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The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory

Data publikacji: 15 Jul 2022
Tom & Zeszyt: AHEAD OF PRINT
Zakres stron: -
Otrzymano: 14 Feb 2022
Przyjęty: 14 Apr 2022
Informacje o czasopiśmie
License
Format
Czasopismo
eISSN
2444-8656
Pierwsze wydanie
01 Jan 2016
Częstotliwość wydawania
2 razy w roku
Języki
Angielski
Introduction

Many factors influence exercise persistence. But broadly speaking, the theory can be grouped into two categories: personal factors and environmental factors. Humans are active creatures, and they do not respond mechanically to external environmental stimuli. The social cognitive theory also points out that individuals have self-rationality. They can generate purposeful behavior to achieve a set goal actively. Individual behavior is neither a passive response to environmental stimuli nor a mechanized judgment and loop on a feedback loop [1]. Individual behavior results from the interaction between the environment, cognition, and behavior, which is the core of the individual's cognitive ability. The intervention of cognition makes the cognition of individual behavior different from both animals and machines. It is manifested as an organism with self-management ability, real-time dynamic change, and an active regulation system. Self-management is a series of behaviors by individuals actively setting goals, taking actions, monitoring and evaluating their performance, and making corresponding adjustments. These behaviors help individuals shape the process of their destiny [2]. This study believes that physical exercise behavior is a kind of physical activity carried out by individuals voluntarily. This action highlights the initiative and self-control of exercise, and the exerciser is the main body and has the leading role. Individuals are very autonomous when performing physical exercise. Physical activity can actively coordinate individual and environmental factors. Self-management of exercise behavior is to use metacognition and social and material environment to set exercise goals and choose exercise content and methods under the guidance of exercise motivation. They achieve the exercise goals by self-monitoring the exercise process and evaluating the exercise results promptly. If college students improve their exercise behavior, they must improve their self-discipline and self-management level. Self-management has powerful applications for improving performance. At the same time, performance has a feedback effect on individual behavior. The quality of performance is an important basis for adjusting behavior. Good exercise effect can promote exercise persistence is the first hypothesis of this study. The level of self-management affects the completion of people's work and study tasks [3]. This indicator ultimately affects the persistence of individual exercise behavior. Therefore, the research on exercise behavior must emphasize the self-management ability of exercisers. This is the certainty of the mutual unity of external and internal causes, other masters, and autonomy.

Some studies have found a significant correlation between exercise motivation and exercise persistence. Exercise atmosphere is also an important factor affecting exercise persistence. If you want to improve the exercise behavior of college students, college students must improve their self-discipline and self-management level. Therefore, we believe that exercise motivation and exercise atmosphere have predictive effects on exercise persistence. Self-management of physical exercise behavior is that individuals actively adjust the external exercise environment, internal exercise motivation, and other factors. And this principle has an impact on exercise persistence [4]. This satisfies the criterion for the mediation effect. Therefore, Hypothesis 2 is that self-management of physical exercise behavior plays a mediating role between exercise motivation, exercise atmosphere, and persistence. In addition, studies have shown that physical exercise behavior has age and gender differences. Therefore, whether there are age and gender differences in the self-management model of physical exercise behavior is another question to be studied in this study. This also becomes hypothesis 3 of this study.

The term “central limit theorem” was introduced by Polya in 1920. The central limit theorem is a class of theorems in probability theory that study the sequence parts and distributions of random variables. The theorem asserts that the probability distribution of the sum of a large number of independent random variables approximates the normal distribution under appropriate conditions. It is an important part of probability theory and one of the cornerstones of mathematical statistics [5]. For two centuries, the limit theorem was a central research topic in probability theory. At present, few thinkers of the limit theorem in the system research center at home and abroad, especially the introduction to the probability thought of the St. Petersburg School of Probability Theory, can only be found in the general history of mathematics works. No scholar has yet combined probability theory with the academic theory of sports. This is undoubtedly a pity. Therefore, this paper studies the relationship between college students' physical exercise motivation and self-control ability by using the mathematical model of probability theory. We use probabilistic path analysis to test the fit and difference of the relationship between the two. To explore the effect of physical exercise behavior self-management on exercise atmosphere, exercise motivation, and exercise persistence.

