Analysis of Kindergarten Enrollment Accessibility and Its Influencing Factors in the Main Urban Area of Lanzhou City

GUO Nianfa¹, WANG Lucang¹,²

¹School of Geography and Environmental Science, Northwest Normal University, Lanzhou 730070, Gansu, China
²Key Laboratory of Resource Environment and Sustainable Development of Oasis, Lanzhou 730070, Gansu, China

Abstract

As a foundational yet often overlooked component of the education system, the precise quantification of kindergarten enrollment accessibility is crucial for evaluating the spatial allocation efficiency of preschool education resources. This study examines the main urban area of Lanzhou City as a case study, integrating data on kindergarten locations, school-age children, available places, road classifications, and other relevant factors. Using kernel density analysis and a multi-level, multi-travel-mode Gaussian accessibility algorithm, we quantify the agglomeration characteristics and enrollment accessibility of different kindergarten tiers. Spatial regression models and bivariate spatial autocorrelation are employed to explore the factors influencing the distribution of enrollment accessibility. The results reveal that: (1) Kindergartens exhibit a "one core, four centers" belt-shaped distribution pattern, with density decreasing from east to west. Provincial-standard, municipal-standard, district-standard, and general kindergartens each display distinct "single-core" spatial distribution characteristics. (2) The overall accessibility hierarchy shows an eastward-weighted, "south-superior-north-inferior" spatial bias. Accessibility across different quality tiers follows a "multi-center" structural pattern, with general kindergartens showing the highest accessibility values, reflecting their primary role in facilitating local enrollment. (3) School-age population, family economic status, and kindergarten enrollment quotas exert significant positive effects on accessibility, while road network density and bus stops show negative but non-significant effects. Additionally, kindergarten tuition fees demonstrate a negative effect on enrollment accessibility.

Keywords: kindergarten; spatial distribution; enrollment accessibility; influencing factors; main urban area of Lanzhou City

1. Introduction

Following social development and improvements in livelihoods, parental attention to kindergarten education has intensified, shifting the focus from equitable access ("having a school to attend") to quality-based equity ("attending a good school"). Kindergarten education constitutes a vital urban public service, and the rationality and balance of its spatial configuration directly affect children's educational convenience. However, research on kindergarten accessibility remains limited in terms of study objects, data sources, methodologies, and scales.

First, existing studies often treat kindergartens as a homogeneous category, overlooking the four-tier classification system (provincial-standard, municipal-standard, district-standard, and general kindergartens). This homogenization fails to reveal differential access opportunities across quality tiers. Second, most research substitutes the 0-5 age group for school-age children, inadequately capturing demographic characteristics. Furthermore, accessibility studies typically rely on single travel modes, neglecting the varying time costs associated with multiple transportation options.

Common accessibility methods include the ratio model, shortest distance method, potential model, and two-step floating catchment area (2SFCA) method. The ratio model lacks intra-regional differentiation, while the shortest distance method ignores supply-demand dynamics. Both the potential model and 2SFCA consider supply and demand scales and distance effects, but differ in distance processing. The potential model lacks a maximum service radius constraint, whereas 2SFCA's binary distance treatment effectively identifies low-accessibility areas. However, single-mode calculations fail to reflect the flexibility of travel choices and associated time costs. Accessibility fundamentally concerns efficiency and convenience, where distance alone cannot capture true enrollment convenience in urban environments.

This study addresses these gaps by employing a 200m grid as the basic analytical unit for the main urban area of Lanzhou City. Through kernel density analysis and a multi-level, multi-travel-mode Gaussian 2SFCA method, we examine kindergarten resources, providing scientific evidence for optimizing educational resource allocation.

1.1 Study Area

Lanzhou, a key inland hub city in northwest China, is constrained by natural geography into a narrow valley between north and south mountains, resulting in poor accessibility. This study focuses on the main urban area (8 subdistricts in Chengguan District, 8 in Anning District, 7 in Qilihe District, and 7 in Xigu District). According to municipal education bureau data, by the end of 2022, Lanzhou's municipal districts had 157,900 kindergarten children across 799 kindergartens. Within the main urban area, 626 kindergartens included 42 provincial-standard, 67 municipal-standard, 51 district-standard, and 466 general kindergartens. As urbanization accelerates, the number of school-age children from migrant families increases annually, while the valley topography—with limited land and dense population—poses significant challenges for kindergarten spatial planning.

