The Educational Values of Olympiad Maths in China: A Structural Model

Peijie Jiang, Tommy Tanu Wijaya, Maximus Tamur

ABSTRACT

Chinese students’ learning of Olympiad Maths has gradually evolved into the entrance examination, and the educational value of Olympiad Maths has been alienated. The purpose of this research was to clarify the educational values of Olympiad Maths and avoid the distortion of education attribute of it using a confirmatory factor analysis approach. The literature on education of Olympiad Maths was sorted out, relevant concepts were defined, and the educational values of Olympiad Maths were summarized. The educational values’ structural model of Olympiad Maths was established and a second order model is proposed based on the overall framework of the core literacy system of Chinese students’ development. A survey was carried out with a effective sample of 427 secondary maths teachers from 28 provinces in China. The questionnaire consists mainly of 12 Likert scale questions. IBM SPSS 22.0 and AMOS 22.0 were used to analyze the data and the structural models. The results showed that the questionnaire had good reliability and validity. The adaptive degree of the structural model was very high and the adaptive index was good. The model clarifies the educational values of Olympiad Maths itself, indicating that education attribute is the essential attribute of Olympiad Maths in China. Relevant researchers should better explore new methods, create new ideas and take practical actions to realize the educational values of Olympiad Maths, so as to avoid the alienation of education attribute of it, rather than merely talk about “keeping or abolishing” it.

Key words: Olympiad Maths; Educational Value; Structural Model; Mathematics

INTRODUCTION

A recent survey pointed out that, “in order to enable primary and secondary school students to achieve ideal results in all kinds of Olympiad Maths, targeted training has become the norm in China. Primary and secondary school students’ learning of Olympiad Maths deviates from the truth of Olympiad Maths, and it has evolved into the second field of education entrance examination”. (Suijun, J., & Shangzhi, W., & Shihu, L., & Yufeng, G., 2018) This truly presents the current situation of activities related to Olympiad Maths in China. Over the years, the drastic debate about Olympiad Maths had never stopped. Many people had waved flags for math competitions, but some had shouted angrily to cancel it at the same time. For

mathematical education researchers, they thought more calmly. They put forward that the educational value of Olympiad Maths was beyond doubt. They also proposed that every coin has two sides, and anything that goes beyond a certain point goes the other way. (Huawei, Z., 2007) Under the current situation that the theoretical basis of mathematical education itself was not firm, and the quality of its research was generally not high, (Lester, F. K., 2005) both debate and silent practice are beneficial exploration of mathematical education. While many students benefited from Olympiad Maths, many more seemed to suffer from it. However, the consensus needed to emphasize that, as part of the education of mathematics, Olympiad Maths itself was not wrong, and the educational values of it still needed to be further developed. Revealing the education attribute of Olympiad Maths was the key to reconciling arguments.

It’s not that the mathematical Olympiad itself is bad. It is not right for everyone to learn the Olympic mathematics. (Han, X., 2009) As is known to all, about 5 percent of students are suitable to study Olympiad Maths. It was also believed that Olympiad Maths is mainly for those who have strong learning ability and are interested in mathematics. It is not suitable for most students. The object of the Olympiad Maths education can only be those rare mathematical talents who account for about 3%. (Anjun, Y., 2009) But from a education fair point of view, it’s not appropriate to divide by pure proportion. Olympiad mathematics do have important educational value, and everyone is entitled to choose whether to study or not. Anyone who really voluntarily studies the Olympiad Maths and has enough learning capacity in the middle school mathematics should be accepted. In other words, though Olympiad Maths is part of mathematics education, the participants of learning Olympiad Maths are merely: students who are willing to participate in Olympiad mathematics study and have strong learning ability.

Some researchers have pointed out that math competitions not only selected a few top students, but also exercised the majority of teenagers who had participated in the activity. It is impossible and unnecessary for competition mathematics to undertake the weighty responsibilities of higher education and the whole society. (Zengru, L., 2005) The selection feature of Olympiad Maths is not its own attribute, but social additional. And the purpose of the Olympiad Maths is not to train mathematicians or even professional mathematical researchers. Olympiad Maths is never that powerful. In fact, there has never been enough evidence to prove that the study of Olympiad Maths is highly correlated with the study of modern mathematics. It is of highly importance to clarify the true educational values of Olympiad Maths and avoid the alienation of its education attribute.

