English Learning Motivation of College Students Based on probability Distribution

Example 6. To study college students' English learning motivation based on probability distribution, we should study the obedience conditions of key codes from two aspects: one is uniform distribution, the other is normal distribution.

From the perspective of uniform distribution, assuming that the compliance condition of waiting sort key a[n]. Key on interval [C, d] is uniform distribution, the actual density function is shown as follows: ϕ(x)=1d−c \phi \left(x \right) = {1 \over {d - c}}

Combining the above formula to calculate the number of bucket where a[n]. Key resides, the following formula can be obtained: s(a[i].key)=[∫ca[i].keyϕ(x)dx1n∫cdϕ(x)dx] s\left({a\left[i \right].{key}} \right) = \left[{{{\int_c^{a\left[i \right].{key}} {\phi \left(x \right)dx}} \over {{1 \over n}\int_c^d {\phi \left(x \right)dx}}}} \right]

From the perspective of normal distribution, the actual density function formula is as follows: ϕ(x)=12πxe−(x−m)22π2 \phi \left(x \right) = {1 \over {\sqrt {2\pi x}}}{e^{{{- {{\left({x - m} \right)}^2}} \over {2{\pi ^2}}}}}

In the above formula, m represents the mean and Z represents the mean square deviation.

At the same time, although the original function of the integral of the normal distribution function φ (x) exists, it cannot be expressed by the elementary function, so a function should be constructed in the interval [C, d] to approximate the function φ (x). It should be noted that the curve of sinx function on interval [−π2,−3π2] \left[{- {\pi \over 2}, - {{3\pi} \over 2}} \right] is very similar to the curve of function φ (x) on interval [c, d]. Therefore, only valid coordinate and function conversions are required. The function can better approximate the normal distribution function φ (x). Because both φ (x) and sinx functions belong to symmetric functions, [c, d] represents the actual distribution space of key code A [I].key. Generally speaking, the average is m≠d−c2 m \ne {{d - c} \over 2} , so the interval [c, d] should be appropriately expanded to [c′, d′], the specific formula is: c′=m−max(m−c,d−m)d′=m+max(m−c,d−m) \eqalign{& c^{'} = m - \max \left({m - c,d - m} \right) \cr & d^{'} = m + \max \left({m - c,d - m} \right) \cr}

Thus, it can be obtained: m=d′−c′2 m = {{d^{'} - c^{'}} \over 2}

And meet the following conditions: [c,d]⊆[c′,d′] \left[{c,d} \right] \subseteq \left[{c^{'},d^{'}} \right]

Assuming pm = ϕ(m), the formula for calculating the change of the function is: φ(x)=m2(sin(2x(x−c′)d′−c′−π2)+1) \varphi \left(x \right) = {m \over 2}\left({\sin \left({{{2x\left({x - c^{'}} \right)} \over {d^{'} - c^{'}}} - {\pi \over 2}} \right) + 1} \right)

After transformation, the function still has the mean and mean square deviation of the original normal distribution density function. The calculation result of the mean is as follows: m=1n∑i=1na[i].key m = {1 \over n}\sum\limits_{i = 1}^n {a\left[i \right].{key}}

The calculation results of mean square error Z are as follows: z2=1n∑i=1n(a[i].key−m)2=1n∑i=1n(a[i].key2−2a[i].key.m+m2)=1n∑i=1n(a[i].key2−2m∑i=1na[i].key+∑i=1nm2)=(∑i=1na[i].key−2nm2+nm2)=(∑i=1na[i].key2−nm2) \eqalign{& {z^2} = {1 \over n}\sum\limits_{i = 1}^n {{{\left({a\left[i \right].{key} - m} \right)}^2} =} \cr & {1 \over n}\sum\limits_{i = 1}^n {\left({a\left[i \right].{key}^2 - 2a\left[i \right].{key}.m + {m^2}} \right) =} \cr & {1 \over n}\sum\limits_{i = 1}^n {\left({a\left[i \right].{key}^2 - 2m\sum\limits_{i = 1}^n a \left[i \right].{key} + \sum\limits_{i = 1}^n {{m^2}}} \right) =} \cr & \left({\sum\limits_{i = 1}^n {a\left[i \right].{key} - 2n{m^2} + n{m^2}}} \right) = \cr & \left({\sum\limits_{i = 1}^n {a\left[i \right].{key}^2 - n{m^2}}} \right) \cr}

