The Effect Of Primary School Size On Learning Mandarin As A Second Language: An Empirical Research On Ethnic Minority Students In China
Abstract
The purpose of this study was to explore the effects of school size in relation to the addedvalue of the Mandarin performance test. Data were collected from 5^{th} & 6^{th} Grades Mandarin academic tests, and a questionnaire. 3642 students and 158 principals were identified through stratified sampling from 158 primary schools in the Xinjiang Autonomous Region in China. The Hierarchical Linear Model (HLM) was used to analyse the data. Findings demonstrated that: 1) There is a positive linear relationship between school size and the Mandarin addedvalue scores, therefore the valueadded scores are greater. 2) Under the condition of nocontrolling background variable on the stated school sizes, students in the schools of more than 810 students got significantly higher addedvalue scores than their counterparts in the schools of less than 810 students. However, under the additional condition of controlling background variables, there is no such relationship between them. This study may help the educators and government improve Mandarin education in minority areas in China.
Keywords: School SizeAddedvalue scoresMandarin performance test
Introduction
The influence of school size (school scale) has been central to the field of education research for half a century. In international studies, the school size is widely associated with the number of students and the school number. Considering the comparability between them, the school size concept will be used in demonstrating the empirical results here.
Background
China is a multiethnic country, where different ethnic groups have their own languages. In these autonomous regions, Mandarin is the second language which they learn in school. Mandarin can make ethnic minority students in China become more competitive and have more chances of employment. They start to learn how to speak, read, and write in Mandarin since their primary education. For most of these students, however, school is the only place where they can practice or communicate with each other in Mandarin. School is the most important factor here, a place for them to learn Mandarin. In addition, the influence of school size on students’ Mandarin learning also cannot be ignored.
Literature Review——Effects of School Size on students' academic performance
The effects of School Size can be traced back to 1960s which have determined the results of the empirical researches on school factors including the school size influence on the students' academic achievement. The American scholar Kiesling et al. (1968) stated that there was a significant negative correlation between the primary students' school performance and high school size in New York school districts. After 20 years, especially in the primary stage, most empirical studies showed that smaller schools had more independent and positive effects on the student's academic performance than the larger ones. Since 1990, based on a large sample of empirical research, 57 studies were made on school size. The research data used were generated by The Trends in International Mathematics and Science Study (TIMSS) and the National Education Longitudinal Study of 1988 (NELS: 88). 9 out of these studies were related to primary school, however, no significant correlation between school size and students’ academic performance was found (Saddoski & Willson, 2016). In 1990, the studies conducted by Ebert et al. demonstrated that there was a significant negative correlation between them, which means that, the smaller the school is, the better the student's academic achievement is. In the previous literature of school size and academic performance, there were 19 studies related to high school. Bradley and Taylor et al. developed five studies (1998), and they identified that as the school size grew, students’ academic performance and the annual increment soared. Evidence from Swakins et al’s six studies indicated that an inverted Ushape relationship existed between the school size and the academic performance and the optimal school size was 1200 students. Before the inflection point of 1200 students, student’s academic performance increased while after that point, a decline followed.
Andrews et al. (2002) found from their eight studies that along with the growth of the school size, there was a trend of decline in the students' academic performance. In 2009, Kenneth published a paper based on the relationship between school size and students’ social and economic background. Kenneth concluded that for primary schools, when most of the students were from disadvantaged or complex social and economic groups, the optimal number of students should be limited below 300; when the students they serve are largely from the advantaged social and economic groups or of diverse backgrounds, the school size should be below 500 students. For high schools, most of the students were from disadvantaged or complex social and economic groups, the optimal number of students should be limited below 600; when the students they serve are from a diverse social and economic background or a single student groups, the school size should be below 1000 students.
Apparently, the abovementioned empirical research led to different results regarding the influence of school size on students’ performance. The American scholar Jacob (2009) pointed out that the three factors attributed to the difference. First of all, there was a lack of unified definition of the core concepts in previous literature. For instance, the criteria of delimiting the school size, the critical path to distinguish largesize from smallsize school, was not fully defined. Another example is the measurement of student’s academic achievement. It was measured by the standardized test scores and graduation rates. The measurement should be replaced by the current annual academic performance? Which one is more valuable? Second, in terms of data analysis method and its design, most researchers did not consider the characteristics of nested data, and they mainly use the traditional correlation analysis, regression, analysis and other methods. Finally, there are background variables that may affect the education fair. While studies did not usually control the background variables, some studies control socioeconomic variables; in the meantime, some studies also controlled other variables such as school regional, students' gender variables.
Problem Statement
Although there was a large quantity of literature about the influence of school size on student’s academic performance internationally, there are no research on the relationship between school size and Chinese ethnic minority students' performance in Mandarin learning. In order to address this gap, there should be more empirical research of a larger sample on the relationship between school size and ethnic minority students’ academic performance in Mandarin learning.
