# Oral English Development of EFL Learners from the Perspective of Complexity Dynamic Theory

Authors: Qiang Dou; Guohua Li; Yuan Tang
Journal: Complexity
 (2021)

---

## Abstract

With the development of economic globalization and cultural integration, the learning of a second language has become increasingly important for economic, political, and cultural exchanges in the world today. Complex dynamic system theory is an important research theory of foreign language learning methods for nonnative speakers. However, the research and application of the complex dynamic system theory in oral foreign language learning of English as a Foreign Language (EFL) learners are not prominent. The purpose of this paper is to explore the learning situation of oral English of EFL learners from the perspective of the complex dynamic system theory and provide some new learning methods and suggestions for EFL learners’ oral English learning based on the research of complex dynamic system theory. First, this article discusses and analyzes the current situation of oral English learning of EFL learners through literature research and a questionnaire survey. Then, based on the related research on the theory of complex dynamic systems, this article proposes countermeasures and learning method recommendations for the problems existing in the current oral English learning of EFL learners. After that, this paper sets up a controlled test of oral English learning through the learning method formulated by the complex dynamic system theory and verifies the learning effect of the oral English learning method proposed in this paper according to the mathematical theory research method of the complex dynamic system. Finally, this article discusses the reliability of the experimental research conclusions based on the error analysis and confidence level estimation of the experimental results. The research results show shows that there is 95% confidence that the second language learning method proposed in this paper under the perspective of the complex dynamic system theory has a positive effect on the oral English learning of EFL learners.


---

## Body

## 1. Introduction

### 1.1. Background and Significance

The theory of complex dynamic systems can be helpful to the study of foreign language learning methods of nonnative language learners (i.e., EFL learners). As the name implies, the theory of complex dynamic systems is a discussion of the systematic and comprehensive methods of language learning based on the ideas of complexity theory and dynamic system theory [1]. Complexity theory was first applied to the study of business complex systems of business competition and development in a market environment. The original purpose of dynamic system theory is to imitate complex systems and analyze and predict the development trend and direction of events on this basis [2]. Many foreign language teaching researchers have found that both the common progress research ideas of complex theory and the dynamic analysis concept of dynamic system theory are very suitable for foreign language teaching. Therefore, complex dynamic system theory has become a research hotspot in foreign language learning system teaching methods [3].At present, the theory of complex dynamic systems has been applied in many fields. For example, according to the theory of a complex dynamic system, Huang proposed a hybrid trajectory planning algorithm based on a potential field fluid dynamics model and bidirectional fast search random tree to improve the adaptation of UAV formation to complex dynamic environment capabilities [4]. Under the theory of complex dynamic systems, the language system is a complex and dynamic nonlinear system; English learning is a system that constantly interacts and develops with internal subsystems. Language ability, environment, and learners all develop dynamically and interact and influence each other, thus forming a larger system. Different people, different cultural backgrounds, and different learning experiences are different, and learners have different goals in different periods. Drawing on the theory of complex dynamic systems for dynamic attention to the development of spoken English skills has opened a new window for English learning research.