Contribution of this paper to the literature

the educational value structural model of Olympiad
6 educational values of Olympiad Maths: cultural awareness, literacy development, interest cultivation, willpower training, extracurricular learning and creativity cultivation.
the essential attribute of Olympiad Maths is education

The general objective of the study is to sort out the educational values of Olympiad Maths in China and propose a structural model to describe the essential attribute of Olympiad Maths. The specific objectives are:

to sorting out and extracting educational values of Olympiad maths from relevant literature;
to construct educational value structural model of Olympiad mathematics;

to analyze the model by confirmatory factor

LITERATURE REVIEW

Olympiad Maths

Olympiad Maths, also known as competition mathematics, is a special mathematical discipline gradually formed with the development of mathematical competition. (Yuan, W., 1990) Its content is mainly defined by the outline of the national junior high school mathematics union competition and the national senior high school mathematics union competition formulated by the popularization work committee of Chinese mathematics society. The content of junior high school includes six modules: number, algebraic expression, equation and inequality, function, geometry and logical reasoning. The content of senior high school includes not only the mathematics knowledge of ordinary senior high school, but also the four modules of plane geometry, algebra, elementary number theory and combinatorial problem which specially examined in the addition test of senior high school mathematics joint contest. (Chuanli, C., & Tongjun, Z., 2005) The characteristics of Olympiad Maths are creative, challenging and developmental. The Olympiad Maths problem-solving methods and strategies include maths transformation, transformation to absurdity, symbolic-graphic combination, mathematical induction, pigeonhole principle, inclusion-exclusion principle, extreme principle, odd-even analysis, invariant, construction method, area method, calculate twice, dyeing method, recursive method, the method of graph theory and other particular methods. (Bin, X., & Yijie, H., 2012) Zun Shan, one of the top experts in Olympiad Maths in China, considers that Olympiad Maths is alive, it constantly exhales the old and inhales the new. (Wenxuan S., 2002) Therefore, Olympiad Maths itself is constantly changing and improving.

Education Attribute of Olympiad Maths

According to the interpretation of the modern Chinese dictionary (2012), attribute is the inherent property of things themselves. It is the inevitable, basic and inseparable property of matter, and it is also the qualitative expression of a certain aspect of things. Things are characterized by a multitude of attributes, with nature and not nature. Nature attribute is refers to the things’ fundamental properties which decided their appearances and developments. Education is to cultivate new generation ready to engage in the process of social life. It is mainly refers to the school training process for children and youth. Thus, education is the process of developing students’ knowledge, ability and quality through school (internal and external) courses. There are six educational values of Olympiad Maths from literature review: cultural awareness, literacy development, interest cultivation, willpower training, extracurricular learning and creativity cultivation.

Cultural Awareness

Olympiad Maths is one kind of education which benefits students to understanding mathematical culture. Some researchers had pointed out that Olympiad Maths was the popularization education of mathematical culture, and a lot vivid mathematics which reflects modern mathematical thinking and higher background were transported to middle schools through the bridge of it. (Zengru, L., 1996) This point of view is worth discussing in the word “popularization”, but there were some students who can indeed understand the thought and culture of mathematics from Olympiad Maths. Some even became excellent mathematician benefiting to mathematical competitions. The understanding of mathematical culture is mainly embodied in understanding mathematical thinking methods, understanding the context of specific mathematical concepts or propositions and realizing the value of mathematics.

