary school accessibility and the mechanisms generating these patterns have become a major focus in research on education equity [10,11,12]. In the state of West Virginia in the United States, Emily Talen [13] found substantial spatial injustice in access to primary school, varying by county and school district. Research conducted in four European cities revealed significant spatial imbalances in primary school accessibility conditioned by population density (the higher the population density, the better the primary school accessibility) [14]. A study in China also showed that in Hangzhou, primary school accessibility decreased from the city’s center to its periphery [15].

Studies of primary school accessibility typically use case studies and tools designed in urban areas or developed world contexts rather than rural areas in the developing world. However, primary school accessibility issues in rural areas differ markedly from those in urban areas or developed contexts. Considering their own stated goals alongside the broader international agendas, particularly ‘Education for All’ [16], governments in developing countries have adopted various primary education reform measures to increase educational accessibility, such as increasing funding for primary school education [17,18], reforming curriculum [19], and so on. First, in recent decades governments of developing countries have often framed policies ordering school consolidation by merging or closing small-scale rural primary schools as a response to trends of fertility decline, population aging, and rural out-migration, pursuing the efficiency and economy of education [20]. Developing countries such as Brazil, India, and China have been experiencing the process of primary school consolidation in rural areas [21,22,23], while wealthier countries have completed this process or followed a rather de-centralizing trend [24]. Consequently, schools in many rural communities have been closed, resulting in longer distances to primary schools for residents of those communities and reducing education accessibility. Primary school consolidation is a complex process that is influenced by the willingness of the government at different levels and the reactions of the affected people [25]. Clearly, this process is spatially unbalanced, meaning school closures are not evenly distributed across communities, which may lead to spatial injustice in education provision, but its spatial characteristics and driving factors within rural areas have not yet received enough attention [9,26].

School accessibility depends not just on location but on transportation. Transportation networks have been expanding worldwide [27], with unprecedented growth in the developing world in recent decades [28]. Rapid road network growth is widely recognized as a key means of poverty reduction in rural areas through increasing economic efficiency and enhancing opportunities for livelihoods, training, education, shops, and social connections [29,30]. In the Tonle Sap Basin, Cambodia, the Rural Roads Improvement Project (RRIP) was implemented from 2010 to 2016 to improve approximately 505.4 km of rural roads across seven provinces and to provide 560,000 beneficiaries with all-year road access to provincial and agricultural towns [31]. In China, the Building a New Socialist Countryside program, initiated in 2005, accelerated road network expansion in rural areas [32]. By reducing travel times, road access could potentially offset the burdens school consolidation brings, but this effect depends on the extent and evenness of road expansion. Limited local budgets and physical features make the distribution of road network construction projects spatially heterogeneous, especially in mountainous rural areas in developing countries [32]. This unevenness can limit the extent to which road construction reduces spatial injustice of primary school accessibility. Road expansion that favors some areas over others could amplify uneven primary school accessibility. The extent to which either effect occurs is an empirical question. Although research on transportation has emphasized the importance of connectivity between roads and education and other public facilities for rural development, empirical studies are scant [33]. There is a pressing need for empirical studies that address the combined effects of school consolidation and road expansion on primary school accessibility in rural areas.

Topography must be the core focus of this work. Previous studies conducted in urban areas of the developed world, which are minimally constrained by topography, have greatly improved our understanding of the spatial distribution of primary school accessibility and factors that influence it, especially socioeconomic predictors. Many rural areas have rugged terrain, which is an important natural limiting factor in the construction and maintenance of roads and schools. Additionally, studies have shown that hilly and mountainous topographies have profound effects on social and economic development [2,34,35], influencing population, arable agricultural land area, and agricultural product prices, which may further affect decisions surrounding primary school consolidation and road construction. While remote mountainous areas are often cited as primary school accessibility deserts [4], empirical studies of the effects of topographic factors on primary school accessibility remain rare.

School consolidation and road network expansion are reconfiguring patterns of access to rural primary schools. Topography appears to mediate these relationships. In this study, we, therefore, examine variation in primary school accessibility following school consolidation and road expansion in a mountainous area of southwestern China. By examining how topography and community attributes shape primary school accessibility in this context, we demonstrate a methodology for accurately identifying areas with poor access to schools and the mechanisms that produce spatial injustice. This work both furthers theoretical understandings of spatial injustices related to education and provides starting points for policymakers to make targeted efforts to increase educational equity.

2. Literature Review

2.1. School Consolidation in the Developing World

School consolidation, entailing merging small rural schools into large-scale town schools, has become a common strategy to economize and create a better-resourced environment for staff and students amid demographic change. Consolidation has greatly decreased the number of rural primary schools in many locales. In Brazil, official statistics show that the number of rural primary schools dropped by 31% between 2007 and 2017, from 88,386 rural primary schools to 60,694 [36]. Meanwhile, in India, the state of Haryana merged schools by first combining same-campus schools, then integrating nearby schools having low enrollments and fewer teachers [21]. A consolidated school is supposed to offer an expanded curriculum and a more prominent identity in the community while reducing public costs through economies of scale [37]. Numerous studies have also highlighted the negative impact of school closures on the population and the economic development of communities that lose schools [20,22,38]. Communities with closed primary schools often experience a greater exodus than other communities [39,40]. Another study found rural families in communities with closed primary schools have experienced a sense of disconnection from their community and other families [41].