Research methods
Subject sampling

We used a stratified random sampling method. At the same time, we sampled by grade at 3 universities. A total of 600 college students were tested in groups in this experiment. The scale was filled out on the spot and returned. Five hundred sixty-three valid questionnaires were recovered (170, 152, 160, and 81 from freshman to senior year, respectively [6]. The ratio of males and females in each grade was equal: 320 males and 243 females). The effective recovery rate was 93.8%.

Measuring tools

The Physical Exercise Motivation Scale for College Students contains 4 subscales. The content includes self-breakthrough, ability, independent choice, and personal input. A total of 16 projects. We use a 5-point Likert scale. The scoring is indicated from “1” (none at all) to “5” (very strong). The internal consistency reliability of the measurements was 0.79.

“College Students' Physical Exercise Atmosphere Scale” is adapted from the Youth Outdoor Sports Atmosphere Scale [7]. A total of 5 subscales. The content includes 17 interpersonal associations, natural associations, information acquisition, interpersonal barriers, and conditional barriers. We use a 5-point Likert scale. The scoring is indicated from “1” (none at all) to “5” (very strong). The internal consistency reliability of the measurements was 0.81.

The Physical Exercise Persistence Scale for College Students was adapted from the Outdoor Sports Persistence Scale for Teenagers. A total of 6 projects. We use a 5-point Likert scale. The scoring is indicated from “1” (none at all) to “5” (very strong). The internal consistency reliability of the measurements was 0.78.

We selected 81 students from two classes in the first year of colleges and universities. We performed test-retest reliability tests at 3-week intervals. The test-retest reliability was 0.78, 0.71, and 0.75, respectively. A total of 5 experts (4 professors of physical education and 1 professor of psychology) were invited to evaluate the validity of the questionnaire. The effective rates were 82%, 86%, and 90%, respectively.

The “College Student Physical Exercise Behavior Self-Management Scale” contains 4 subscales. The content includes method management, time management, content management, and motivation management. A total of 19 projects. We use a 5-point Likert scale. The scoring is indicated from “1” (completely disagree) to “5” (completely agree). The internal consistency reliability of the measurements was 0.71.

Statistical analysis of probability theory

This study used SPSS13.0 and AMOS7.0 statistical software to analyze the data. Results are expressed as (mean ± standard deviation). Mathematical test P<0.01 was considered to be very significant.

Generating function method to prove the central limit theorem

We use the generating function to prove the central limit theorem of probability theory. Laplace introduced the generating function in the 19th century. It was the first systematically applied transformation method in probability theory. This method is useful for integer-valued random variables [8]. This theory is the precursor to the characteristic function. The Z-transform method developed has become an important method to solve many problems. The most basic property of the generating function is that the generating function of the sum of independent random variables is equal to the product of the original generating function. This brings convenience to the calculation. Chebyshev gave the following proof:

We assume that the probability of random variable X, Y, Z, L taking the value of xi, yi, zi, L is pi, qi, ri, …, (i = 1, 2, …, n) respectively.

We assume that EX=a,EY=b,EZ=c,,EX2=a1,EY2=B1,EZ2=C1,,a+b+c+=Aa1a2+b1b2+c1c2+=BP(X+Y+Z+=s)=Ps \matrix{{EX = a,\,EY = b,\,EZ = c, \ldots,} \hfill \cr {E{X^2} = {a_1},\,E{Y^2} = {B_1},\,E{Z^2} = {C_1}, \ldots,} \hfill \cr {a + b + c + \ldots = A} \hfill \cr {{a_1} - {a^2} + {b_1} - {b^2} + {c_1} - {c^2} + \ldots = B} \hfill \cr {P\left({X + Y + Z + \ldots = s} \right) = {P_s}} \hfill \cr}