Literacy Development

Olympiad Maths is the education which develops a high level of literacy. A high level of mathematical literacy means a deep understanding and comprehensive application of mathematical knowledge and methods. The problems of Olympiad Maths often involve little knowledge, but require a deep understanding of the knowledge. Only with a full insight into the relationship between knowledge and a skillful grasp of methods can the problems be solved. Research results show that Olympiad Maths is the quality-oriented education of developing intelligence. (Zengru, L., 1996) There are also studies express the view that the Olympiad Maths should be targeted at a small number of math talents, which is a kind of talent education. (Anjun, Y., 2009) In addition, since the general approach to the design of Olympiad Maths problems is the elementary achievement of higher mathematics, the regeneration of historical problems and the adaptation of the problems, (Zengru, L., 2005) the study of it requires high self-study and comprehension ability. The content of competition mathematics itself standardizes a kind of higher mathematics accomplishment.

Interest Cultivation

Olympiad Maths is the education which develops students’ interests in mathematics. The real interest in mathematics is in the intellectual activity of mathematics. It is a hobby of independent thinking that will have a lifelong impact on thoughts and character. (Polya, G., 1963) Some researchers emphasize that, contrary to the original purpose of promoting students’ interest in mathematics, the current mathematics competition has killed the interest of most teenagers in learning mathematics and hindered the overall and healthy development of most teenagers. (Ling, Z., 2010) However, what kills teenagers’ interest in mathematics and hinders their all-round development may be caused by the pressure of college entrance examination, incorrect guidance or excessive study burden. The reasons are complicated but the problem is not really in Olympiad Maths. On the contrary, the learning of Olympiad Maths mainly relies on students’ self-study, which is one of the best alchemy stones for students with real interest in mathematics. Through the study of Olympiad Maths, students can find out whether they really like mathematics or not. The study of competition mathematics does not affect the regular study of mathematics. On the basis of students’ willingness, if they do not do well in the study of Olympiad Maths, they can just give up and it has no impact on the daily study of mathematics. Through the learning of competition mathematics, one can experience the process of mathematical inquiry and rediscovery in solving competitive problems, comprehend the thinking and methods of mathematics, and experience the tension and joy of mathematical discovery. They are all conducive to the development of real interest in mathematics.

Willpower Training

Olympiad Maths is the education which sharpens the willpower of students. The learning competition mathematics requires strong self-study ability and strong willpower of students. The learning process of Olympiad Maths is the formation process of many good qualities and habits. Olympiad mathematics is developmental education mathematics, creative problem mathematics and challenging mathematics. Taking part in competitions enables students to experience that no pains, no successes. (Wenxuan, S., 2002) Competition mathematics learning requires students to take the initiative to participate in. Students should not flinch when they encounter a difficult problem, but take the initiative to think of ways to solve it. Students need to develop the habit of thinking slowly about problems that cannot be solved temporarily, and not be eager to achieve them in a moment. The study of competition mathematics takes a lot of time and students have to learn to sit on a cold stool. All these can temper students’ character. As is known to all, non-intellectual factors are crucial to the study of Olympiad Maths. In the face of difficult problems, to carry out psychological adjustment and to find a breakthrough need a series of intellectual factors and non-intellectual factors in the role. The study of competition mathematics helps

students to be determined, rational, calm and psychologically mature. Therefore, competition mathematics is the tempering of character of will.

Extracurricular Learning

Olympiad Maths is the extracurricular education which is highly competitive. For primary and secondary schools, Olympiad Maths is still mainly extracurricular education, and no school lists it as a formal mathematics course. Those “super high schools” just help students to learn competition math through the form of advanced placement classes. In the extracurricular, the students’ competition mathematics study is very common. “Aoshu fever” is not an overstatement. The process of students’ extracurricular participation in Olympiad mathematics is actually a process of choice and transaction: they voluntarily trade property to exchange the opportunity to accept Olympiad mathematics education and expect to reap the individual education benefits brought by education. (Ailiang, L., 2011) Although many students find it difficult to study competition mathematics, they are still willing to study hard, try hard, overcome difficulties and participate in some competitions. Everyone is competing with each other. Because the winners of the math contest can often get preferential treatment in terms of admission to higher education, competition in the study of Olympiad Maths is very fierce. It almost become the second school field outside the college entrance examination in China. That is why Olympiad Maths is controversial. As an extracurricular education, the training of competition mathematics often occurs in training institutions with different qualifications. However, the purpose and overall effect of those training seem to be inconsistent with the spirit of mathematics education. In a word, Olympiad mathematics is a competitive extracurricular learning content.