### 1.2. Related Research at Home and Abroad

Regarding the second language learning of EFL learners, there have been rich research results at home and abroad. For example, Reza K explored the vocabulary complexity of Iranian EFL learners from the perspective of dynamic system theory. He evaluated several lexical complexity analyzer indexes of five intermediate and advanced Iranian female EFL learners in the six-month IBT foreign language learning course [5]. The results show that in the academic vocabulary, there is a positive correlation and a significant relationship between time and average, which can be used as an indicator of vocabulary complexity, while repeated measures analysis of variance only improves vocabulary complexity. It was also Bahari who integrates the nonlinear dynamic system into a form-centric method, develops listening skills through external language testing tools, and proposes a form-centric foreign language practice model [6].In a long-term study of 67 EFL learners, he found that the performance measures taken before and after the intervention have improved significantly, confirming the effectiveness of the model in developing listening and speaking skills in terms of form, meaning, and communication-oriented strategies. Kim used a combination of two longitudinal data sources to examine students' views on the development of a new task-based language teaching curriculum and quantitatively and qualitatively analyzed the task unit survey of project portfolio entries from 27 Korean EFL learners. Research shows that students’ understanding of TBLT changes over time, and multiple factors affect learners’ perception of task-based teaching [7]. Farahani uses the theory of complex dynamic systems as a framework to study the dynamic interaction of writing complexity, accuracy, and fluency in second language learning [8].Through a questionnaire survey of school leaders, we came to a conclusion. China has always maintained a high degree of attention to the learning of students’ second language and also attached great importance to the development of nonnative language English teaching. Dong investigated the development trajectory of listening strategy use and listening performance of EFL learners and explored the dynamic correlation between the two variables from the perspective of dynamic systems [9]. The study found that the learners’ listening strategy use and listening performance showed a nonlinear development pattern. The regression of listening performance can predict the progress of listening strategy use to some extent, and the approach of a new stage has great volatility and variability. Aiming at the current situation where EFL learners focus on foreign language learning, vocabulary, vocabulary learning strategies, and receptive vocabulary skills, Ning proposed that EFL learners should improve their productive vocabulary skills through writing. It turns out that writing does help to improve the productive vocabulary ability of EFL learners in foreign language learning and promotes the learners’ understanding of vocabulary meaning [10]. He uses a language model based on usage as the theoretical basis and proposes a complex adaptive system method to analyze language expression, discussing the complex dynamics and nonlinear development of network languages from the perspectives of meaning construction, grammaticalization, and semantics [11]. The research shows that network language can be seen as a complex adaptive system, affected by the interaction between user perception, social culture, and the surrounding environment. Based on the cognitive processing model supported by multimedia in second language learning, Yang S proposed how to teach words and realize dialogue reading while EFL learners watch multimedia stories to improve their oral narrative ability. The results show that bilingual students’ literacy skills are higher than literacy skills, which helps to narrow the gap in the text-level literacy between EFL English learners and native English speakers [12]. From the literature reading of the domestic complex dynamic system theory, there are relatively few studies on the application of complex dynamic system theory to the oral English learning of English majors. Therefore, the author believes that, with the help of the research results of the complex dynamic system theory in the field of English learning, the complex dynamic system theory is applied to the oral English school of the English major, and the method of dynamic observation is used to conduct a case study on the development of the oral English ability of college English majors. An effective way of oral English teaching in colleges and universities is necessary and feasible.


### 1.3. Innovations in This Article

For EFL, nonnative English learners usually cannot understand the meaning of English in various contexts and fields in the same way as native English speakers [13]. This study explains the development of English majors’ oral ability from the perspective of a complex dynamic system, provides a theoretical reference for private undergraduate college English majors in their education and teaching process to improve the quality of education and teaching, and helps promote teachers to update teaching principles and help students Improve oral English ability in terms of fluency, accuracy, and complexity so that students can develop their ability to communicate in the target language more effectively. Through complex dynamic system detection and recognition methods, we can accurately grasp the learner’s oral English learning situation and propose targeted learning suggestions and systems and efficient learning methods [14, 15].


## 1.1. Background and Significance

The theory of complex dynamic systems can be helpful to the study of foreign language learning methods of nonnative language learners (i.e., EFL learners). As the name implies, the theory of complex dynamic systems is a discussion of the systematic and comprehensive methods of language learning based on the ideas of complexity theory and dynamic system theory [1]. Complexity theory was first applied to the study of business complex systems of business competition and development in a market environment. The original purpose of dynamic system theory is to imitate complex systems and analyze and predict the development trend and direction of events on this basis [2]. Many foreign language teaching researchers have found that both the common progress research ideas of complex theory and the dynamic analysis concept of dynamic system theory are very suitable for foreign language teaching. Therefore, complex dynamic system theory has become a research hotspot in foreign language learning system teaching methods [3].At present, the theory of complex dynamic systems has been applied in many fields. For example, according to the theory of a complex dynamic system, Huang proposed a hybrid trajectory planning algorithm based on a potential field fluid dynamics model and bidirectional fast search random tree to improve the adaptation of UAV formation to complex dynamic environment capabilities [4]. Under the theory of complex dynamic systems, the language system is a complex and dynamic nonlinear system; English learning is a system that constantly interacts and develops with internal subsystems. Language ability, environment, and learners all develop dynamically and interact and influence each other, thus forming a larger system. Different people, different cultural backgrounds, and different learning experiences are different, and learners have different goals in different periods. Drawing on the theory of complex dynamic systems for dynamic attention to the development of spoken English skills has opened a new window for English learning research.