Using the properties of the generating function, we get pst2=(p1tx1+p2tx2++pntxn)(q1ty1+q2ty2++qntyn)(r1tz1+r2tz2+rntzn)ps=1/2πππ[p1exp(ix1ϕ)+pnexp(ixnϕ)](r1exp(iz1ϕ)+rnexp(iznϕ)][]exp(isϕ)dϕ=1/2πππexp(Bϕ2/2)exp(Aϕi)exp(sϕi)dϕ=1/π0πexp(Bϕ2/2)cos[(As)ϕ]dϕ \matrix{{\sum {{p_s}{t^2} = \left({{p_1}{t^{{x_1}}} + {p_2}{t^{{x_2}}} + \ldots + {p_n}{t^{{x_n}}}} \right) \circ}} \hfill \cr {\left({{q_1}{t^{{y_1}}} + {q_2}{t^{{y_2}}} + \ldots + {q_n}{t^{{y_n}}}} \right) \circ} \hfill \cr {\left({{r_1}{t^{{z_1}}} + {r_2}{t^{{z_2}}} + \ldots \,{r_n}{t^{{z_n}}}} \right) \ldots} \hfill \cr {{p_s} = 1/2\pi \int_{- \pi}^\pi {\left[{{p_1}\,\exp \left({i{x_1}\phi} \right) + \ldots} \right.}} \hfill \cr {\left. {{p_n}\,\exp \left({i{x_n}\phi} \right)} \right] \ldots \left({\left. {{r_{1\,}}\,\exp \left({i{z_1}\phi} \right) + {r_n}\,\exp \left({i{z_n}\phi} \right)} \right]} \right.} \hfill \cr {\left[\ldots \right]\,\exp \,\left({is\phi} \right)d\phi} \hfill \cr {= 1/2\pi \int_{- \pi}^\pi {\exp \left({- B{\phi ^2}/2} \right)\,\exp \left({A\phi i} \right)\,\exp \left({- s\phi i} \right)d\phi}} \hfill \cr {= 1/\pi \int_0^\pi {\exp \left({- B{\phi ^2}/2} \right)\,\cos \left[{\left({A - s} \right)\phi} \right]d\phi}} \hfill \cr}

Since B is the sum of variances, positive numbers increase as the number of random variables increases. Chebyshev assumes that the upper limit of the integral is infinite, then we have Ps=(1/2πB)1/2exp[(As)2/2B] {P_s} = {\left({1/2\pi B} \right)^{1/2}}\,\exp \left[{- {{\left({A - s} \right)}^2}/2B} \right]

Then we get the integral theorem P(u2B<sA<u2B)=2/π0uexp(t2)dt P\left({- u\sqrt {2B} < s - A < u\sqrt {2B}} \right) = 2/\sqrt \pi \int_0^u {\exp \left({- {t^2}} \right)dt}

The method of moments proves the central limit theorem

Chebyshev used the method of moments to solve many difficult limit estimation problems. We apply it to the proof of the Central Limit Theorem. We use 0Af(x)dx \int_0^A {f\left(x \right)dx} , 0Axf(x)dx \int_0^A {xf\left(x \right)dx} , 0Ax2f(x)dx \int_0^A {{x^2}f\left(x \right)dx} , … to determine the integral value 0Af(x)dx \int_0^A {f\left(x \right)dx} . Here A > a and f (x) are unknown functions and are assumed to be always positive in the integration interval. Chebyshev gave the value range of the integral 0xf(x)dx \int_0^x {f\left(x \right)dx} and some inequalities by decomposing the continued fraction to the series but did not prove it in detail.

Markov made an in-depth study of Chebyshev's moment problem. In the article, he extended the Chebyshev problem as follows:

Known (1) mk=abxkf(x)dx(k=0,1,2,,n+1) {m_k} = \int_a^b {{x^k}f\left(x \right)dx\left({k = 0,\,1,\,2, \ldots,\,n + 1} \right)}

(2) 0 ≤ f (x) ≤ L (L is a constant)

(3) g (x) is a known real function on (a, b). Thus we determine the maximum value of the integral abf(x)g(x)dx \int_a^b {f\left(x \right)g\left(x \right)dx} overall f (x).

Here comes the rudiment of the functional. Markov solved the problem under the condition that the n + 1 derivative of g (x) exists and the sign is invariant on (a, b).

Dutch mathematician Stergis also conducted similar research at the same time. He gave results similar to Markov's. This theory solves the moment problem on the infinite interval (0, ∞). They give continuous fraction expressions for all integer moments of the function they are looking for. Markov's “Two Proofs of Convergence of Certain Continued Fractions,” published in 1895, gave the necessary and sufficient conditions for achieving Sgyersian continued fractions.