Research Questions
This research uses stratified sampling (classes) in proportion of 10%. Because several counties in Xinjiang Province almost have no minority students although there are 98 counties in total. According to the proportion of 10% extraction below 1 class, the number of extracting counties is 91. Moreover, 158 primary schools in Xinjiang including 3642 6^{th} Grade student took part in this research. Among them, there are 1658 male students and 1984 female students, which account for 45.5% and 54.5% of sampling students respectively. All the information comes from the statistical data of "Xinjiang Assessment toward Bilingual Education Quality " (20122013).
The data collection tools include 5^{th} Grade Mandarin academic test, 6^{th} Grade Mandarin academic test, 6^{th} Grade student questionnaire, and school principal questionnaire.
Mandarin academic tests
The Mandarin academic tests used in the research are set by language experts in line with the "Chinese Curriculum Standards for Compulsory Education" (
Student Questionnaire and School Principal Questionnaire
The student questionnaire is set based on the study of the literatures regarding the assessment of educational quality. Prior to this research, we conducted indepth interviews for Mandarin teachers and sixth grade students. Psychological and Educational experts were invited to participate in the preparation of the questionnaire process. The student questionnaire includes demographic information, such as students’ family background information and the school principal questionnaire includes the bilingual teaching type of school, school district, school size, etc.
Purpose of the Study
This study is based on the provincial compulsory education of tracing data characteristics of academic quality monitoring, using the method of empirical study, along with suitable methods with nested data structure of the multilayers linear model method. This is controlled under the students’ condition and the school background variables to explore the relationship between the school size and students’ academic performance (percent of pass, valueadded scores). The findings here may help the educators and government improve the mandarin education in minority areas in China. Furthermore, this study will explore other variables which may affect students’ mandarin learning, such as students’ level of background variables including gender, ethnic category, and family socioeconomic status, and the level of school background variables including the schools’ socioeconomic status, school areas, and school type.
Research Methods
Samples of 3642 students from 2011 to 2013 participated in the
Variable Selection
In the research, we use the
School Size, (SCHSIZE) : Independent Variable, classified variable. Based on the documents specified on "Primary School Management" which was made by the former State Education Commission of China (1996), the number of classes should notexceed 45 students. Accordingly, we first determined that there is only one class in each grade, and six grades in each school. Therefore, we take this as a starting point for calculating that 45students × 6grades = 270 students, and then escalating step by step and formulating our school size.

AddedValue: Dependent Variable, continuous variable, the increasing scores of Mandarin competency test or the academic performance indicators in this research. This refers to the students from fifth grade to sixth grade valueadded scores of the Mandarin competency test, which reflects the improvement of students’ Mandarin competency in a year. 
Gender: Control Variables, classified variable. 
Ethnic Groups (ETHGRO) : Control Variables, classified variable. According to the Ethnic Group which the students belonged to, we divided the students into eight groups, including Kazak, Han, Hui, Khalkhas, Mongolian, Tajik, Uighur, Uzbek, and we encoded them from 1 to 8. 
Social Economic Status(SES): Control Variables, continuous variable. Based on the International Standard Classification of Education (ISCED) (OECD, 2009), our SES index is derived from three variables related to family background: highest level of parental education (in number of years of education according to the ISCED classification), highest parental occupation (HISEI score) and the number of home possessions (WLEs). Specifically, we used these three variables because the socioeconomic status is usually based on education, occupational status, and income. As no direct income measure is available from the data collected, the existence of household items is used as an approximate measure of family wealth. 
School Social Economic Status(SCHSES): Control Variables, continuous variable. We use the mean of students’ family socioeconomic status scores to calculate our social and economic status index. 
School District(SCHDIS): Control Variables, classified variable. According to the school district, we divided all schools in the research into four districts 
School Type(SCHTYPE): Control Variables, classified variable, based on the forms of teaching organization. All the schools are public in our research, and we divided these schools into two types: 1. Mandarin is just said in their Mandarin class, or students used it just for the Mandarin competency test, which means that they almost don’t use Mandarin in other courses; 2. All courses at school are mainly taught in Mandarin.
Data Analysis Method
The missing values for students with one missing response and two valid responses were imputed with predicted values plus a random component based on a regression of the variable with missing responses on the other two variables. Variables with imputed values were then transformed into an international metric using the OECD averages of 0 and the OECD standard deviations of 1. These OECD standard variables were used for a principal component analysis by applying an OECD population weight giving each OECD country a weight of 1000.
We use the method for a multilayer Linear Model to process the data. Comparing it to the traditional regression method, it has a relatively weak statistical hypothesis, and it can make full use of the given information of different levels. It has the advantage of estimating more accurately and interpreting more reasonably. The multilayer linear analysis software package HLM6.08 is the common tool to deal with nested data. In this research, we mainly use two main layers of linear model: the first layer level for the students, the second level for the school.