## 1.2. Related Research at Home and Abroad

Regarding the second language learning of EFL learners, there have been rich research results at home and abroad. For example, Reza K explored the vocabulary complexity of Iranian EFL learners from the perspective of dynamic system theory. He evaluated several lexical complexity analyzer indexes of five intermediate and advanced Iranian female EFL learners in the six-month IBT foreign language learning course [5]. The results show that in the academic vocabulary, there is a positive correlation and a significant relationship between time and average, which can be used as an indicator of vocabulary complexity, while repeated measures analysis of variance only improves vocabulary complexity. It was also Bahari who integrates the nonlinear dynamic system into a form-centric method, develops listening skills through external language testing tools, and proposes a form-centric foreign language practice model [6].In a long-term study of 67 EFL learners, he found that the performance measures taken before and after the intervention have improved significantly, confirming the effectiveness of the model in developing listening and speaking skills in terms of form, meaning, and communication-oriented strategies. Kim used a combination of two longitudinal data sources to examine students' views on the development of a new task-based language teaching curriculum and quantitatively and qualitatively analyzed the task unit survey of project portfolio entries from 27 Korean EFL learners. Research shows that students’ understanding of TBLT changes over time, and multiple factors affect learners’ perception of task-based teaching [7]. Farahani uses the theory of complex dynamic systems as a framework to study the dynamic interaction of writing complexity, accuracy, and fluency in second language learning [8].Through a questionnaire survey of school leaders, we came to a conclusion. China has always maintained a high degree of attention to the learning of students’ second language and also attached great importance to the development of nonnative language English teaching. Dong investigated the development trajectory of listening strategy use and listening performance of EFL learners and explored the dynamic correlation between the two variables from the perspective of dynamic systems [9]. The study found that the learners’ listening strategy use and listening performance showed a nonlinear development pattern. The regression of listening performance can predict the progress of listening strategy use to some extent, and the approach of a new stage has great volatility and variability. Aiming at the current situation where EFL learners focus on foreign language learning, vocabulary, vocabulary learning strategies, and receptive vocabulary skills, Ning proposed that EFL learners should improve their productive vocabulary skills through writing. It turns out that writing does help to improve the productive vocabulary ability of EFL learners in foreign language learning and promotes the learners’ understanding of vocabulary meaning [10]. He uses a language model based on usage as the theoretical basis and proposes a complex adaptive system method to analyze language expression, discussing the complex dynamics and nonlinear development of network languages from the perspectives of meaning construction, grammaticalization, and semantics [11]. The research shows that network language can be seen as a complex adaptive system, affected by the interaction between user perception, social culture, and the surrounding environment. Based on the cognitive processing model supported by multimedia in second language learning, Yang S proposed how to teach words and realize dialogue reading while EFL learners watch multimedia stories to improve their oral narrative ability. The results show that bilingual students’ literacy skills are higher than literacy skills, which helps to narrow the gap in the text-level literacy between EFL English learners and native English speakers [12]. From the literature reading of the domestic complex dynamic system theory, there are relatively few studies on the application of complex dynamic system theory to the oral English learning of English majors. Therefore, the author believes that, with the help of the research results of the complex dynamic system theory in the field of English learning, the complex dynamic system theory is applied to the oral English school of the English major, and the method of dynamic observation is used to conduct a case study on the development of the oral English ability of college English majors. An effective way of oral English teaching in colleges and universities is necessary and feasible.


## 1.3. Innovations in This Article

For EFL, nonnative English learners usually cannot understand the meaning of English in various contexts and fields in the same way as native English speakers [13]. This study explains the development of English majors’ oral ability from the perspective of a complex dynamic system, provides a theoretical reference for private undergraduate college English majors in their education and teaching process to improve the quality of education and teaching, and helps promote teachers to update teaching principles and help students Improve oral English ability in terms of fluency, accuracy, and complexity so that students can develop their ability to communicate in the target language more effectively. Through complex dynamic system detection and recognition methods, we can accurately grasp the learner’s oral English learning situation and propose targeted learning suggestions and systems and efficient learning methods [14, 15].