Chebyshev Moment Method Proof of Central Limit Theorem

Chebyshev used the method of moments to prove the Central Limit Theorem. Suppose the random variable sequence ξ1, ξ2ξn …, has the mean 0. We denote its normalized ξn=ξ1++ξnD(ξ1++ξn) {\xi _n} = {{{\xi _1} + \ldots + {\xi _n}} \over {\sqrt {D\left({{\xi _1} + \ldots + {\xi _n}} \right)}}} corresponding k order moment as mk, and the k order moment of the standard normal distribution as μk. According to Chebyshev's point of view, we need to prove the following propositions to prove the central limit theorem.

any k has mkμk when n → ∞;

For any k, if there is mkμk, then Fξn (x) → Φ (x) where Φ (x) is the distribution function of the standard normal distribution.

Markov proved some of the inequalities given by Chebyshev in 1884. This undoubtedly accelerated Chebyshev's research. In 1886 Chebyshev proved that if mk = μk, there is F (x) = Φ (x). He believed that the condition was equivalent to (b), but Markov disagreed. In 1887, Chebyshev proved (a). The final central limit theorem given by Chebyshev is:

If (1) u1, u2un … is a random variable column and Eui=αi(1)=0(i=1,2,) E{u_i} = \alpha _i^{\left(1 \right)} = 0\left({i = 1,\,2,\, \ldots} \right) .

(2) Suppose Euik=αi(k)=0(i=1,2,) Eu_i^k = \alpha _i^{\left(k \right)} = 0\left({i = 1,\,2,\, \ldots} \right) is uniformly bounded for all k. then there are limn(z1<u1+u2++un2(α1(2)+α2(2)+αn(2))<z2=1πz1z2ex2dx \mathop {\lim}\limits_{n \to \infty} \left({{z_1} < {{{u_1} + {u_2} + \ldots + {u_n}} \over {\sqrt {2\left({\alpha _1^{\left(2 \right)} + \alpha _2^{\left(2 \right)} + \ldots \alpha _n^{\left(2 \right)}} \right)}}} < {z_2} = {1 \over {\sqrt \pi}}\int_{{z_1}}^{{z_2}} {{e^{- {x_2}}}} dx} \right. Here (b) is converted to (2). The conditions given by Chebyshev are not strict. He does not state that random variables must be independent of each other. This is the practice of academic research at that time. He fails to take into account that expression (1/n)k=1nαk(2) \left({1/n} \right)\sum\nolimits_{k = 1}^n {\alpha _k^{\left(2 \right)}} may tend to 0 when n → ∞. In this case, the conclusion is wrong. Clause (2) is too harsh. It depends on the order of the moments, and in fact, it is not necessarily required to hold for all k. It is this condition that makes the proof quite complicated.

Results and Analysis
Descriptive statistics and correlation analysis of each variable

The mean, standard deviation, and Pearson correlation coefficient of each variable are shown in Table 1 and Table 2.

Mean, standard deviation, and difference comparison of scores for each test variable

Test variable Gender
Male Female F
Exercise atmosphere 55.51±6.91 51.45±7.65 0.27
Exercise motivation 51.26±9.95 44.79±10.82 1.71
Self-management 65.87±12.57 61.15±12.04 0.08
Method management 10.22±6.45 27.41±6.55 0.09
Time management 12.81±1.14 11.92±1.21 0.06
Content management 10.92±2.57 9.98±2.58 0.51
Motivation management 11.90±2.19 11.81±2.16 0.51
Persistence 20.88±4.62 16.89±5.62 6.44
Test variable Grade
Primary level Senior grades F
Exercise atmosphere 54.61±7.19 51.11±7.61 0.81
Exercise motivation 48.91±10.92 41.87±11.58 1.42
Self-management 61.91±12.11 59.81±12.17 0.61
Method management 28.95±6.48 26.88±6.71 0.61
Time management 12.11±1.18 11.91±1.28 0.77
Content management 10.55±2.61 9.61±2.55 0.02
Motivation management 12.09±2.19 11.16±2.25 0.54
Persistence 19.25±5.19 15.82±5.81 4.78