School consolidation processes dramatically change primary school accessibility. In China, rural primary school consolidation has led to a significant increase in the average distance to school for students, while longer travel distances negatively impact children’s school enrollment and educational outcomes [16,23,36]. In recent years, increasing attention has been paid to the spatial justice of education policies [42]. A study in Pakistan, for example, showed that policy interventions that seek to increase primary school enrollment rates could potentially be more effective if vulnerable communities are targeted [17]. A study in the United States shows that school closures are unevenly distributed, disproportionately affecting places where poor communities and communities of color live [43]. While the increase in distance to a primary school for students made by school consolidation varies among communities, a form of spatial injustice in primary school accessibility whose causes have not attracted enough attention in rural developing contexts.

2.2. Road Expansion in the Developing World

Inadequate rural transportation systems often constrain primary school accessibility in rural areas. Road access for rural residents tends to lag behind their urban counterparts [29]. In recent years, developing countries have increased their investments in rural transportation infrastructure, aiming to reduce rural poverty caused by limited access to economic opportunities [28,30,44]. Over the next 40 years, nine-tenths of all road construction is expected to occur in developing nations [45]. Road expansion has the potential to alleviate the negative impact of school consolidation on primary school accessibility in rural areas, while increasing evidence of unequal mobility and accessibility raises concerns about meeting the transportation needs of the poor, especially in rural areas [32]. Evidence in China illustrates that mobility inequity exists not only between cities and hinterlands but also between township residents and villagers in rural areas [29]. Research in rural Kenya indicates that areas where it takes people a long time to reach a good road are typically poorer [46]. Although road expansion converges with school consolidation to increase the spatial complexity of rural primary school accessibility patterns, the combined impact of these two spatially imbalanced changes on primary school accessibility remains unclear.

2.3. Impacts of Topography on School Accessibility in Rural Areas

Covering 27% of the world’s surface [47], mountains—rugged land at least 300 m above sea level—are home to about 1.11 billion of some of the world’s poorest people, and their access to services and infrastructure is lower than in the lowlands [48]. Many rural communities are located in mountainous areas [49], where rugged landscapes are an important natural feature affecting rural development [35,50]. Rugged terrain is detrimental to agriculture outputs and also impedes scale and modernizing agriculture production [51]. Additionally, based on its important ecological value, commercial activities in mountainous areas are usually resource extraction and not conducive to the sustainable livelihood of mountain residents [52,53]. As a result, mountainous areas have a limited economic development level compared with flat areas.

Topography may affect spatial patterns of primary school accessibility in rural areas in several ways. First, in line with the original motivation of rural primary school consolidation, governments close small-scale community schools due to low enrollment and efficiency, retaining and enlarging larger-scale town or township schools. Since rural towns are mainly located in relatively flat, lower-elevation places, communities located at higher elevations and communities built on rugged terrain may become vulnerable to the school consolidation process. For example, following the rural primary school consolidation policy in China, primary schools in mountainous areas tend to be distributed in areas with low elevation and flat terrain [54,55]. Additionally, the cost of road construction increases with elevation and ruggedness, resulting in fewer miles of roads in rural areas with limited funding [32]. People who live in rugged areas suffer from low road accessibility and poor road connectivity [32]. School placement in flat areas and disproportionate costs of road building in rugged areas differentiate communities by topography. The higher elevation and more rugged the village itself, possibly the worse the primary school accessibility. The topography of the land between the school and the village also plays an important role. Limited by topographical conditions, winding roads are often needed to ensure safety in mountainous areas. The elevation and ruggedness of the zone between villages and schools may affect the spatial layout of roads by shaping where and how roads are constructed, potentially increasing the actual travel distance between homes and schools.

2.4. School Consolidation and Road Expansion in Rural China

In 2001, the State Council of the People’s Republic of China issued the Decision on the Reform and Development of Compulsory Education, which explicitly required that the educational quality of rural schools be improved by restructuring how schools are placed and integrating education resources. Before the implementation of this policy, almost all administrative villages (the smallest administrative unit in the Chinese government system often composed of several distinct hamlets or natural villages) had their own village schools, meaning that there were hardly any disparities in primary school accessibility across administrative villages. Under the school consolidation policy, local governments withdrew and merged administrative village-level schools and promoted boarding schools, mainly shifting primary schools from administrative villages to townships. Yet the policy also stipulates that school placement should be properly planned and adjusted in accordance with the principles of enabling primary school students to enroll in schools near their homes (jiujinruxue 就近入学). Additionally, in areas with transportation constraints, primary education centers (Primary education centers incomplete primary schools, generally encompassing grades 1–3, located in administrative villages, managed by a township primary school, and regarded as a small branch. Some scholars use the term “teaching site.”) (jiaoxuedian 教学点) should retain to prevent students from dropping out due to the school placement adjustments. While more concrete instructions about travel distances and enrollment rates were lacking, the State Council decision left the detailed implementation of adjustments primarily to county-level governments. At the same time, funding for public primary schools, which in the past was mainly the responsibility of township governments and villagers, was handed over to county-level governments.