## 2. EFL Learners’ Oral English Learning Based on Complex Dynamic System Theory

### 2.1. Dynamic System Collection of Spoken English Teaching Resources

Through a questionnaire survey of students, we learned that for learners whose native language is not English, the most important and difficult aspect of oral learning is oral communication. To improve oral communication ability, the choice of oral teaching resources is very important. This paper collects oral English teaching resources that meet the learning needs and interests of EFL learners as much as possible through the big data platform based on the dynamic system theory. The collection of spoken language teaching resources in this study is mainly realized through software tools such as CALL and Vocab Profile [16, 17]. The principle of the data collection method of these software tools is based on the dynamic system theory and related big data algorithms. They screen the multimedia resources of spoken English multiple times and then select the learners of spoken English through each mobile terminal. In the selection of multimedia data resources, based on the difference in data relevance and importance, a preliminary selection is made through big data technology. The similarity judgment formula of the data source is as follows:(1)Lsi,sj=li,lj=0,lj,li=0,minlsi,sj+c,otherwise.In formula (1), li represents the length of the data string si in the computer and lj represents the length of the data string sj. The principle is to convert English multimedia resources spoken in the network into a data table and relevance the data through similarity metrics such as the length of the strings in the data table and the edit distance lsi,sj between the two strings. The formula for determining the importance of the data source is as follows:(2)R=1N∑si,j∈SLsi,sj,D=maxRN,Lsi,sj.In formula (2), N represents the number of data tables of all spoken English multimedia data resources in the database. The correlation discriminant value and importance judgment value R determined according to the string edit distance can obtain the highest correlation to meet the needs of learners. The data resource D. Filter the collected data according to the above conditions and then compare the field weights from the field level for the second round of screening. In the data table of the collected data, the more relevant and important a field is, the greater the weight [18, 19]. Therefore, the calculation of the field weight plays a decisive role in the discrimination of repeated data screening, and the weight calculation formula is as follows:(3)wi=12xi∑i=1nxi+yi∑i=1nyi.In formula (3), xi and yi, respectively, represent different field levels, and the weight wi of the field can be obtained by comparing the weights of these fields with each other. According to the relevance of these resources to the learning of spoken English, the similarity componentSmof the corresponding fields of the data can be further calculated. The calculation formula is as follows:(4)Smsi,sj=∑i=1nsmisi,sj⋅wi∑i=1nwi.


### 2.2. Measurement of EFL Learners’ Oral English Ability

According to related literature research, this article measures the oral English proficiency of EFL learners from the accuracy, fluency, and complexity of spoken English [20, 21]. Among them, the accuracy measurement method mainly has three aspects, namely, the frequency of word errors, the comparison of verb forms, and the proportion of error-free clauses. The calculation formula for accuracy is(5)accuracy=words countwrong words count=verbs countwrong verbs count.Formula (5) is the accuracy measured by the method of comparing word error frequency and verb form. However, for nonnative learners, the semantics and pronunciation of words and verb forms are difficult to accurately identify, so the error-free clause ratio is often used to measure the accuracy of oral expression. The calculation formula for the error-free clause ratioREFCis shown below.(6)REFC=no error clausestotal number of sentences.The complexity measurement of the oral English ability of EFL learners is measured and calculated according to the clause grammatical complexity ratioSCT. It reflects the complexity of the learner’s oral English expression through the number of clauses expressed by the EFL learner’s spoken language per unit time. The calculation formula is as follows:(7)SCT=total number of clausesnumber of clauses per unit time T.For the fluency measurement of EFL learners’ oral English ability, it is mainly calculated by the learners’ speaking speed, the total number of word syllables, and the number of wrong syllables. The formula for calculating the fluency rateSR of English speaking ability is as follows:(8)SR=the total number of syllables in the spoken language sampletime required for spoken sample including pauses.Although the measurement of spoken English fluency can be determined to a certain extent by the ratio of the total number of syllables in the spoken sample to the time required for the spoken sample, including pauses in formula (8), it is also affected by many factors. For example, learners’ speaking speed, pauses, repetitions, corrections, errors, and substitutions in the oral test. This article summarizes and analyzes these influencing factors through related research surveys. The survey results are shown in Table 1.Table 1
Factors affecting oral English fluency.
Influencing factorsDescription of influencing factorsPauseNumber of silences or pauses used for thinkingRepeatUsed to repeat the number and time of words, phrases, or clausesReviseNumber or time used to correct or regroup words, phrases, or clausesMistakeSentences to give up before saying the correct sentenceReplaceReplace one vocabulary item with anotherSpeaking rateThe total number of syllables of speech output per minute