Pearson correlation analysis for each variable

Test variable 1) 2) 3) 4) 5) 6) 7) 8)
1) Exercise atmosphere -
2) Exercise motivation 0.514 -
3) Self-management 0.512 0.635 -
4) Method management 0.485 0.688 0.855 -
5) Time management 0.368 0.564 0.816 0.656 -
6) Content management 0.426 0.658 0.664 0.646 0.468 -
7)Motivation management 0.316 0.421 0.614 0.468 0.266 0.516 -
8) Persistence 0.462 0.660 0.668 0.628 0.466 0.628 0.408 -

There are significant gender differences in the three indicators of exercise atmosphere, motivation, and adherence in college students' self-management of exercise behavior (P<0.01). Boys scored significantly higher than girls. This study classified first- and second-year students as lower grades [9]. The third and fourth grades are classified as the senior group. The scores of method management, content management, motivation management, exercise motivation, and exercise adherence in the self-management of the lower grades were higher than those of the upper grades. The data were very significant (P<0.01). Self-management and its four dimensions were significantly correlated with exercise atmosphere, motivation, and persistence (P<0.01).

Fit test of the model

This study constructed a mediating model of exercise behavior self-management between exercise motivation, exercise atmosphere, and persistence. Among them, exercise behavior self-management is the mediating variable of exercise motivation and exercise atmosphere on exercise persistence. We use AMOS7.0 for path analysis. The initial model contains all the path relationships between the independent and dependent variables. The analysis results showed that the direct path coefficients from exercise atmosphere to persistence were not significant [10]. According to this result, we delete the insignificant paths and analyze the fitting degree of the data. The results show that the modified comprehensive cognitive model has a better fitting degree. The path coefficients of each model are shown in Figure 1. The model fit index is as follows: χ2=3.584,df=1,P=0.068,RMSEA=0.071(<0.08),GFI=0.996(>0.90),AGFI=0.956(>0.90),NFI=0.996(>0.90),GFI=0.997(>0.90) \matrix{{{\chi ^2} = 3.584,\,df = 1,\,P = 0.068,\,RMSEA = 0.071\left({< 0.08} \right),} \hfill \cr {GFI = 0.996\left({> 0.90} \right),\,AGFI = 0.956\left({> 0.90} \right),} \hfill \cr {NFI = 0.996\left({> 0.90} \right),\,GFI = 0.997\left({> 0.90} \right)} \hfill \cr}

Figure 1

The mediating effect model of exercise behavior self-management

The results show that the model fits well. The relationship between the training atmosphere and the persistence of exercise is carried out through the full mediating effect of self-management. However, self-management in the relationship between exercise motivation and persistence is only a partial mediator. It increases the direct effect of exercise motivation on persistence. In addition, the effect of exercise motivation on self-management of exercise behavior is greater than that of exercise atmosphere on self-management of exercise behavior [11]. All path coefficients of the modified model are significant. The fit of the whole model reached a high standard of fit. The hypothetical model proposed in this study fits well with the observed data. The external quality of the model is good.

Gender-grade differences in the revised model

The purpose of multi-group structural equation model analysis is to explore whether the path model diagram suitable for a certain group is also suitable for other groups. The article evaluates whether the hypothetical model proposed by the researcher is equal or the parameters are invariant among different samples. In this study, the fitting test of the multi-group structural equation model was carried out using different demographic characteristics of college students and the exercise behavior self-management hypothesis model. This explores how the variables in the hypothetical model behave in different groups.

We used multi-group comparisons to test gender and grade differences in the revised exercise behavior self-management model [12]. The path coefficients corresponding to the two groups of the different group-defining structural model parts are equal. Table 3 lists the path coefficients of the exercise behavior self-management models for different gender and grade groups. By comparing the critical values of the differences between model parameters, it is found that there are significant differences in the paths of exercise motivation pointing to self-management and exercise motivation pointing to persistence. The critical ratios on these two pathways were −2.131 and 2.040 for men and women, respectively. These values were all greater than 1.96 (P<0.05). The other path coefficients are less than 1.96, and the difference is insignificant (P>0.05). There was no significant difference in path coefficients (P>0.05). This indicates that gender has a significant moderating effect on the self-management model of college students' exercise behavior, but grade has no moderating effect. In the influence of exercise motivation on self-management, the path coefficient of boys is significantly higher than that of girls. In the influence of exercise motivation on persistence, the path coefficient of girls is significantly higher than that of boys.