Creativity Cultivation

Olympiad Maths is the education which is the practical training of creative thinking. Mathematics is the gymnastics of the mind. Competition mathematics, which emphasizes the flexibility of thinking, is conducive to the development of students’ exploring intelligence and ability. (Weizhong, Z., 2004) It is one of the best ways to cultivate innovative thinking and creation awareness. Olympic mathematical problems are not routine exercises that can be solved only by memorizing and imitating, but problems with obstacles and probing factors. Under the guidance of general thinking rules of problem solving, it can be solved by comprehensive and flexible application of basic mathematical knowledge and methods on the basis of mastering basic skills, which is shown as a kind of creative activity. (Zengru, L., 2005) The problem solving process of competition mathematics, as Polya put it, is to find a way out of the difficulty to get over the obstacle and reach a goal that is not easy to achieve immediately. Problem solving is a special achievement of intelligence, (Polya, G., 1963) and the process of exploring and constructing a solution is a creative process. Creativity is the characteristic of competition mathematics. However, it

should also be pointed out that doing competition mathematics is conducive to innovation, but does not equal to innovation. (Zikun, G. & Naiqing, S., 2004) The creation here is not to create something that has never been done before, because competition mathematics is the mathematics that has already been done, and its problems are questions that have been preordained with clear answers. Although the problem has been solved, the students have worked out the solution by themselves. The construction of solutions by students is actually a process of re-creation. Therefore, doing competition mathematics is the practical training of creative thinking education.

George Polya’s Theory of Problem Solving

To answer the oft-asked question “how does a good solution come to mind?” George Polya specializes in the thought process of solving problems. He wrote his research results in the book How to Solve It, and later wrote Mathematics Discovery and Mathematics and Conjecture as the continuation of his thought. He established the thinking principle that can be used to solve mathematical problems at any level, which is known as the father of the theory on mathematical problem solving. He believes that the primary task of middle school mathematics teaching is to teach students to think, and one of the main ways for teaching students to think is to strengthen the the training of problem solving. The core of its problem solving theory is a problem solving table and its practical application. The table consists of four steps: identifying the problem, developing the plan, implementing the plan, and reviewing. It decomposes the thinking process of seeking solutions into five Suggestions and 23 enlightening questions, so that the problem solving table can constantly inspire people to make associations in the process of solving problems. (Alexanderson, G.L. & Pedersen, J., 1986)

The Conceptual Framework

Based on the above analysis, the general framework of Chinese students’ core quality development system led by Chongde Lin is the basic framework (Figure 1) of this research. Chinese students’ core qualities develop with “well-rounded people” as the core, including three fields of independent development, social participation and cultural foundation, and six core qualities indicators: learning to learn, live a healthy life, responsibility to bear, practice innovation, cultural atmosphere, scientific spirit. Culture is the root and soul of human existence, autonomy is the fundamental attribute of human being as the subject, and sociality is the essential attribute of human being. (Chongde, L., 2017) According to this general framework, we can further put forward the specific performance requirements of students in each section according to their age characteristics and subject characteristics.

Figure 1. General framework of Chinese students’ core literacy development system

The Hypothetical Structural Model

As an education task, the accomplishment goal to be achieved by competition mathematics is divided into three parts: cultural foundation, independent development and social participation. The cultural foundation emphasizes the ability to acquire knowledge and skills in humanities, science and other fields, master and apply the outstanding intellectual achievements of human beings, and cultivate the inner spirit. When it comes to competition mathematics, it can be described from two factors: cultural awareness and literacy development. Independent development emphasizes the ability to effectively manage one’s own study and life, recognize and discover one’s own value, explore one’s own potential, and effectively cope with the complex and changeable environment. When it comes to competition mathematics, it can be described from two aspects: interest cultivation and willpower training. The emphasis of social participation is to deal with the relationship between self and society, improve the spirit of innovation and practical ability. When it comes to competition mathematics, it can be described from the two aspects of extracurricular learning and creating practical training.