### 2.3. Cointegration Theory of Complex Dynamic System in Oral English Teaching

Regarding the development of spoken English of EFL learners, this paper studies the theory of complex dynamic systems and cointegration analysis. Cointegration analysis is used to study the effects of complex dynamic system theory on the development of oral English in EFL learners [22, 23]. The main principle of cointegration analysis theory is similar to the method of sample testing in statistics. The formula for calculating the average value of the test sample of the learner’s English speaking ability in the time series is shown below.(9)x¯t=Ext=1T∑i=1Txi.In formula (9), xt is the sample data of the oral English proficiency test of the EFL learners in the time series of the complex dynamic system theory method, and T is the length of the time series of the sample test. The calculation formula for the sample variances2of the test data in the time series is as follows:(10)s2=Vxt=1T−1∑i=1Txi−x¯t2.The formula (10) calculates the variance of the EFL learner’s oral English proficiency test data sample in the time series, which reflects the fluctuation of the learner’s English speaking proficiency test data, which can eliminate abnormal data and make the test result more realistic. According to the calculation of the sample variance, the sample covariance γm can be further obtained. Its calculation formula is as follows:(11)γm=Covxi,xi−m=1T∑i=1Txi−x¯txi−m−x¯t.Formula (11) calculates the covariance of EFL learners’ oral English proficiency test data samples in a time series. It reflects the importance of complex dynamic system theory to the development of EFL learners’ oral English through the correlation degree of the test data of learners’ English oral proficiency influences. You can also calculate the autocorrelation coefficient of the test sample data to more clearly characterize the correlation between the complex dynamic system theory and the oral English development of EFL learners in the time series. The autocorrelation coefficient ρm calculation formula is shown below.(12)ρm=γt,mγt,t⋅γm,m=Covxt,xmCovxt,xtCovxm,xm.


### 2.4. Development Trajectory and Variation of EFL Learners’ Oral English

In the development of spoken English of EFL learners, studies have found that there are variations in the spoken English vocabulary of these learners. Simply put, it involves two main aspects. One is that the learner makes “noise” in the oral expression due to the unique voice and local accents during the oral learning, and the other is that the learner has been verbal for a long time during the oral learning. If you do not communicate, there is a situation where the knowledge that has been learned is lost or degraded [24, 25]. This shows that oral English learning is a process of perseverance, reviewing the past, and learning the new. The unit root test is to test the regression model based on the variable variation characteristics proposed by Monrocat’s simulation experiment theory. Its function expression is as follows:(13)yt=α⋅yt−1+μt.Formula (13) is an earlier unit root test method, where α is the regression coefficient. In the actual situation, the noise test in the learner’s oral expression generally has a measurement bias μt, and the above test method is not an unbiased estimate for this bias [26, 27]. There are certain limitations that affect the credibility of the test results of the oral development variation. Therefore, this article has made improvements based on related research, and the difference form of unit root test is as follows:(14)Δyt=α−1yt−1+∑i=1nβiΔyt−i+μt.After the unit root test is carried out to initially verify the existence of the learner’s spoken English development variation, the learner’s spoken English development variation is strictly and accurately tested according to the Akaike information criterion. The expression of the test functionAIC is as follows:(15)AICn=ln2π+lnet2T+2nT+1.In formula (15), n represents the order of the test model, and T represents the test cycle time. In addition, it can also be tested based on the above test and the characteristic root locus of the statistics of the detection data of the learner’s spoken language development variation. The characteristic root locus test is based on the principle of maximum likelihood estimation, and its statistic η is calculated as follows:(16)η=−T∑i=r+1nln1−λin−r,r=0,1,…,n−1.