According to the statistics from the Ministry of Education of China, from 1997 to 2010, 371,470 primary schools were shut down nationwide, including 302,099 in rural areas, accounting for 81.3% of the total reduction, greatly changing the spatial allocation of primary schools. It is true that school consolidation policy has contributed to the improvement of physical facilities of primary education [23], but its negative impacts on educational equity in rural areas are also evident, including but not limited to high dropout rates, rising cost of living, and issues concerning student safety. A case study in North China demonstrated that urban-oriented school consolidation exacerbated educational inequality, actually increasing gaps between urban and rural areas and between rich and poor [23]. As mentioned above, before school consolidation, almost every administrative village had a village school. However, following policy implementation, the spatial balance of primary school accessibility at the administrative village level was broken. Children lost opportunities to learn in local administrative villages and had to travel various distances to primary schools daily or weekly [20].

Recognizing these issues, and in the context of the rural revitalization program initiated in 2017 [56], the State Council issued a guideline in 2018 on strengthening the construction of small-scale rural schools (administrative village-level primary schools and primary education centers within 100 students). By strengthening the operation of small-scale rural schools, this policy seeks to strike a balance between primary students’ travel distances to primary schools and educational quality. Given the conditions surrounding school consolidation, China presents a promising context for studying rural primary school accessibility and its correlates. As county governments oversee of primary school consolidation process, and this process appears to yield uneven accessibility across administrative villages, it is reasonable to study spatial patterns of primary school accessibility across villages within a county.

As mentioned before, China launched a series of rural road construction projects across the country supporting the Building a New Socialist Countryside program. This has been accomplished through construction projects aimed at linking every administrative village to paved roads (cun cun tong 村村通) [57]. According to the Highway and Waterway Transport Industry Development Statistical Bulletin of the Ministry of Transport, by 2008, 99.24% of townships and towns and 92.86% of administrative villages had paved roads. Since 2015, the Chinese government has further increased investment in rural road construction with the goal of eliminating rural poverty. At the end of 2019, a village in Liangshan Prefecture, Sichuan Province, became the last administrative village in China to be provided with concrete paved road access. According to the Administrative Principles for Rural Road Construction issued by the Ministry of Transport of China 2006, these road expansion projects have a multi-channel funding mechanism. More precisely, government investment serves as the mainstay, supplemented by investments from administrative villages and other sectors, such as private business. Differences in local government and private resources may generate spatial disparities. Lacking supplemental funding, less developed and isolated administrative villages are likely to be further marginalized. Case studies have shown that government programs disproportionately benefit administrative villages that already have better resources [25,58]. Accordingly, school consolidation and rural road expansion have changed the geographic scale at which spatial variation in primary school accessibility occurs [12]. An empirical study is needed to understand how the nature and impacts of these things change.

2.5. Research Questions

In summary, according to the initial concept of accessibility, amid rural primary school consolidation and road network expansion, villages are not equally affected, creating potential for spatial injustice in rural education. In accordance with calls for research into spatial justice in rural areas [10], valuations of rural primary school accessibility should combine the impacts of school consolidation and road network expansion and work at a fine geographic scale, so as to accurately identify vulnerable villages with inadequate accessibility. Topography—specifically, elevation and ruggedness—may affect spatial patterns of primary school accessibility through policy decisions and physical constraints. Hence, topography is a crucial consideration. Accordingly, we address two research questions: (1) how great are spatial differences in the school access net of both consolidation and road construction, and (2) what topographical factors affect primary school accessibility in rural areas, and how?

This study assesses primary school accessibility among administrative villages in a poor, mountainous county in southwest China. The route planning function in a digital mapping application was adopted to improve assessment accuracy. This evaluation method helps to reveal the spatial characteristics of primary school accessibility among administrative villages under the dual effects of school consolidation and the rapid expansion of rural roads. We analyze the effects of elevation and ruggedness on spatial differences in primary school accessibility between administrative villages, so as to provide empirical evidence for the impact of topography on primary schools. Finally, we construct linear regression models to analyze the impacts of topographic factors on primary school accessibility.