Comparison of critical ratios of standardized path coefficients for each group model by grade and gender

Path Path coefficient
Boy Girl Critical ratio Difference test (P value)
1 0.36 0.278 −0.586 >0.05
2 0.882 0.678 −2.131 >0.05
3 0.126 0.122 −0.075 >0.05
4 0.181 0.288 2.04 >0.05
Path Path coefficient
Primary level Senior grades Critical ratio Difference test (P value)
1 0.224 0.431 1.587 >0.05
2 0.731 0.635 1.442 >0.05
3 0.082 0.156 1.236 >0.05
4 0.308 0.224 1.766 >0.05
Discussion
Group characteristics of college students' exercise behavior self-management development

There are significant gender differences in the three indicators of exercise atmosphere, motivation, and adherence in college students' self-management of exercise behavior (P<0.01). Boys scored significantly higher than girls. Most existing studies have found significant differences between boys and girls in their motivation to exercise. Boys tend to be more intense, aggressive big ball games and small ball games that reflect personal skills. Girls are more likely to choose sports with a small amount of exercise or a body sculpting effect. However, research shows that most students hope to improve their physical fitness through physical exercise to adapt to the competitive social environment in the future. This intrinsic motivation is long-term and persistent. This is unshakable in the subjective consciousness. This is also the ultimate goal for male and female college students to exercise motivation management. Therefore, gender differences in motivation management were not significant. This is consistent with the results of this study. Social and cultural influences on gender shaping and biological differences. Most boys have stronger athletic abilities and hobbies than girls. As a result, boys have stronger self-management skills than girls.

There are gender differences between boys and girls informing exercise habits and persisting in physical exercise. Boys exercise longer than girls. Because social role positioning endows men with robustness and liveliness. Women tend to be slender and quiet. Therefore, boys are more able to participate and persist in exercising. The scores of method management, content management, and motivation management in the self-management of the lower grades are higher than those of the upper grades. This may be due to the introduction of physical education classes in the first and second years of college. Students scored higher than their seniors in third and fourth grades who did not have physical education in all aspects of method management, content management, and motivation management. Because of the physical exam, the lower grades are also more motivated to exercise than the upper grades. College students of all grades have relatively little time to participate in physical exercise objectively due to their wide range of hobbies and learning tasks. Some college students do have certain deficiencies in time management. Therefore, the grade difference in time management was not significant. The exercise atmosphere can play an exemplary role, a driving role, a motivating role, and an educational role. Still, people can only identify the exercise group by gender rather than grade. Therefore, exercise climate affects gender regardless of grade.

The mediating role of college students' exercise behavior self-management function

In this study, exercise climate and exercise motivation were used as independent variables, and persistence was used as the dependent variable to test the mediating effect of exercise behavior self-management in the two. The fit analysis of college students' exercise behavior self-management model shows that the revised model fits better. Physical exercise motivation refers to the psychological motivation of people to participate in and maintain physical exercise behavior, and it is the direct cause of physical exercise behavior. The exercise atmosphere can play an exemplary role, a driving role, a motivating role, and an educational role. This is an important factor affecting the formation of physical exercise habits of middle school students. After confirming the relationship between exercise climate and exercise motivation and persistence, it is particularly important to explore how self-management affects persistence. We must explore the mechanism of self-management affecting persistence to analyze the psychological mechanism of the relationship between the two. Some scholars have pointed out two modes in which individual behavior can be changed: one is external influence. This is a model managed by others. The other is the mode of individual self-management. The individual himself is always the “protagonist” of the entire process of behavior change, and the actor himself participates in the process of making plans, specifying goals, arranging the environment, implementing operations, and evaluating effects in the process of behavior change.

Individuals need to use various cognitive and behavioral strategies to regulate their thoughts, emotions, behaviors, and the environment in which they live to achieve set goals. This is the individual self-rationality pointed out by social cognitive theory. This indicates the mediating effect of self-management among exercise climate, exercise motivation, and persistence. The mediating variables are the intrinsic and substantive reasons exercise climate and exercise motivation affect exercise persistence. Exercise behavior self-management plays a mediating role in the relationship between college students' exercise atmosphere, motivation, and persistence. This validates Hypothesis 2 of this study. At the same time, this also proves the effect of exercise behavior self-management on exercise persistence. Our conclusion makes Hypothesis 1 also verified.