## 2.1. Dynamic System Collection of Spoken English Teaching Resources

Through a questionnaire survey of students, we learned that for learners whose native language is not English, the most important and difficult aspect of oral learning is oral communication. To improve oral communication ability, the choice of oral teaching resources is very important. This paper collects oral English teaching resources that meet the learning needs and interests of EFL learners as much as possible through the big data platform based on the dynamic system theory. The collection of spoken language teaching resources in this study is mainly realized through software tools such as CALL and Vocab Profile [16, 17]. The principle of the data collection method of these software tools is based on the dynamic system theory and related big data algorithms. They screen the multimedia resources of spoken English multiple times and then select the learners of spoken English through each mobile terminal. In the selection of multimedia data resources, based on the difference in data relevance and importance, a preliminary selection is made through big data technology. The similarity judgment formula of the data source is as follows:(1)Lsi,sj=li,lj=0,lj,li=0,minlsi,sj+c,otherwise.In formula (1), li represents the length of the data string si in the computer and lj represents the length of the data string sj. The principle is to convert English multimedia resources spoken in the network into a data table and relevance the data through similarity metrics such as the length of the strings in the data table and the edit distance lsi,sj between the two strings. The formula for determining the importance of the data source is as follows:(2)R=1N∑si,j∈SLsi,sj,D=maxRN,Lsi,sj.In formula (2), N represents the number of data tables of all spoken English multimedia data resources in the database. The correlation discriminant value and importance judgment value R determined according to the string edit distance can obtain the highest correlation to meet the needs of learners. The data resource D. Filter the collected data according to the above conditions and then compare the field weights from the field level for the second round of screening. In the data table of the collected data, the more relevant and important a field is, the greater the weight [18, 19]. Therefore, the calculation of the field weight plays a decisive role in the discrimination of repeated data screening, and the weight calculation formula is as follows:(3)wi=12xi∑i=1nxi+yi∑i=1nyi.In formula (3), xi and yi, respectively, represent different field levels, and the weight wi of the field can be obtained by comparing the weights of these fields with each other. According to the relevance of these resources to the learning of spoken English, the similarity componentSmof the corresponding fields of the data can be further calculated. The calculation formula is as follows:(4)Smsi,sj=∑i=1nsmisi,sj⋅wi∑i=1nwi.


## 2.2. Measurement of EFL Learners’ Oral English Ability

According to related literature research, this article measures the oral English proficiency of EFL learners from the accuracy, fluency, and complexity of spoken English [20, 21]. Among them, the accuracy measurement method mainly has three aspects, namely, the frequency of word errors, the comparison of verb forms, and the proportion of error-free clauses. The calculation formula for accuracy is(5)accuracy=words countwrong words count=verbs countwrong verbs count.Formula (5) is the accuracy measured by the method of comparing word error frequency and verb form. However, for nonnative learners, the semantics and pronunciation of words and verb forms are difficult to accurately identify, so the error-free clause ratio is often used to measure the accuracy of oral expression. The calculation formula for the error-free clause ratioREFCis shown below.(6)REFC=no error clausestotal number of sentences.The complexity measurement of the oral English ability of EFL learners is measured and calculated according to the clause grammatical complexity ratioSCT. It reflects the complexity of the learner’s oral English expression through the number of clauses expressed by the EFL learner’s spoken language per unit time. The calculation formula is as follows:(7)SCT=total number of clausesnumber of clauses per unit time T.For the fluency measurement of EFL learners’ oral English ability, it is mainly calculated by the learners’ speaking speed, the total number of word syllables, and the number of wrong syllables. The formula for calculating the fluency rateSR of English speaking ability is as follows:(8)SR=the total number of syllables in the spoken language sampletime required for spoken sample including pauses.Although the measurement of spoken English fluency can be determined to a certain extent by the ratio of the total number of syllables in the spoken sample to the time required for the spoken sample, including pauses in formula (8), it is also affected by many factors. For example, learners’ speaking speed, pauses, repetitions, corrections, errors, and substitutions in the oral test. This article summarizes and analyzes these influencing factors through related research surveys. The survey results are shown in Table 1.Table 1
Factors affecting oral English fluency.
Influencing factorsDescription of influencing factorsPauseNumber of silences or pauses used for thinkingRepeatUsed to repeat the number and time of words, phrases, or clausesReviseNumber or time used to correct or regroup words, phrases, or clausesMistakeSentences to give up before saying the correct sentenceReplaceReplace one vocabulary item with anotherSpeaking rateThe total number of syllables of speech output per minute


## 2.3. Cointegration Theory of Complex Dynamic System in Oral English Teaching

Regarding the development of spoken English of EFL learners, this paper studies the theory of complex dynamic systems and cointegration analysis. Cointegration analysis is used to study the effects of complex dynamic system theory on the development of oral English in EFL learners [22, 23]. The main principle of cointegration analysis theory is similar to the method of sample testing in statistics. The formula for calculating the average value of the test sample of the learner’s English speaking ability in the time series is shown below.(9)x¯t=Ext=1T∑i=1Txi.In formula (9), xt is the sample data of the oral English proficiency test of the EFL learners in the time series of the complex dynamic system theory method, and T is the length of the time series of the sample test. The calculation formula for the sample variances2of the test data in the time series is as follows:(10)s2=Vxt=1T−1∑i=1Txi−x¯t2.The formula (10) calculates the variance of the EFL learner’s oral English proficiency test data sample in the time series, which reflects the fluctuation of the learner’s English speaking proficiency test data, which can eliminate abnormal data and make the test result more realistic. According to the calculation of the sample variance, the sample covariance γm can be further obtained. Its calculation formula is as follows:(11)γm=Covxi,xi−m=1T∑i=1Txi−x¯txi−m−x¯t.Formula (11) calculates the covariance of EFL learners’ oral English proficiency test data samples in a time series. It reflects the importance of complex dynamic system theory to the development of EFL learners’ oral English through the correlation degree of the test data of learners’ English oral proficiency influences. You can also calculate the autocorrelation coefficient of the test sample data to more clearly characterize the correlation between the complex dynamic system theory and the oral English development of EFL learners in the time series. The autocorrelation coefficient ρm calculation formula is shown below.(12)ρm=γt,mγt,t⋅γm,m=Covxt,xmCovxt,xtCovxm,xm.