1.2 Data Sources

Research data include kindergarten POI data, road network data, kindergarten capacity, kindergarten tier classifications, and school-age child data. Kindergarten locations were crawled from Amap in 2022 and preprocessed. Capacity data were obtained by substituting in-kindergarten child numbers from the Lanzhou Education Special Plan. Tier classifications were sourced from Lanzhou Education Bureau evaluation data, including operational nature, level, and public-benefit status. Road network data were obtained from Amap and georeferenced in ArcMap according to Lanzhou's "one horizontal, three rings, nine verticals" system to extract road grade attributes. School-age child data were estimated using a multiple linear regression model fitted with seventh census data at subdistrict level and WorldPop population grid data.

2. Methods

2.1 Kernel Density Analysis

Kernel density analysis is a widely used spatial method for estimating unknown density functions. The calculation formula follows established literature \cite{}.

2.2 Multi-Level, Multi-Travel-Mode Enrollment Accessibility Measurement

Family enrollment choices are typically proximity-based, with decreasing attraction over distance—a pattern that aligns with Gaussian functions where decay accelerates then decelerates. Therefore, we employ a Gaussian impedance function. With improved public transit and private vehicle普及, enrollment travel modes include walking, bicycling/e-biking, public bus, and car. Different road grades affect travel speeds across modes.

Based on Amap data, we assigned travel speeds for each mode across road grades (Table 1). Mode choice is distance-dependent: walking dominates within 0.5 km, bicycling/e-biking within 1.5 km, and cars beyond 2.5 km. According to the Lanzhou Citizen Travel Mode Survey Report, mode proportions are determined by home-school distance (Table 2). Considering physiological constraints on children and caregivers, we set maximum travel time limits and different search radii for each kindergarten tier (Table 3).

Step 1: Using kindergarten capacity ($S_j$) as supply point $j$, we sum all children within search radius $d_r$ of a given tier, weight them using a Gaussian function, and calculate the supply-demand ratio ($R_j$):

$$
R_j = \frac{S_j}{\sum_{m} \sum_{i \in {d_{ij}^m \leq d_r^m}} p_i^m \times G_K}
$$

where $k$ represents kindergarten tier; $m$ represents travel mode; $d_{ij}^m$ is travel time from grid centroid $i$ to school $j$ under mode $m$; $d_r^m$ is the search radius for tier $k$ under mode $m$; $p_i^m$ is the number of children traveling from grid $i$ under mode $m$; and $G_K$ is the Gaussian weight:

$$
G_K = \exp\left(-\beta \frac{d_{ij}^2}{d_r^2}\right)
$$

Following Cheng et al. \cite{}, distance friction coefficients $\beta$ are set at 0.001, 0.002, 0.003, and 0.004 for provincial, municipal, district, and general kindergartens respectively. $G_K = 0$ when exceeding the service radius.

Step 2: From each grid centroid $i$, we search for supply points $j$ within the service radius, weight their $R_j$ values using the Gaussian function, and sum them to obtain mode-specific accessibility ($A_i^m$):

$$
A_i^m = \sum_{j \in {d_{ij}^m \leq d_r^m}} R_j \times G_K
$$

Step 3: Different travel modes yield varying accessibility quality, ranking as: walking > bicycling/e-biking > public transit > car. Using Analytic Hierarchy Process (AHP) with consistency ratio $CR = 0.044 < 0.1$, we derive mode weights and calculate comprehensive accessibility ($A_i$):

$$
A_i = 0.56 \times \text{walking} + 0.26 \times \text{bicycling/e-biking} + 0.12 \times \text{bus} + 0.06 \times \text{car}
$$

2.3 Spatial Regression Model

Spatial regression models examine spatial associations in geographic phenomena \cite{}. Following Lagrange Multiplier (LM) tests on OLS regression, we selected the Spatial Error Model (SEM) as more appropriate for explaining spatial effects, given non-significant robust LM (lag) results.