The relationship between exercise atmosphere and exercise persistence in the self-management model of college students' exercise behavior is carried out through the full mediating effect of self-management. Self-management is only a partial mediator in the relationship between exercise motivation and persistence. The content contains the direct effect of exercise motivation on persistence. In addition, the mediating effect of exercise self-management between exercise motivation and persistence is larger than that between exercise atmosphere and persistence. Students can consciously regulate and control their thoughts, motivations, and behaviors. And the effect of exercise behavior on exercise motivation is stronger. Because motivation is an internal controllable factor, and the environment (atmosphere) is an external, uncontrollable factor. Therefore, the individual's subjective initiative for motivation is stronger than the effect on the atmosphere. This shows that college students' exercise motivation is very important to their exercise persistence. It has an irreplaceable role in self-management.

Gender differences in the self-management model of college students' exercise behavior

Gender has a significant moderating effect on college students' exercise behavior self-management model, but grade has no moderating effect. This part verifies Hypothesis 3 of this study. Specifically, in the influence of exercise motivation on self-management, the path coefficient of boys is significantly higher than that of girls. In the influence of exercise motivation on persistence, the path coefficient of girls is significantly higher than that of boys. Boys have stronger self-management skills than girls. Boys are also more motivated to exercise than girls. In addition, motivation is an inherently controllable factor. Environment (atmosphere) is an external and uncontrollable factor. The individual's subjective initiative for motivation is stronger than the effect on the atmosphere. Therefore, in the influence of exercise motivation on self-management, the path coefficient of boys is significantly higher than that of girls. The appearance motivation of female college students is stronger than that of boys, which is in line with the psychological characteristics of contemporary women's pursuit of physical beauty. Appearance motivation belongs to internal motivation and is more conducive to exercise behavior. Therefore, girls' strong demand for physical beauty will generate positive exercise motivation and directly affect exercise behavior. Girls' exercise motivation has a stronger direct effect on persistence than boys.

Conclusion

This study investigated the model of college students' exercise behavior persistence from self-management. The conclusions of this study enrich the theory of exercise psychology. This provides a scientific basis for implementing the study of exercise persistence among college students. The college stage is a critical period for developing lifelong sports. Good exercise behavior self-management ability will effectively ensure exercise persistence. The conclusions drawn from the article can promote lifelong sports in adolescents. This study provides preliminary support for gender and grade differences in the mediating effect of exercise behavior self-management.

Figure 1

The mediating effect model of exercise behavior self-management
The mediating effect model of exercise behavior self-management

Comparison of critical ratios of standardized path coefficients for each group model by grade and gender

Path Path coefficient
Boy Girl Critical ratio Difference test (P value)
1 0.36 0.278 −0.586 >0.05
2 0.882 0.678 −2.131 >0.05
3 0.126 0.122 −0.075 >0.05
4 0.181 0.288 2.04 >0.05

Mean, standard deviation, and difference comparison of scores for each test variable

Test variable Gender
Male Female F
Exercise atmosphere 55.51±6.91 51.45±7.65 0.27
Exercise motivation 51.26±9.95 44.79±10.82 1.71
Self-management 65.87±12.57 61.15±12.04 0.08
Method management 10.22±6.45 27.41±6.55 0.09
Time management 12.81±1.14 11.92±1.21 0.06
Content management 10.92±2.57 9.98±2.58 0.51
Motivation management 11.90±2.19 11.81±2.16 0.51
Persistence 20.88±4.62 16.89±5.62 6.44

Pearson correlation analysis for each variable

Test variable 1) 2) 3) 4) 5) 6) 7) 8)
1) Exercise atmosphere -
2) Exercise motivation 0.514 -
3) Self-management 0.512 0.635 -
4) Method management 0.485 0.688 0.855 -
5) Time management 0.368 0.564 0.816 0.656 -
6) Content management 0.426 0.658 0.664 0.646 0.468 -
7)Motivation management 0.316 0.421 0.614 0.468 0.266 0.516 -
8) Persistence 0.462 0.660 0.668 0.628 0.466 0.628 0.408 -

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