Based on the above framework and analysis, the preliminary model diagram (Figure

2) was set up according to the analysis of education attribute of competition mathematics. In the structural model, the education values of Olympiad Maths consist of three parts (cultural foundation, independent development and social participation) and six factors: cultural awareness, literacy development, interest cultivation, willpower training, extracurricular learning and creativity cultivation. The path coefficient of the six error variables was set as 1, and only the error variance of the six error variables was estimated.The initial covariant relationship between the six error variables is assumed to be 0. Since the error variables are not independent, the correlation of error variables can be added according to the need of model correction. In the CFA measurement model, the path coefficient of one indicator of each latent variable is fixed at 1. There are two observational indicators for each factor. The model has 39 free parameters (t) and 78 data points (DP), so the degrees of freedom

(DF) of the model is 78-39=39>0. The model is over-identified and further analysis can be carried out.

Figure 2. The hypothetical structural model

RESEARCH METHODOLOGY

The research is designed to construct a structural model of the Olympiad Maths’ educational values in China using a confirmatory factor analysis approach. Confirmatory factor analysis (CFA) takes the relevant theory and exploratory factor analysis (EFA) as the premise. It proposes a factor analysis model including implicit variables, and uses the actual data to fit the specific factor model and test it. CFA evaluates whether the measured indicators are consistent with the design objectives, verifies whether the specific factor analysis model is established, and estimates the factor load of hidden variables. The basic steps of CFA model include model setting, model estimation, model evaluation and model modification. (Tieniu, Z. & Hongwu,

& Guifen, L., 2010) The construction of the model is based on the literature and relevant theories. Survey is a common method to measure mathematics teachers’ attitude towards Olympiad Maths. This study is a quantitative and qualitative study, employing the questionnaire consists mainly of 12 Likert scale questions to collect data. The questionnaire was prepared and issued on WeChat platform. A total of 606 mathematics teachers in China participated in this study. Data from the questionnaire were keyed-in analyzed using IBM SPSS 22.0 software. AMOS 22.0 were used to establish structural models and verify them.

Cultural awareness (F1), literacy development (F2), interest cultivation (F3), willpower training (F4), extracurricular learning (F5) and creativity cultivation (F6)

are six potential variables reflecting education attribute of competition mathematics. The observation indexes (s1-s12, see Table 1) constitute 12 Likert scale questions in the questionnaire.

Table 1. latent variables and their observation indexes of the model

Structure	Latent Variables	Observation Indexes
	Cultural Awareness (F1)	Learning Olympiad Maths helps students understand the context of mathematics better (S1)
Cultural Foundation		Learning Olympiad Maths helps students to understand the value of mathematics (S2)
	Literacy Development (F2)	Olympiad Maths is the elementary of higher mathematics (S3)
		Learning Olympiad Maths requires higher mathematical literacy (S4)
	Interest Cultivation (F3)	Learning Olympiad Maths can cultivate students’ real interest in mathematics (S5)
Independent Development		Learning Olympiad Maths can develop students’ interest in intellectual thinking (S6)
	Willpower Training (F4)	Learning Olympiad Maths can shape students’ calm character (S7)
		Learning Olympiad Maths can cultivate students’ willpower (S8)
	Extracurricular Learning (F5)	Little Olympiad Maths will be taught in the form of an a-level training class in the school(S9)
Social Participation		Social training institutions are the main battlefields for students to learn Olympiad Maths (S10)
	Creativity Cultivation (F6)	There is often no ready-made solution for solving problems in Olympiad Maths (S11)
		Good imagination is needed to learn Olympiad Maths (S12)

The questionnaire consists of 2 information items and 12 Likert items. Sample items: (Information items) .

Do you know anything about Olympiad Maths? (Yes or No )

What’s your job title? (Junior, intermediate, subsenior, senior)

Sample items (Likert items): Scale 1 (Totally Disagree) – 5 (Totally Agree). 1.Learning Olympiad Maths helps students to understand the value of mathematics. 2.Olympiad Maths is the elementary of higher mathematics.