3. Methods

3.1. Study Area

Nanjiang County is a mountainous county in the Qinling-Bashan Mountain region in southwest China. As shown in Figure 1, Nanjiang is characterized by deep valleys and steep slopes, with elevations ranging from 335 m to 2491 m and an average elevation of 1100 m. In the northern half of Nanjiang, the topography is relatively complex, and the overall elevation is higher, while the southern half is lower and flatter. Nanjiang County has jurisdiction over 561 administrative villages or communities and has a total population of 609,000. The county was announced by the provincial government to be removed from the Chinese national poverty-stricken county list by 2019. Before rural primary school consolidation, every village in Nanjiang had a primary school, so primary school accessibility did not differ between administrative villages. From 2000 to 2005, the number of primary schools decreased from 512 to 65, a decrease of 87.30%. In the following decade, the number of primary schools continued to fall at a slower rate, stabilizing at 39 (including six-year complete primary schools and nine-year compulsory schools) in 2015. Most primary schools are distributed in low-elevation areas, and only five are above 1000 m. Meanwhile, from 2001 to 2018, road mileage in Nanjiang County increased from 917 km to 5359 km. The significant decrease in the number of primary schools and the rapid expansion of road networks, as well as the complex topographic features in Nanjiang, make it a suitable area for this study.

3.2. Primary School Accessibility Assessment

In related research, numerous studies have optimized accessibility assessment methods by improving the accuracy of the capacity and spatial-temporal variation characteristics, of services, demands, and the transportation system between them [59,60,61], such as capturing the temporal variation of food service accessibility, due to the dynamics both of traffic conditions and of individuals’ intensities in performing activities at different times of day [62]. Given this study’s emphasis on physical accessibility and the Chinese government’s nearby enrollment policy, we adopt the classical measure of travel distance impedance to the nearest school to evaluate primary school accessibility. This method assumes that residents always prefer the nearest primary school, and hence the shorter the distance, the better the primary school accessibility [63].

Due to the constraints of rugged terrain and winding roads, traditional distance calculation methods based on plane distance may bias primary school accessibility assessment results in mountainous areas. Network and cost-distance analysis tools in digital map applications enable an accurate measurement of the real commute distance from the starting point to the destination. This function has been used by some studies on accessibility assessment in urban areas [64,65]. We believe this method should also be applied in studies conducted in rural areas to increase the accuracy of measurement of primary school accessibility.

Taking the location of the committee office of each administrative village as the starting point and all primary schools as the destinations, we used the route planning function of Gaode Map (the top downloaded digital map application in China) to calculate the actual driving commute distance from each administrative village to each primary school. The geographical location information of the 561 administrative village committee offices and the 39 primary schools in Nanjiang County are points of interest (POIs) downloaded from Gaode Map. The shortest commute distance from each village to schools was identified using map service calculation results. The longer the commute distance from the administrative village to the nearest primary school, the worse the primary school accessibility in the administrative village. We then normalized commute distances using min-max normalization, yielding values between 0 and 1, with higher values indicating better primary school accessibility.

3.3. Topographic Factors and Datasets

The characterization of topographic features is a complex issue. Our literature review suggests that elevation differences and the ruggedness within villages and between a village and the nearest school are potentially important factors influencing primary school accessibility. Considering these facts, we calculated the average elevation and standard deviation of the slope of each village territory to reflect the village’s elevation and ruggedness. The elevation and ruggedness features between the village and its nearest school are delineated by a 12.5 m wide zone surrounding a straight line extending from the village committee office to the nearest school (hereafter straight zone). The average elevation and standard deviation of the slope of this straight zone are calculated to measure elevation and ruggedness, respectively. The data source for these variables was DEM data for Nanjiang County with 12.5 m pixels (downloaded from the official NASA website).

3.4. Data Analysis

To understand differences in primary school accessibility of administrative villages, we adopted the Hierarchical and k-means cluster methods to classify all administrative villages according to elevation and ruggedness, respectively. We used hierarchical cluster to determine the number and centroid of each classification and then used k-means clustering to classify administrative villages.

Exploratory spatial data analysis (ESDA) was adopted to quantify the spatial patterns of primary school accessibility. Within this broad group of techniques in ESDA, global Moran’s Index and local Moran’s Index analysis methods are commonly used. Notably, global Moran’s Index is a way to measure spatial autocorrelation, which is wildly used in geography and geographic information science to measure how closely clustered different features are. A positive and significant global Moran’s Index value indicates a general pattern of clustering in spaces with similar values. Formula (1) shows the calculation of Moran’s I:

$$I=\frac{{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{w}_{ij}\left(x_i-\overline{x}\right)\left(x_j-\overline{x}\right)}{{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{w}_{ij}{{\displaystyle \sum }}_{i=1}^n{\left(x_i-\overline{x}\right)}^2}$$

(1)

Note: $n$ represents the number of spatial units indexed by $i$ and $j$, $x$ is the variable of interest (accessibility of administrative villages in the study area), and $w_{ij}$ is a matrix of spatial weights.