In the process of analysis, it mainly includes three models:
Level1: (Student Level) ${\mathrm{Y}}_{\mathrm{i}\mathrm{j}}$ = ${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ + ${\mathrm{\gamma}}_{\mathrm{i}\mathrm{j}}$
Level2: (School Level) ${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ = ${\mathrm{\gamma}}_{\mathrm{00}}$ + ${\mathrm{\mu}}_{\mathrm{0}\mathrm{j}}$
Level1: (Student Level) ${\mathrm{Y}}_{\mathrm{i}\mathrm{j}}$ = ${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ + ${\mathrm{\gamma}}_{\mathrm{i}\mathrm{j}}$
Level2: (School Level) ${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ = ${\mathrm{\gamma}}_{\mathrm{00}}$ + ${\mathrm{\gamma}}_{\mathrm{0}\mathrm{j}}$SCHSIZE + ${\mathrm{\mu}}_{\mathrm{0}\mathrm{j}}$
Level1: (Student Level) ${\mathrm{Y}}_{\mathrm{i}\mathrm{j}}$ = ${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ + ${\mathrm{\gamma}}_{\mathrm{i}\mathrm{j}}$
Level2: (School Level) ${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ = ${\mathrm{\gamma}}_{\mathrm{00}}$ + ${\mathrm{\gamma}}_{\mathrm{01}}$SCHSIZE + ${\mathrm{\gamma}}_{\mathrm{02}}{\mathrm{S}\mathrm{C}\mathrm{H}\mathrm{S}\mathrm{I}\mathrm{Z}\mathrm{E}}^{\mathrm{2}}$ + ${\mathrm{\mu}}_{\mathrm{0}\mathrm{j}}$
Level1: (Student Level)
${\mathrm{Y}}_{\mathrm{i}\mathrm{j}}$ = ${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ + ${\mathrm{\beta}}_{\mathrm{1}\mathrm{j}}$SES + ${\mathrm{\beta}}_{\mathrm{2}\mathrm{j}}$Gender + ${\mathrm{\beta}}_{\mathrm{3}\mathrm{j}}$ETHGRO + ${\mathrm{\gamma}}_{\mathrm{i}\mathrm{j}}$
Level2: (School Level)
${\mathrm{\beta}}_{\mathrm{0}\mathrm{j}}$ = ${\mathrm{\gamma}}_{\mathrm{00}}$ + ${\mathrm{\gamma}}_{\mathrm{01}}$SCHSIZE + ${\mathrm{\gamma}}_{\mathrm{02}}$SCHSES + ${\mathrm{\gamma}}_{\mathrm{03}}$SCHDIS + ${\mathrm{\gamma}}_{\mathrm{04}}$SCHTYPE + ${\mathrm{\mu}}_{\mathrm{0}\mathrm{j}}$
${\mathrm{\beta}}_{\mathrm{1}\mathrm{j}}$ = ${\mathrm{\gamma}}_{\mathrm{10}}$ ; ${\mathrm{\beta}}_{\mathrm{2}\mathrm{j}}$ = ${\mathrm{\gamma}}_{\mathrm{20}}$ ; ${\mathrm{\beta}}_{\mathrm{3}\mathrm{j}}$ = ${\mathrm{\gamma}}_{\mathrm{30}}$ ;
${\mathrm{\mu}}_{\mathrm{0}\mathrm{j}}$ is the random effects of Level 2, the mean is 0, and the variance is ${\mathrm{\tau}}_{\mathrm{00}}$.
Findings
The influence of school size valueadded scores to the school

Analysis about Null Model results and the relationship between school size and school valueadded scores
From the Null Model, we get the results and find the relationship between school size and school valueadded score analysis as follows:
From table
Based on Model 1, we add school variables in Level2 of Model 2, and we get the results as follows:
In the Model 2b, we add variables school size and school size square, and the results are as follows:
From table
Analysis regarding the influences of school size on valueadded scores
The research analysis is based on the linear relationship of school size and the addedvalue scores. We explore whether there is a critical point of the school size that has influenced the school valueadded scores on a changing path.
As table
In Model 2a (noadding control variables), we find that size 1, size 2, and size 3 vary significantly between different schools compared to size4, size 5, size 6. Schools with size 13 are significantly lower than those schools with size 46 on the addedvalue scores of the Mandarin competency tests. We didn’t find a significant difference between schools with size 46, and there was no significant difference between schools with size 13 in the research either. On the noadding control variables condition, there is a critical value between size 3 and size 4 (size = 810 students), the schools with size > 810 students get a higher added value than the schools with size ≤ 810 students. However, on the adding control variables condition, after we added the school district, the school socialeconomic status, the school teaching type into the school model, added gender, ethnic group, and family socialeconomic status into the student model, we found that there were no significant differences between different school sizes.