After the coordinate transformation, the interval can be effectively extended according to the symmetry of function φ (x), but there is no distributed key code inside. When calculating the serial number, the integral interval still stays in the original [C, D] interval. At this point, the serial number calculation formula is as follows[4.5]: s(a[i].key)=[∫ca[i].keyφ(x)dx1n∫cdφ(x)dx]=[n∫ca[i].keypm2(sin(2π(x−c′)d′−c′−π2)+1)dx∫cdpm2(sin(2π(x−c′)d′−c′−π2)+1)dx] s\left({a\left[i \right].{key}} \right) = \left[{{{\int_c^{a\left[i \right].{key}} {\phi \left(x \right)dx}} \over {{1 \over n}\int_c^d {\phi \left(x \right)dx}}}} \right] = \left[{{{n\int_c^{a\left[i \right].{key}} {{{pm} \over 2}\left({\sin \left({{{2\pi \left({x - c^{'}} \right)} \over {d^{'} - c^{'}}} - {\pi \over 2}} \right) + 1} \right)dx}} \over {\int_c^d {{{pm} \over 2}\left({\sin \left({{{2\pi \left({x - c^{'}} \right)} \over {d^{'} - c^{'}}} - {\pi \over 2}} \right) + 1} \right)dx}}}} \right]

Assumptions: k=n∫cd(sin(2π(x−c′)d′−c′−π2)+1)dx k = {n \over {\int_c^d {\left({\sin \left({{{2\pi \left({x - c^{'}} \right)} \over {d^{'} - c^{'}}} - {\pi \over 2}} \right) + 1} \right)dx}}}

Then we can get: s(a[i].key)=[K(−d′−c′2πcos(2π(x−c′)d′−c′−π2)+x)∫ca[j].key]=[K(−d′−c′2πcos(2π(a[i].key−c1)d′−c′−π2)+a[i].key+d′−c′2π−cos(2π(c−c′)d′−c′−π2)−c)]1.3 \eqalign{& s\left({a\left[i \right].{key}} \right) = \left[{K\left({- {{d^{'} - c^{'}} \over {2\pi}}\cos \left({{{2\pi \left({x - c^{'}} \right)} \over {d^{'} - c^{'}}} - {\pi \over 2}} \right) + x} \right)\int_c^{a\left[j \right].{key}} {}} \right] = \cr & {\left[{K\left({- {{d^{'} - c^{'}} \over {2\pi}}\cos \left({{{2\pi \left({a\left[i \right].{key} - c1} \right)} \over {d^{'} - c^{'}}} - {\pi \over 2}} \right) + a\left[i \right].{key} + {{d^{'} - c^{'}} \over {2\pi}} - \cos \left({{{2\pi \left({c - c^{'}} \right)} \over {d^{'} - c^{'}}} - {\pi \over 2}} \right) - c} \right)} \right]^{1.3}} \cr}

During data sort, it is clear that the array to be read into is a[n], and the corresponding type is: struct ss [float key;struct ss×next;]a[n]; \left[{float\,key;struct\,ss \times next;} \right]a\left[n \right];

Meanwhile, the data type of pointer array q[n] is: int×q[n+1] {\mathop{\rm int}} \times q\left[{n + 1} \right]

The description of the sorting algorithm is as follows:

FIG. 1

In view of the current situation of college students' English learning, this paper conducts a questionnaire survey on students' learning motivation based on probability distribution. Practical problems involve the following points: First, to understand the self-state of college students' English learning motivation; Secondly, the self-systematic characteristics of English learning motivation of students of different ages, majors, genders and levels should be clarified. Finally, the impact of the differences on English language teaching should be deeply explored.

In this paper, the probability distribution method is used to collect relevant data and information, and quantitative and qualitative methods are combined for in-depth discussion. The actual research tool is the self-questionnaire of motivation proposed by Taguchi, Magid, Papi et al., and the questionnaire of college students' English learning motivation proposed by Liu Fengge et al. In the design of the questionnaire, two aspects are mainly concerned: on the one hand, the background investigation of students; on the other hand, combined with the second language motivational self system theory, the four aspects of learning motivation intensity, ideal self, should self and learning experience of students are systematically investigated. After completing the initial questionnaire, the Likert rating scale was used to set the option score, and the one-to-one semi-structured interview was proposed in combination with qualitative analysis.[6.7]

In this study, a certain university was taken as the data source, and questionnaires were sent to college students through QQ group or wechat group. After 400 questionnaires were collected, invalid questionnaires that did not meet the requirements due to disciplines, age and other factors were removed, and 369 valid samples were finally obtained. Statistical software S P S S 17.0 was used to analyze the probability distribution and validate the validity of the data, and descriptive statistical analysis was conducted on the participants' second language learning motivation self-system, which involved correlation, one-way variance, robustness and other test methods.