The local Moran’s Index is used to detect the extent and location of outliers or clusters. The local indicators of spatial association (LISA) clustering map is a visualization of local Moran’s I statistic, providing a way to categorize the nature of spatial autocorrelation into four types, corresponding to spatial clusters and spatial outliers. Specifically, observations labeled in low-low and high-high represent potential spatial clusters, meaning values surrounded by similar neighbors, whereas observations labeled in low-high and high-low suggest potential spatial outliers, meaning values surrounded by dissimilar neighbors. In this study, by using Geoda software, we calculated global Moran’s I of the primary school accessibility of each administrative village in Nanjiang County and drew LISA clustering map to signify the spatial clustering pattern. Specifically, we used the first-order Queen method to define the spatial relationships between counties, meaning if two villages share the same boundary or vertex, they are defined as neighbors.

Regression analysis is an approach for modeling the relationship between a scalar response and one or more explanatory variables. In this study, we used regression analysis to explore whether and how different topographic factors influence primary school accessibility. If a significant spatial autocorrelation relationship of primary school accessibility is tested by using global Moran’s I analysis, the spatial regression model should be considered; otherwise, non-spatial linear regression should be adopted. The spatial regression model mainly emphasizes the impact of the proximity of the studied units on the dependent variables of the units in the model. According to the influence of neighboring units, the spatial models can be divided into three types, namely, the spatial lag model (SLM), the spatial error model (SEM), and the spatial Durbin model (SDM). Specifically, SLM refers to the fact that the dependent variable of a region is affected by the independent variables of the surrounding regions. SEM, on the other hand, refers to the fact that the dependent variable in a region is affected by the unobservable error variable in adjacent regions. SDM means that the dependent variable is jointly affected by the dependent variable and the independent variable of neighboring regions. Usually, researchers use the spatial Lagrange Multiplier (LM) test and the robust LM test to test the fitting degrees of the spatial regression models. Formulas (2)–(4) show the mathematical formulas of SLM, SEM, and SDM, respectively.

$$y=\rho Wy+X\beta +\epsilon , \epsilon ~N\left[0,{\sigma }^{2}I\right]$$

(2)

$$y=X\beta +u, u=\theta Wu+\epsilon , \epsilon ~N\left(0,{\sigma }_{\epsilon }^{2}I\right)$$

(3)

$$y=X\beta +u, u=\lambda Wu+\epsilon , \epsilon ~N\left(0,{\sigma }_{\epsilon }^{2}I\right)$$

(4)

Note: $y$ is the dependent variable, $X$ stands for the independent variable, and $W$ is the spatial weight matrix. $\epsilon$ represents error term. $\rho , \lambda , \theta$ represent the spatial regression coefficients of dependent variable, spatial error term, and independent variable, respectively.

The primary school accessibility of each administrative village was the dependent variable, and the elevation and ruggedness of administrative villages and of the straight zone were independent variables of interest in the regression models. Generally, with a longer Euclidean distance, the commute distance is longer, and thus Euclidean distance between the village and its nearest school was also used as a control variable. Since primary school accessibility is clearly affected by socioeconomic factors and population [11], socioeconomic and demographic factors were included as control variables. Village-scale socioeconomic data in China are extremely limited in availability. Hence, we used the commute distance from each village to the county seat, calculated by Gaode Map, as proxy variable for socioeconomic development conditions. Studies show strong negative correlations between distance and socioeconomic conditions; the longer the distance, the weaker development conditions tend to be [66,67]. We include the total population of each village, based on the population data in a 100 m grid provided by WorldPop, as demographic control variable.

We are also interested in the potential mediating effect of population on primary school accessibility (Figure 2). Hence, we adopted Baron and Kenny’s mediator analysis method [68] by adding two other regression models to analyze whether the elevation and ruggedness of administrative villages and of the straight zone have an indirect impact on primary school accessibility by influencing administrative village population, conceptual formulas were shown in

Table 1. Conceptual formula of Baron and Kenny’s mediator analysis.

Model Number	Conceptual Formula
1	$Accessibility=i_1+{\alpha }_{1}Topography+\beta Demography+{\gamma }_{1}Z+{ϵ}_1$
2	$Demography=i_2+{\alpha }_{2}Topography$ + ${\gamma }_{2}Z+{ϵ}_2$
3	$Accessibility=i_3+{\alpha }_{3}Topography+{\gamma }_{3}Z+{ϵ}_3$

Note: $i_1$, $i_2$, $i_3$, ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$, $\beta ,{\gamma }_1$, ${\gamma }_2$, and ${\gamma }_3$ are coefficients; $Z$ represents control variables; $\mathrm{and} {\epsilon }_1$, ${\epsilon }_2$, and ${\epsilon }_3$ are residuals.

.

4. Results

4.1. Overview of Primary School Accessibility

According to our calculation results in

Table 2. Overview of primary school accessibility.