Conclusion
The relationship between school size and Mandarin competency test
Research has shown that there is a positive linear relationship between school size and Mandarin scores, so the greater the school size is the higher the addedvalue scores are. While this result is incompatible with what the previous studies showed, it is consistent with other findings in this area. Schreiber (2002) studied the effects of school size, gathering students’ scores of 1839 students in TIMSS test from 162 schools, and the result showed that larger school size is associated with higher academic achievement. In 2003, the research conclusion of PISA has also shown that there is a significant positive correlation between school size and academic achievement. Considering the status quo of the bilingual ethnic groups teaching in China, compared to the smaller schools, the immediate cause of largersize primary schools’ Mandarin performance may be better because it has better teaching conditions, students with a better status background, a higher amount of quality teachers, however, this still needs more evidence through further research.
The effects of school size borderline for the school addedvalue scores
Focusing on the school size borderline, we found that it is consistent with the pursuit of increasing the educational efficiency and quality. In our research, for Mandarin addedvalue scores, under the nocontrolling variables condition, students’ academic performance in schools of more than 810 students had significantly higher addedvalue scores than their peers in the schools of less than 810 students. This means that 810 students could be the borderline of Mandarin addedvalue, however, 810 is the minimum number of school size. But after adding the controlling variables (family social economic status, gender, ethnics into the student level; and we add school social economic status, school district, school teaching type into the school level), the borderline vanished. The result is very different from Kenneth’s (2009) statement that 500 was the borderline.
Although some valuable conclusions are obtained in this research, the present situation of bilingual education in ethnic primary schools in China is complex. Further exploration and discussion are needed. In ethnic minority areas in China, the government tends to invest more on larger primary schools, so larger ethnic schools’ educational conditions will be better than smaller ones with richer resources. This means that there are other factors that could mediate or moderate the relationship between school size and Mandarin addedvalue scores.
References
 Andrews, M., Duncombe, W., & Yinger, J. (2002) Revisiting economies of size in American education: Are we any closer to a consensus? [J]. Economics of Education Review, 2002, (21).
 Bradley, S., & Taylor, J. (1998) The effect of school size on exam performance in secondary schools [J]. Oxford Bulletin of Economics and Statistics, 1998, (3).
 Eberts, R. W., Schwartz, E. K., & Stone, J. A. (1990) School reform, school size and student achievement [J]. Economic Review, 1990, (2).
 Jacob, W. (2009) The Impact of high school size on math Achievement and dropout rate [J]. The High School Journal, 2009, (3).
 Kenneth, L., & Doris, J. (2009) A review of empirical evidence about school size effects: A policy perspective [J]. Review of Educational Research, 2009, (1).
 Kenneth, L., & Doris, J. (2009) A review of empirical evidence about school size effects: A policy perspective [J]. Review of Educational Research, 2009, (1).
 Kiesling, H. (1968) High School Size and Cost Factors [M]. Washington, DC: U.S. Department of Health, Education and Welfare, Office of Education, Bureau of Research, 1968:1150.
 OECD (2012) Scaling Procedures and Construct Validation of Context Questionnaire Data [R]. Source OECD Education & Skills, 2012, (3).
 OECD. (2004) Learning for Tomorrow’s World First Result from 2003[R]. OECD Publishing, 2004: 255260.
 Sadoski, M., & Willson, V. L. (2006) Effects of a theoretically based large size reading intervention in a multicultural urban school district [J]. American Educational Research Journal, 2006, (1).
 Sawkins, J. W. (2002) Examination performance in Scottish secondary schools: An ordered logic approach[J]. Applied Economics, 2002, (34).
 Schreiber, J. B.(2002) Institutional and student factors and their influence on advanced mathematics achievement[J]. Journal of Educational Research, 2002, (95).
 William, J. F., William, J., & Walberg, H. J. (1991) school size, characteristics and outcomes [J]. Educational Evaluation and Policy Analysis, 1991, (2).
Copyright information
This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.
About this article
Publication Date
16 October 2017
Article Doi
eBook ISBN
9781802960303
Publisher
Future Academy
Volume
31
Print ISBN (optional)

Edition Number
1st Edition
Pages
11026
Subjects
Education, educational psychology, counselling psychology
Cite this article as:
Zhang, Y., Bian, Y., & Peng, H. (2017). The Effect Of Primary School Size On Learning Mandarin As A Second Language: An Empirical Research On Ethnic Minority Students In China. In Z. Bekirogullari, M. Y. Minas, & R. X. Thambusamy (Eds.), ICEEPSY 2017: Education and Educational Psychology, vol 31. European Proceedings of Social and Behavioural Sciences (pp. 226235). Future Academy. https://doi.org/10.15405/epsbs.2017.10.21