Combined with the results of the self-questionnaire on college students' second language motivation as shown in Table 1 below, it is found that the mean values of emotion and behavior in motivation intensity are both over the median of 3.5, which proves that college students' English learning motivation is positive, but the actual level is not high. The overall average value of ideal self and learning experience is more than 3.5, which proves that these two factors are dominant influencing factors, which often appear in students' English learning and are the main contents of learning motivation. The overall mean value of the should self is the median, so it is a non-dominant factor, but it contains components, whether defensive motivation or family influence factors are dominant factors. According to these four description result, the study found the ideal self has the highest average value, so the second language ego ideal for college students of English learning effect is the largest, the second is the learning experience, this and other scientific research scholar's research results both at home and abroad, thus proves that motivation system yourself in English learning motivation research in our country has a certain application advantages.

This paper uses one-way anOVA to compare and discuss the differences in English learning motivation among college students of different grades. The actual results are shown in Table 2 below:

According to the analysis results in the table above, there are significant differences in learning anxiety, motivated behavior and emotional motivation, while there are no significant differences in other parts. From the average value, the order of emotional motivation is freshman, junior, senior and sophomore; The ranking results of behavioral motivation were junior, freshman, senior and sophomore. The ranking results of learning anxiety were senior year, sophomore year, junior year and freshman year. In practice, some researchers found that the higher the grade of college students, the stronger the motivation of English learning, which is quite different from the research results in this paper. The reason for this phenomenon is that there is a discrepancy between the actual questionnaire and the subjects of the study. According to the analysis of relevant numerical changes, it is found that the students with the strongest emotional learning motivation are the students with the strongest behavioral motivation. Through one-to-one interviews with students, it is found that students have higher interest in learning and higher actual expectations. However, due to the lack of professional and systematic guidance and management, students do not have a strong sense of independent control, so they cannot achieve good learning results. Sophomores' behavioral motivation and emotional motivation are all at the lowest level, because their professional courses are getting more and more difficult, their knowledge is too boring, and their interest in English learning is getting lower and lower. At this stage, students are in a downturn. Most of the junior college students are facing the postgraduate entrance examination or examination, the actual learning motivation is stronger; However, as senior students have basically completed their undergraduate learning tasks, their actual motivation to learn English begins to decline slowly.[9.10]

The T test of independent samples was used to judge the differences between boys and girls in the motivational self system, and the specific results are shown in Table 2 below:

According to the research results in the table above, the emotional motivation value of both male and female students is 0.005, which proves that there is a significant difference in their motivation during English learning. On average, girls are higher than boys. However, the constitutions of motivation behavior are all over 0.05, which proves that girls' interest in learning is higher than boys', but there is no significant difference in learning behavior. It can be seen that gender differences in self are not obvious, but the actual mean value proves that male students have stronger defensive motivation than female students and are highly susceptible to the influence of the surrounding environment.

According to the results of self-variance test of motivation shown in Table 3 below, there are significant differences in students' motivation under different academic backgrounds. Among them, science students have higher learning emotional motivation and motivated behavior, and art students have the lowest learning motivation.

According to the self-examination results of motivation of students at different levels as shown in Table 4 below, primary means below LEVEL 4, intermediate means between level 4 and level 6, and senior means above level 6.

Combined with the numerical analysis in the table above, it is found that students at different English learning levels have significant differences in experience, ideal self and motivation intensity. For example, in motivation intensity, the higher the English learning level of college students, the higher the behavioral motivation and emotional motivation; In terms of ideal second language self, the higher the English learning level of college students, both the stimulative tool and the international perspective motivation are constantly enhanced; During the application of SECOND language self, although there are obvious differences due to the influence of surrounding environmental factors, the actual average value is not a significant result, which proves that there is no significant difference in second language self. This research result is consistent with the content proposed by current scientific research scholars. In addition, students at different learning levels also have different self-confidence. The stronger the actual ability, the higher the self-learning consciousness, which is consistent with the conventional phenomenon.[11.12]