Commute Distance (km)	Mean	Median	Max	Min	SD
	10.69	9.65	49.3	0.3	7.12
Level of accessibility	Commute distance (km)		Number of villages		Percentage
Low	>20		54		9.93%
Medium	10–20		207		38.05%
High	<10		283		52.02%

, the average commute distance from each administrative village in Nanjiang County to its nearest primary school is 10.69 km, and the median distance is 9.65 km. Additionally, the commute distance from each village to its nearest school varies greatly, ranging from 0.3 km to 49.3 km with a standard deviation of 7.12 km, indicating large differences in primary school accessibility among administrative villages.

Hierarchical and k-means cluster analyses classified administrative villages into three categories by distance to the nearest school, which we label “low”, “medium”, and “high”. The “low” group comprises 54 administrative villages that are more than 20 km away from the nearest primary school. These villages are mainly located at the edge of the county or at higher elevations (Figure 3). A total of 207 administrative villages had a “medium” level of primary school accessibility, with commute distances ranging from 10 km to 20 km. These villages are located in higher elevation regions and interior parts of the county and are spatially aggregated in groups (Figure 3). There were 283 administrative villages with “high” primary school accessibility, commuting distances to their nearest schools are between 0 km and 10 km. These administrative villages are mainly in low-elevation areas near schools. Some are in middle- or high-elevation regions, some of which had a primary school within them.

We note that since the real commute distance was used as the basis of primary school accessibility assessment, adjacent villages in some cases show sharp differences in primary school accessibility. Although adjacent to a village with a primary school, some villages surprisingly had a low level of primary school accessibility. This situation is probably caused by topographical factors, such as the villages being separated by a ridge and not having a direct road connection, and this study will further analyze the mechanism behind it. We colored villages served by the same school with the same color. As shown in Figure 3, the number and area of villages served by schools also vary widely, indicating unbalanced education service provision pressure among schools.

The primary school accessibility of administrative villages in Nanjiang County shows a significant positive spatial autocorrelation, with a global Moran’s Index value of 0.54 (p = 0.000). As shown in Figure 3c, villages with high primary school accessibility were clustered in the northern flat areas and southern central parts of Nanjiang, while villages with low primary school accessibility were mostly clustered in the peripheral areas.

4.2. Characteristics of Primary School Accessibility Based on Topographic Factors

This study divided administrative villages into five categories according to their elevation by using Hierarchical and k-means clustering methods: 337–625 m, 626–817 m, 818–1023 m, 1024–1243 m, and 1258–1623 m (

Table 3. Accessibility of Villages with Different Elevations.

Categories of Elevation	Mean Elevation (m)	Number of Villages	Mean	SD	Max	Min	Median
Low-elevation villages	337–625	129	0.784	0.151	0.994	0.210	0.793
Moderate–low-elevation villages	626–817	196	0.818	0.122	1.000	0.339	0.837
Medium-elevation villages	818–1023	122	0.760	0.145	1.000	0.255	0.779
Moderate–high-elevation villages	1024–1243	57	0.747	0.178	0.992	0.000	0.757
High-elevation villages	1258–1623	40	0.798	0.156	1.000	0.333	0.837

). Among villages at different elevations, the ranges of commute distance from each administrative village to its nearest primary school are nearly the same, meaning there were administrative villages with different levels of primary school accessibility in each elevation category. However, if we use standard deviation as a criterion of variability, primary school accessibility of moderate–high-elevation villages (1024–1243 m) stands out, with the highest standard deviation of 0.178. With regard to the mean accessibility of each elevation category, primary school accessibility increases with a shift from low to moderate–low elevation, falls from moderate–low to medium to high-elevation villages, and then rises again in the highest elevation category.

We used the same method to classify administrative villages into four categories based on their ruggedness, namely flat villages, moderate flat villages, medium flat villages, and rugged villages, as shown in

Table 4. Accessibility of Villages with Different Ruggedness.

Categories of Ruggedness	SD of Slope	Number of Villages	Mean	SD	Max	Min	Median
Flat villages	2.85–7.40	38	0.865	0.114	0.994	0.563	0.901
Moderate flat villages	7.50–9.45	184	0.802	0.123	0.996	0.335	0.824
Medium flat villages	9.50–11.28	237	0.780	0.153	1.000	0.000	0.796
Rugged villages	11.31–14.63	85	0.744	0.162	0.986	0.210	0.747

. In the four clusters of administrative villages with different ruggedness, the results differed slightly from the elevation results. Across the four categories, maximum primary school accessibility levels are nearly the same, while minimum levels are markedly different. Measured by the standard deviation of primary school accessibility, the accessibility of rugged villages shows the greatest variability. Overall, with an increase in ruggedness, primary school accessibility decreases.

4.3. Quantitative Identification of Topographic Effects

According to the spatial LM test results, the accessibility of primary schools in each village in Nanjiang County conforms to the spatial error model, as shown in

Table 5. Test Results of Spatial LM Tests.