Good imagination is needed to learn Olympiad

RESEARCH FINDINGS

Demography

A total of 606 valid questionnaires were collected. Among them, 576 questionnaires were filled out by mathematics teachers who knew Olympic mathematics. Excluding the copies: filled in less than 60 seconds, IP address repeat, only filled agree and disagree with completely within two options (extreme thought), filled by the teachers who did not understand the competition mathematics, a total of 427 questionnaires are real effective. Teachers who provided the effective copies consists of junior teachers (17.56%), intermediate teachers (47.31%), subsenior teachers (31.38%), senior teachers (3.75%). The teachers are from 28 provinces in China, including Shanghai, Beijing, Jiangsu, Zhejiang, Hunan, Hubei, Guangdong, Guangxi and Yunnan.

Assessment of the Questionnaire

The reliability and validity of the questionnaire should be evaluated before the statistical analysis of the questionnaire survey to ensure the reliability and accuracy of the research results. Reliability mainly evaluates the accuracy, stability and consistency of the scale, that is, the degree of variation of the measured value caused by random errors in the measurement process. The assessment of reliability based on internal consistent reliability in this research. The coefficient work out according to Cronbach formula is the Cronbach Alpha coefficient. The higher the Alpha coefficient is, the better the correlation between items will be. In general, Alpha greater than 0.8 indicates excellent internal consistency, Alpha greater than 0.6 to 0.8 indicates good internal consistency, and Alpha lower than 0.6 indicates poor internal consistency. Validity mainly evaluates the accuracy, validity and accuracy of the scale, that is, the deviation between the measured value and the real value of the target. (Xiaohua, J., & Zhuozhi, S., & Nannan, Z. & Hongxiu, L., & Haiyan, X., 2010) In this study, structural validity was used. Factor analysis is a common statistical method for structural validity evaluation. KMO (kaiser-meyer-olkin) test statistics are indicators used to compare simple correlation coefficients and partial correlation coefficients between variables. KMO tests focus on the degree of correlation between indicators to

determine whether principal component or factor analysis can be performed. The closer the KMO value is to 1, the stronger the correlation between variables and the more suitable the original variables are for factor analysis. Kaiser has given the commonly used KMO measurement standard: 0.9 or above is very suitable; 0.8 indicates suitability; 0.7 means general; 0.6 means not suitable; Less than 0.5 is not appropriate. (Liping, Y., & Jun, L., 2018) The Cronbach Alpha coefficient of the questionnaire is 0.777(>0.7), and the reliability of the questionnaire is acceptable. The KMO value of the questionnaire is 0.852(>0.8), and the structural validity of the questionnaire is good. In SEM statistics, especially when researchers want to infer the sample results to the population, the sample requirements are higher. With the increase of sample size, the accuracy of covariance is enhanced, so that SEM analysis can provide more reliable results. Some researchers suggest that the ratio of the number of subjects to the free parameters should be at least 10:1. (Ping, F., & Duanqin, X., & Xuemei, C., 2002) There were 39 free parameters in the questionnaire and 427 sample papers were filled out effectively. The ratio between the number of samples and the number of free parameters exceeds 10:1, which can ensure the validity of the model significance test.