The SEM formula is:

$$
y = \rho W_y + X\beta + \varepsilon
$$

where $y$ is the dependent variable (overall kindergarten accessibility); $X$ represents explanatory variables; $\beta$ are coefficients; $W_y$ is the spatial lag term; $\rho$ is the spatial lag coefficient; and $\varepsilon$ is the error term.

Kindergarten location directly affects accessibility, closely linked to permanent population, educational finance, and transportation. We construct indicators from supply-demand perspectives (Table 4): (1) School-age children: distribution and quantity directly affect kindergarten placement and enrollment choices; (2) Family economic status: better-off families have more enrollment options, while disadvantaged families face constrained choices; (3) Road network density: high density can alleviate congestion and improve accessibility; (4) Bus stops: given Lanzhou's valley topography, residents rely heavily on walking and buses; (5) Kindergarten tuition: high fees burden families, reducing accessibility to quality kindergartens; (6) Enrollment quota: directly affects resource allocation and enrollment opportunities.

2.4 Bivariate Spatial Autocorrelation

Bivariate spatial autocorrelation analyzes spatial dependency between accessibility and explanatory variables, visualized through LISA cluster maps. Formulas follow established literature \cite{}.

3. Results

3.1 Spatial Distribution Characteristics

3.1.1 Overall kindergarten distribution
Kindergarten density follows the pattern: Chengguan > Qilihe > Anning > Xigu, showing clear "one core, four centers" characteristics (Figure 2). The "core" is a high-density zone around Yannan, Yanbei Subdistricts, and the High-tech Zone, with concentration far exceeding other areas. This core formation results from multiple factors: the High-tech Zone, formerly an old urban district and national high-tech industrial park, hosts numerous research institutions, forming an education center that attracts kindergarten resources. Yannan and Yanbei Subdistricts, developed during Lanzhou's eastward expansion, contain large commercial residential complexes with dense populations and strong demand.

The four "centers" are: (1) Zhangye Road, Jinquan Road, Wuquan, and Guangwumen Subdistricts in Chengguan; (2) Xiyuan, Xihu, Xizhan, and Dunhuang Road Subdistricts in Qilihe; (3) Yintan Road, Kongjiawan, and Xilu Subdistricts in Anning; (4) Xigucheng, Sijiqing, and Lin Tao Street Subdistricts in Xigu.

3.1.2 Distribution by kindergarten tier
Provincial, municipal, district-standard, and general kindergartens each show "single-core" patterns. Provincial-standard kindergartens cluster around Jinquan Road, Zhangye Road, and Guangwumen Subdistricts—the true old city with concentrated high-quality educational resources. Municipal-standard kindergartens center on Yannan, Yanbei, and Weiyuan Road Subdistricts, driven by strong population attraction. District-standard kindergartens concentrate in Xiuchuan, Tumen Dun, Xizhan, and Dunhuang Road Subdistricts in Qilihe. General kindergartens share the "core" with overall distribution, surrounding Yannan, Yanbei, and the High-tech Zone (Figure 3).

3.2 Accessibility Distribution Characteristics

3.2.1 Overall accessibility
Using geometric interval classification, accessibility is divided into five levels: high, relatively high, medium, relatively low, and low. The main urban area shows an eastward-weighted, "south-superior-north-inferior" pattern, with Chengguan-Qilihe clusters outperforming Anning-Xigu clusters, and southern Yellow River banks surpassing northern banks (Figure 4). High and relatively-high accessibility areas are located at growth poles in each cluster, though economic development differences create varying scales. Chengguan and Qilihe have the most high-accessibility grids (1,051 and 1,022, representing 10.5% and 10.2% respectively), while Anning and Xigu have the most low-accessibility grids (3,580 and 3,870, representing 35.8% and 38.7% respectively). This reflects peripheral areas' "high location value but low resource allocation" dilemma, with poor road networks and long distances reducing accessibility.