		Model 1	Model 2	Model 3
Dependent Variable		Accessibility	Village Population	Accessibility
Moran’s I		0.542 ***	0.351 ***	0.542 ***
LM test	LM-lag	25.139 ***	72.275 ***	24.978 ***
	LM-error	59.389 ***	68.340 ***	63.692 ***
	RLM-lag	0.059	4.558 **	0.271
	RLM-error	34.310 ***	0.622	38.984 ***
	LM-SARMA	59.448 ***	72.897 ***	63.962 ***
Best-fit model		SEM	SLM	SEM

Note: ** indicates significance at the 0.05 level, and *** indicates significance at the 0.01 level.

. As presented in

Table 6. Spatial Regression Results.

Model Number	1	2	3
Model Type	SEM	SLM	SEM
	Accessibility	Village Population	Accessibility
	Standardized Coefficient
Square of village elevation	0.198 *		0.198 *
Village elevation	−0.206 *	−0.046 **	−0.207 *
SD of village slope	0.007	0.012	0.007
Elevation of straight zone	−0.046	−0.028	−0.047
SD of straight zone slope	−0.083 ***	0.007	−0.082 ***
Village population	0.018 *
Distance to county seat	−0.135 ***	−0.035 ***	−0.134 ***
Euclidean distance	−0.627 ***		−0.627 ***
Lambda	0.519 ***		0.516 ***
Rho		0.208 ***

Note: * indicates significance at the 0.1 level, ** indicates significance at the 0.05 level, and *** indicates significance at the 0.01 level. SD is the abbreviation of standard deviation.

, the results of Model 1 provide quantitative evidence on the effects of topography on rural primary school accessibility. Considering that in the descriptive statistical analysis, with an increase in elevation average primary school accessibility of administrative village groups at different elevations first decreases and then increases, the square of administrative village average elevation was introduced into the model. Results from Model 1 show a significant positive effect of squared average elevation of administrative villages, supporting the finding of a U-curve relationship, meaning that with an increase in the average elevation of each village, primary school accessibility decreases and then increases. However, the standard deviation of a slope, measuring village ruggedness, does not show a significant effect. In Model 1, the mean elevation and ruggedness of the straight zone indicated a negative impact on primary school accessibility, while only ruggedness was significant (p < 0.001). Specifically, the greater the ruggedness of the terrain between the village and its nearest school, the lower the primary school accessibility. Compared with other topographical variables, the average elevation of the villages has the largest standard coefficient. Additionally, the spatial error term (Lambda) has a significant positive impact on primary school accessibility, showing a positive spatial spillover effect. In Model 2, the average elevation of the administrative villages and the distance to the county seat each show a significant negative impact on the villages’ total population. According to the results of the three models, the villages’ total population has a partial mediation effect on primary school accessibility.

5. Discussion

5.1. Spatial Patterns of Accessibility within Rural Areas

With regard to the research question (1), considering the impacts of rural primary school consolidation and road expansion, a spatial disparity in primary school accessibility at the administrative village level is evident, as shown in Figure 3. Spatial regression analyses and LISA clustering map show that within the county, administrative villages near the county seat have better primary school accessibility, while administrative villages toward the county’s boundaries have worse overall primary school accessibility, presenting a core-periphery spatial pattern similar to that observed in cities [69]. In contrast with studies conducted in cities with more diverse transportation systems and a flatter terrain [14], primary school accessibility at the administrative village level in Nanjiang County is more spatially fragmented and discontinuous, as evidenced by how some administrative villages adjacent to villages with schools show very low levels of primary school accessibility. These administrative villages are vulnerable to both consolidation and road construction, a situation which might be ignored if methods commonly used in urban areas, such as school buffer zones, are used in evaluation or planning. Thus, by using real commute distances to measure primary school accessibility, this study can help policymakers to identify needy villages with poor primary school accessibility within a county and avoid misplacing education resources to support the strong. However, in rural areas of the Global South, where spatial data are most scarce, more innovative methods are needed to address these issues [67].

This study also addresses the effects of the administrative village population and the distance to the county seat on primary school accessibility. Findings are consistent with results from studies in urban areas and at other geographical scales [12,70], suggesting the broad relevance of population and distance from administrative centers to primary school accessibility in various geographic regions and scales.