Assessment of the Structural Model

Chi-square value is the most commonly used evaluation index of structural equation model. The smaller chi-square value is, the better fitting effect will be. Researchers usually use the p-value of chi-square test to evaluate the model. When the p-value is greater than 0.05, the model does not reach the significance level of 0.05, and the model has a good fitting effect. Goodness-of-fit index (GFI) represents the variance and covariance obtained by model fitting can explain the variance and covariance degree of data data. Generally speaking, when the GFI is greater than 0.90, the fitting effect of the model is good. AGFI(adjusted GFI) adjusted the GFI using model degrees of freedom and number of parameters. Generally speaking, when AGFI is greater than 0.90, the model fitting effect is good. Another indicator is RMSEA (root mean square error of approximation). RMSEA between 0 and 0.05 indicates that the model fitting effect is very good; RMSEA between 0.05 and 0.08 indicates that the model fitting effect is good; RMSEA between 0.08 and 0.10 indicates that the model fitting effect is general; and RMSEA greater than 0.10 indicates that the model fitting effect is not good. (Song, L., 2008) After fitting, the model converged. The chi-square test value of the overall fitness of the model is 83.659, and the significance probability value is 0.000, reaching the significance level. The model diagram does not fit the observed data. When some items of different indicator variables have some similarity in the characteristics measured, it is theoretically reasonable to set the error variable of these indicator variables as a covariant relationship, which does not violate the empirical rule and the assumption of SEM. Therefore, when the model is modified, the measurement error variables of these indicator variables can be set as covariant. (Minglong, W., 2010) Since there is a theoretical correlation between various indicator variables in the Inappropriate SEM, the corresponding error variables are set

as covariant relations one by one to modify the model. After the model is modified, the degrees of freedom of the modified model is 31, the chi-square test value of the overall fitness of the model is 42.429, and the significance probability value is 0.083>0.05, failing to reach the significance level. It is assumed that the model diagram is compatible with the observed data. From the perspective of adaptation index value, AGFI value is 0.960>0.9, GFI value is 0.984>0.9, RMSEA value is 0.029<0.05, indicating that the model (Figure 3) has a better adaptability.

Figure 3. Adaptive measurement model

Table 2. Regression Weights

Table 2 shows the unstandardized regression coefficients estimated by the maximum likelihood method. Due to set “S5 <—F3” “S3 <— F2” “S9<— F5” “S7 <—F4”

“S2<—F1” “S11 <— F6” are unstandardized regression coefficients of the fixed parameter, and the fixed parameter’s value is 1. These parameters do not need to undertake the path coefficient significance test. The value of critical ratio (C.R.) is equal to the ratio between the parameter estimate and the standard error of estimate (S.E.), which is equivalent to the t-test value. If the absolute value of the value is greater than 1.96, the parameter estimate reaches the significance level of 0.05. The path coefficient estimation test is to determine whether the regression path coefficient estimation is equal to 0. If the significance level is reached (P<0.05), the regression coefficient is not significantly equal to 0. Table 2 shows that the path coefficients are all significantly different from 0.

Table 3. Standardized Regression Weights

Estimate				Estimate			Estimate
	S1<—F1	.859	S5<—F3	.738	S9<—F5	.734

	S2<—F1	.909	S6<—F3	.849	S10<—F5		.370

	S3<—F2	.359	S7<—F4	.734	S11<—F6		.307

	S4<—F2	.853	S8<—F4	.777	S12<—F6		.968

Standardized regression weights is also known as factor weights or factor loads in confirmatory factor analysis. Standardized regression coefficients represent the impact of common factors on measurement variables. The factor load value is between 0.50 and 0.95, indicating that the basic adaptability of the model is good. The larger the factor load value is, the greater the variation of the indicator variable can be explained by the observed indicator, and the indicator variable can effectively reflect the characteristics of the variable to be measured. Take “S1< F1” as an example, Table

3 shows the factor load value is 0.859. It means that when F1 goes up by 1 standard deviation, S1 goes up by 0.859 standard deviations. From the factor load values shown in table 2, the basic adaptability of the model is acceptable.

Table 4. The covariances between latent variables

F1<–>F2

.236 .047

5.014

***

F6<–>F4

.130

.044

2.935

.003

F3<–>F2

.249 .049

5.121

***

F1<–>F4

.386

.049

7.894

***

F3<–>F4

.478 .052

9.188

***

F2<–>F5

.072

.028

2.532

.011

F4<–>F5

.158 .049

3.215

.001

F6<–>F3

.118

.040

2.954

.003

F6<–>F5

.068 .028

2.377

.017

F1<–>F5

-.010

.049

-.200 .841

F1<–>F3

.523 .054

9.666

***

F1<–>F6

.085

.031

2.739

.006

F2<–>F4

.239 .049

4.837

***

F6<–>F2

.067

.025

2.671

.008

Table 5. Correlation coefficients between latent variables

Estimate		Estimate
F1<–>F2	.594	F1<–>F3	.740	F2<–>F5	.211
F3<–>F2	.751	F2<–>F4	.740	F6<–>F3	.483
F3<–>F4	.834	F3<–>F5	.103	F1<–>F5	-.013
F4<–>F5	.268	F6<–>F4	.547	F1<–>F6	.290
F6<–>F5	.269	F1<–>F4	.563	F6<–>F2	.489