3.2.2 Accessibility by kindergarten tier
All tiers show "multi-center" accessibility patterns. Provincial-standard kindergartens have high-accessibility zones near the provincial government in Chengguan, Northwest Normal University in Anning, and Lanzhou University of Technology in Qilihe—areas with government institutions, enterprise compounds, and excellent transport. Municipal-standard kindergartens show fewer high-accessibility zones, with relatively-high zones forming multi-centers around the provincial government, Dongfanghong Square, Lanzhou University, Yannan/Yanbei/Yuanyuan Subdistricts, Yintan Road/Kongjiawan/Peili Subdistricts in Anning, and Jianlan Road/Dunhuang Road Subdistricts in Qilihe.

District-standard kindergartens show prominent relatively-high accessibility in Qilihe, covering most central areas including Xiyuan, Xihu, Xizhan, Dunhuang Road, and Xigucheng/Chenping Subdistricts in Xigu, due to abundant schools and places. General kindergartens show the most high-accessibility zones across all districts in multi-center patterns, reflecting their primary role in meeting local enrollment demand (Figure 5).

3.3 Influencing Factors

Spatial regression analysis (Table 6) and bivariate spatial autocorrelation (Table 7, Figure 6) reveal:

School-age population shows positive correlation with accessibility, consistent with existing research \cite{}. Central areas exhibit "high-high" clusters, while peripheral areas show "low-low" patterns. The valley topography creates a "belt-shaped, multi-center" population layout, with school-age children naturally following this distribution. Central areas' superior location and historical accumulation attract population, driving kindergarten expansion and increasing accessibility.

Family economic status positively correlates with accessibility. "High-high" clusters concentrate around Dongfanghong Square and the provincial government in Chengguan—prime locations with dense commercial, cultural facilities, and advanced transport networks. Adjacent "low-high" areas reflect intense enrollment competition despite high child density, revealing unequal access opportunities across economic strata.

Road network density and bus stops show negative spatial relationships with accessibility, but without statistical significance. This contrasts with some street-scale studies \cite{}. Lanzhou's valley morphology makes walking the dominant mode for school transport. Dense road areas suffer heavy traffic, and constraints like road closures and parking restrictions mean high network density doesn't guarantee high accessibility. However, "high-high" clusters in prime Chengguan and Qilihe areas feature dense bus stops with smooth pedestrian-transit connections, yielding high accessibility.

Kindergarten tuition and enrollment quotas show negative and positive relationships respectively. High tuition burdens families, particularly middle-low income households, forcing some to forego quality kindergartens and reducing accessibility—reflecting how current systems don't ensure fair competition opportunities. Enrollment quotas directly affect place availability; more places increase enrollment opportunities and accessibility. "High-high" clusters for tuition appear in areas dense with provincial, municipal, and district-standard kindergartens, where demand for quality resources creates "educational gentrification" through spatial binding of high-quality, high-income, and high-cost kindergartens.

4. Discussion

This analysis provides references for optimizing kindergarten resource allocation. First, planning should follow urban development and school-age population scales, with reasonable layouts. For capacity-surplus areas like Yannan, Yanbei, and Jinquan Road Subdistricts, control expansion to consolidate quality. For capacity-scarce areas like Yanchang Road, Qingbaishi Subdistrict in Chengguan, and southern Xiuchuan Subdistrict in Qilihe, add facilities to meet urgent demand. Second, multi-department coordination should optimize road networks and enrollment policies, such as staggered school schedules to ensure safe travel and improve accessibility.

Limitations remain. First, education department planning follows "nearby enrollment" and "single-school zoning" principles based on street-level child populations and school scales, while urban planning emphasizes "reasonable service radius," creating spatial conflicts between "zoning boundaries" and "planning boundaries." This study calculates accessibility based on reasonable radii for different tiers without considering zoning effects. Second, industrial relocation, residential demolition/construction, and new fertility policies create uncertainty and complexity in accurately predicting school-age populations, affecting accessibility measurements.