5.2. Impacts of Topography on Primary School Accessibility

In related studies on accessibility, researchers often took the natural environment as the background condition to understand social justice, while as Harvey noted “spatial forms are not inanimate objects within which the social process unfolds”, “we need to formulate concepts which allow us to harmonize and integrate strategies to deal with the intricacies of social process and the elements of spatial form” [71]. According to the results of this study, topographic factors significantly influence primary school accessibility in rural areas. Studies of rural primary school accessibility and its drivers should consider topographic factors. One of the most important findings of this study is that primary school accessibility first increases and then decreases with an increase in a village’s average elevation. This finding contrasts with common understandings of primary school accessibility in remote mountainous areas. This discrepancy could be attributable to the process through which the county government implemented central government policies. According to the official spatial layout adjustment policy, while transforming village primary schools into large-scale township primary schools was the main thrust, necessary primary education centers should be retained to prevent students from dropping out due to transportation challenges. As a result, some primary schools located in administrative villages with poor natural conditions and mobility in the highest elevation areas were preserved, improving the primary school accessibility of these administrative villages. In Nanjiang County, some administrative village primary schools were indeed retained, such as Heichi Village Primary School. This is a result of the interaction between the national system of governance and local decisions, a phenomenon that can also be observed in other developing regions. In Brazil, in transportation planning, where no quantitative indicators are available or accurate enough to foster equitable and inclusive transportation planning, the prioritization of transportation interventions inevitably assumes a biased, arbitrary, and paternalistic fashion [67]. The absence of any effect of administrative village ruggedness on primary school accessibility may be surprising because as the slope fluctuates, the area of land suitable for cultivation gradually decreases and road and school maintenance challenges increase. One possible reason for the unexpected results for ruggedness could be that it might exert a significant impact at a geographical scale smaller than the administrative village since it is a significant factor in rural households’ settlement and access to roads [35]. This study also shows that the ruggedness of the straight zone between a village to its nearest school significantly impacts primary school accessibility. This finding indicates that studies of primary school accessibility mainly based on intra-unit variables may present biases in rural areas.

Aside from its direct effects, we also find that a village’s average elevation influences primary school accessibility through its effect on the village’s population. Studies have emphasized positive relationships between primary school accessibility and population density [39,40], and Chen [35] found a significant relationship between slope and elevation and rural settlements. This study’s findings show a direct impact of topography on primary school accessibility and also a direct impact of topography on population. Hence, it is important to control the impact of topography on population distribution when studying relationships between primary school accessibility and population in rural areas in future studies.

5.3. School Bus Provision

In Nanjiang County, the average commute distance from each administrative village to its nearest school is 10.69 km, within a range of 0.3 km to 49.3 km. These distances far exceed urban school commutes in China [15]. Long school commute distances are always connected to public transportation [69]. Developed countries such as the United States and the United Kingdom have strict and precise guidelines on government provision of school buses for school students. For instance, according to the UK Department for Education’s Home to School Travel and Transport Guidance, local authorities are required to provide free transportation for children of compulsory school age if their nearest suitable school is beyond 3.22 km (for children under 8 years old) or beyond 4.83 km (for children between 8 and 16 years old). There were 416 administrative villages in Nanjiang County whose travel distance to the nearest primary school was over 4.83 km, accounting for 76.47% of the total. However, based on information provided by local people, there was no public school busing available in Nanjiang. Instead, as in many other counties in China, rural boarding primary schools are the norm. As a crucial practical concern, providing school buses for rural primary students in developing countries needs further attention, especially after school consolidation. However, there are few empirical studies in this regard. In India and Brazil, public school busing provision guidelines do not exist. More field studies in rural areas in developing countries are needed to provide a reference for the formulation of school busing provision guidelines.

5.4. Study Limitations and Future Research Proposals

This study analyzed spatial patterns of primary school accessibility in rural areas using the office of each administrative village as the starting point. In reality, rural residents in any given administrative village are usually scattered in a number of hamlets. Hence, commute distances calculated in this study cannot accurately show the primary school accessibility for each rural family. Nonetheless, it can provide an approximate reference. In most cases, this is a conservative measure, as administrative village offices are usually located on trunk roads, while it is often necessary to travel further on branches to reach most hamlets. While this study is a small-scale regional study, and the effects found in this study may not be generalizable to other places, the research results can provide a reference for relevant research and policymaking. We analyzed the spatial injustice in primary school accessibility in the wake of both school consolidation and road construction in this study. In the future, we will consider measuring the impacts of the two policies on primary school accessibility separately by conducting a spatial-temporal analysis and comparing primary school accessibility before rural primary school consolidation and road expansion policies are implemented.

6. Conclusions

Primary school consolidation and road expansion in rural areas in fast-developing countries such as China, India, and Brazil can create spatial injustice in primary education access. Studies of primary school accessibility that examine both school consolidation and road network construction are scant. Topography, a dominant biophysical factor that shapes rural development, can also impact primary school accessibility by influencing the school consolidation process and shaping where and how roads are constructed. Evaluating primary school accessibility across administrative villages in a mountainous county in China, this study addressed the spatial heterogeneity net of primary school consolidation and rural expansion. The primary school accessibility in the study area shows a significant spatial clustering pattern. Villages near the county seat have better primary school accessibility, while administrative villages toward the county’s boundaries have worse overall primary school accessibility, presenting a core-periphery spatial pattern. Both the village elevation and the ruggedness of the zone between a village and its nearest school exert significant effects on primary school accessibility, highlighting the effects of elevation and ruggedness on primary school accessibility. This work both furthers theoretical understandings of spatial injustices related to education and provides starting points for policymakers to make targeted efforts to increase educational equity in rural areas.