Table 4 shows the estimated covariance among the six potential variables. If the covariance test results are significantly different from 0, the potential variables have a significant co-variation relationship. When the covariance of two variables reaches the significant level, the correlation coefficient of them reaches the significant level too. Taking “F3<—>F4” as an example, the covariance of F3 and F4 was 0.478, the standard error of covariance was estimated to be 0.052, and the critical ratio was 9.188, reaching the significance level of 0.05. Table 5 shows that the correlation coefficient of the two potential variables is 0.834 (>0.750), indicating that the two factors may have a higher order common factor. In addition, the measurement error values of 6 potential variables and 12 measurement indexes are all positive, and the estimated value of standard error of variation of them is between 0.025 and 0.065,

indicating that there is no definition error in the model. There is no negative error variance in the parameter estimation and the standard error estimation is very small, which indicates that the basic adaptation of the model is good.

Table 6. Squared Multiple Correlations

	Estimate		Estimate		Estimate		Estimate
S11	.094	S9	.539	S6	.720	S3	.129
S2	.826	S8	.604	S5	.545	S12	.938
S10	.137	S7	.538	S4	.728	S1	.738

The data in table 6 are the square of multiple correlations of the observed variables, indicating the amount of variation that the observed variable is explained by its potential variable, and the value of the explained variation is also the reliability coefficient of the corresponding measurement variable. Among them, except S11, S10 and S3, which are explained by their respective potential variables with the variance less than 0.50, the reliability coefficient of the other observation variables are all above 0.50, indicating that the internal quality test of the model is good.

DISCUSSION

The above model has a good overall adaptability, but it can still be modified. The second-order model can be considered. Overall, the above model clarifies the education value of competitive mathematics and the structural model of education values of competition mathematics can be represented by Figure 4.

It has long been pointed out by scholars that large-scale and younger-age Olympiad maths training does not conform to the basic law of students’ learning mathematics. (Qiping, K. & Xiaoling, Z., 2004) However, with the development of human civilization, the content that students of the same age have to learn is bound to become more and more difficult. The high development of human civilization puts forward higher requirements on human cognitive ability, which is an irresistible law for the development of human culture. In response to the adverse social phenomena related to competition mathematics, as some scholars pointed out, “education value of Olympiad Maths should be correctly recognized, and in-depth research on the relationship between educational value, function and purpose of Olympiad mathematics should be strengthened”. (Anjun, Y., 2009) “Re-examine the value orientation of mathematics competition in primary and secondary schools, change education concept, adjust content and difficulty”, (Bingzhang, X. & Liying, L., 2013) researchers of mathematics education must clearly understand the education attribute

of competition mathematics. It is meaningless to just talk about the “preservation or abolishment” of Olympiad mathematics in China. On the basis of defining the education attribute and its structure of competition mathematics, it is the practice which carry forward the advantages of competition mathematics with practical actions and avoid the limitations of competition mathematics that really benefit to the healthy development of education mathematics.

Figure 4. The structural model of educational values of Olympiad Maths

CONCLUSION

There are six educational values of Olympiad Maths: cultural awareness, literacy development, interest cultivation, willpower training, extracurricular learning and creativity cultivation. Education is the essential attribute of competition mathematics, which determines the nature, appearance and development of competition mathematics. Therefore, education attribute is the essential attribute of competition mathematics. On the basis of the general framework of Chinese students’ core literacy development system and the above analysis, a second-order model of educational values of competition mathematics is proposed in Figure 4. It clearly shows the education values of competition mathematics, and of course needs further refinement.

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