5. Conclusions

1. Spatial distribution: Kindergartens show "one core, four centers" belt-shaped distribution, with highest density in Chengguan District. High-density areas cluster where commercial, cultural, transport, and educational resources converge, while low-density areas appear in economically underdeveloped zones—closely linked to Lanzhou's eastward expansion planning history. Provincial, municipal, district-standard, and general kindergartens each exhibit "single-core" patterns, with strong factor mobility and intensive resource allocation under market mechanisms.

2. Accessibility patterns: Overall accessibility shows eastward-weighted, "south-superior-north-inferior" bias. Peripheral low-accessibility areas face the dilemma of "high location value but low resource allocation," with sparse networks and long distances. Different quality tiers all show "multi-center" accessibility patterns, with general kindergartens having the most high-accessibility areas, confirming their primary role in local enrollment.

3. Influencing factors: Spatial regression shows school-age population, family economic status, and enrollment quotas significantly positively affect accessibility, as dense child populations drive expansion and higher socioeconomic status enables greater educational investment. Road network density and bus stops negatively affect accessibility (non-significantly), reflecting valley topography's promotion of walking and traffic constraints in dense areas. Kindergarten tuition negatively affects accessibility by burdening families and reducing access to quality kindergartens.

References

\cite{} Sha Li, Zhang Xiaojuan, Kang Liying. The creation and evolution of the concept of Kindergarten: Based on an analysis of historical semantics[J]. Educational Research, 2023, 44(9): 51-63.

\cite{} Li A-fang, Wang Xiaoying. The development logic of the supply subjects of preschool education in China based on the perspective of historical institutionalism[J]. Studies in Early Childhood Education, 2021(12): 13-22.

\cite{} Liu Qian. How to control the risk of the implementation of public private partnership model in early childhood education in China: From the perspective of international concern[J]. Educational Development Research, 2016, 36(20): 34-40.

\cite{} Cheng Fangping, Feng Fangfang. The evolution of the government's role in the development of preschool education in China and its influencing factors[J]. Journal of Hebei Normal University (Educational Science Edition), 2024, 26(3): 114-124.

\cite{} National education supervision team's special supervision and inspection bulletin on early childhood education[J]. Preschool Education Research, 2005(9): 5-6.

\cite{} Li Yan, Li Shaomei. A study on Chinese quality evaluation policy changes of kindergarten based on multiple streams theory[J]. Journal of Shaanxi Xueqian Normal University, 2024, 40(5): 105-112.

\cite{} Tao Zhuolin, Dai Teqi, Song Changqing. Improving spatial equity-oriented location allocation models of urban medical facilities[J]. Acta Geographica Sinica, 2023, 78(2): 474-489.

\cite{} Li Bo. Spatial distribution characteristics and accessibility analysis of medical facilities in Dalian based on two step mobile search method[J]. Geomatics & Spatial Information Technology, 2024, 47(5): 87-89.

\cite{} Tao Zhuolin, Cheng Yang. Research progress of the two step floating catchment area method and extensions[J]. Progress in Geography, 2016, 35(5): 589-599.

\cite{} Song Zhengna, Chen Wen, Zhang Guixiang, et al. Spatial accessibility to public service facilities and its measurement approaches[J]. Progress in Geography, 2010, 29(10): 1217-1224.

\cite{} Zhang Yanlin, Li Min, Liu Yuwen, et al. Spatial accessibility analysis of primary educational resources based on student home address and geocoding: A case study in Zhuzhou County, Hunan Province[J]. Scientia Geographica Sinica, 2022, 42(6): 993-1004.

\cite{} Kong Yunfeng, Li Xiaojian, Zhang Xuefeng. Analysis of spatial accessibility for school redistricting in rural China: A case study of the secondary schools in Gongyi City, Henan Province[J]. Journal of Remote Sensing, 2008, 12(5): 800-809.

\cite{} Tang Pengfei, Xiang Jingjing, Luo Jing, et al. Spatial accessibility analysis of primary schools at the county level based on the improved potential model: A case study of Xiantao City, Hubei Province[J]. Progress in Geography, 2017, 36(6): 697-708.

\cite{} Lin Peng. A review of accessibility research methods[J]. Western Resources, 2022(1): 194-200, 202.

\cite{} Wang Jing, Gao Xiangdong. Research on spatial accessibility and equity evaluation to residential care facilities in Shanghai[J]. Shanghai Economy, 2018(3): 44-56.

\cite{} Zhang Jingxiang, Ge Zhibing, Luo Zhendong, et al. Research on equalized layout of urban and rural public facilities: A case study of educational facilities in Changzhou[J]. City Planning Review, 2012, 36(2): 9-15.

\cite{} Han Fei, Luo Renchao. Matching of supply and demand for community service oriented home care facilities based on accessibility measurement: A case study of Nanjing[J]. Economic Geography, 2020, 40(9): 91-101.

\cite{} Cheng Shunqi, Qi Xinhua, Lin Han, et al. The improvement and application of two step floating catchment area method in measuring accessibility to educational public service: A case study of kindergartens in Fuzhou[J]. Human Geography, 2017, 32(3): 53-60.

\cite{} Dai Jiaxin. Research on the concept, measurement and influencing factors of accessibility: A literature review[J]. Learning and Practice, 2017(4): 86-94.

\cite{} Wang Fan, Bai Yongping, Zhou Liang, et al. Spatial pattern and influencing factors of the equalization of basic education public service in China[J]. Geographical Research, 2019, 38(2): 285-296.

\cite{} Mo Huibin, Luo Ke, Wang Shaojian, et al. Spatial heterogenicity and mechanism difference of restaurant in the central urban area of Guangzhou: A comparison between traditional restaurant and take-out restaurant[J]. Geographical Research, 2022, 41(12): 3318-3334.

\cite{} Wang Shiqiong, Liu Rui, Dai Jicai, et al. Availability differences and influencing factors of rural compulsory education resources in Chongqing[J]. Tropical Geography, 2022, 42(8): 1349-1362.

\cite{} Huang Tao, Wang Yanhui, Guan Hongliang, et al. Research on the coupling characteristics of time and space between rural basic public services and multidimensional poverty under the background of rural revitalization[J]. Human Geography, 2021, 36(6): 135-146, 192.

\cite{} Zheng Luanjuan, Xiao Tong, Liu Ye, et al. Using multiple travel mode two step floating catchment area (2SFCA) approach to measure the spatial accessibility of primary schools in Dongguan City, China[J]. Progress in Geography, 2023, 42(7): 1341-1354.

\cite{} Wang Zilin, Li Zhigang, Cheng Hanbei. The equity of urban park green space accessibility in large Chinese cities: A case study of Wuhan City[J]. Progress in Geography, 2022, 41(4): 621-635.

\cite{} Cheng Fanfan, Bai Yongping, Liang Jianshe, et al. Spatial distribution characteristics and influencing factors of vegetable markets in Lanzhou City[J]. Arid Land Geography, 2024, 47(2): 293-306.

[FIGURE:1] Spatial distribution of quality kindergartens of different grades in the main urban area of Lanzhou City
[FIGURE:2] Kernel density of kindergartens in the main urban area of Lanzhou City
[FIGURE:3] Kernel density of kindergartens of different grades in the main urban area of Lanzhou City
[FIGURE:4] Accessibility of all kindergartens in the main urban area of Lanzhou City
[FIGURE:5] Kernel density of kindergartens of different grades in the main urban area of Lanzhou City
[FIGURE:6] Accessibility was autocorrelated with the bivariate space of their respective variables

[TABLE:1] Traffic speed of four modes of travel under each road level
[TABLE:2] Proportion of population under each travel mode
[TABLE:3] Service radius of kindergartens of different levels
[TABLE:4] Explanatory variables
[TABLE:5] Number and proportion of grids with different accessibility in each district
[TABLE:6] Results of spatial regression analysis of the impact of each variable on accessibility
[TABLE:7] Correlation of the respective variables with the bivariate spatial autocorrelation results of school accessibility