## 2.4. Development Trajectory and Variation of EFL Learners’ Oral English

In the development of spoken English of EFL learners, studies have found that there are variations in the spoken English vocabulary of these learners. Simply put, it involves two main aspects. One is that the learner makes “noise” in the oral expression due to the unique voice and local accents during the oral learning, and the other is that the learner has been verbal for a long time during the oral learning. If you do not communicate, there is a situation where the knowledge that has been learned is lost or degraded [24, 25]. This shows that oral English learning is a process of perseverance, reviewing the past, and learning the new. The unit root test is to test the regression model based on the variable variation characteristics proposed by Monrocat’s simulation experiment theory. Its function expression is as follows:(13)yt=α⋅yt−1+μt.Formula (13) is an earlier unit root test method, where α is the regression coefficient. In the actual situation, the noise test in the learner’s oral expression generally has a measurement bias μt, and the above test method is not an unbiased estimate for this bias [26, 27]. There are certain limitations that affect the credibility of the test results of the oral development variation. Therefore, this article has made improvements based on related research, and the difference form of unit root test is as follows:(14)Δyt=α−1yt−1+∑i=1nβiΔyt−i+μt.After the unit root test is carried out to initially verify the existence of the learner’s spoken English development variation, the learner’s spoken English development variation is strictly and accurately tested according to the Akaike information criterion. The expression of the test functionAIC is as follows:(15)AICn=ln2π+lnet2T+2nT+1.In formula (15), n represents the order of the test model, and T represents the test cycle time. In addition, it can also be tested based on the above test and the characteristic root locus of the statistics of the detection data of the learner’s spoken language development variation. The characteristic root locus test is based on the principle of maximum likelihood estimation, and its statistic η is calculated as follows:(16)η=−T∑i=r+1nln1−λin−r,r=0,1,…,n−1.


## 3. Complicated Dynamic System Theory English Oral Teaching Experiment

### 3.1. Objects

The research object of this paper is the development of spoken English of EFL learners from the perspective of complex dynamic system theory. According to the theory of complex dynamic systems, this article provides students with oral English teaching resource selection and plans for oral English learning from three aspects: daily communication needs, practical work needs, and their own interests and hobbies for EFL learners’ oral English learning. In order to study the effect of the oral English learning method based on the complex dynamic system theory proposed in this paper, this paper sets up a control experiment of oral English teaching for EFL learners. The experiment is divided into an experimental group and a control group. The experimental group uses the learning method based on the complex dynamic system theory to learn oral English, and the control group does not use the learning method formulated in this research to learn oral English. The experimental group and the control group, respectively, choose EFL learners who voluntarily participate in this experiment with similar oral English proficiency. The experimental group and the control group each have 20 EFL learners. The research period for the development of oral English in this experiment is six months.


### 3.2. Experimental Design of Oral English Teaching

In this experiment, EFL oral English learners who are nonnative English speakers from various universities are selected. Among these learners, there are 24 English majors, 16 non-English majors, 18 boys, and 22 girls. According to the university majors and oral English level of the EFL learners who voluntarily participated in the research and refering to these EFL learners, including in-class and extracurricular learning time, oral English use and communication, and learning attitude, conduct research for multiple impact indicators. In the course of the experiment, it mainly detects and records the personal basic situation of the tested EFL learners, the situation of oral English learning, the situation of oral English performance, and the use of oral English. Then, according to the complex dynamic system theory, these experimental data are processed and analyzed. The specific analysis content and steps are described in the above method introduction. After analyzing the experimental data and drawing the relevant conclusions of the experiment, this paper verifies and analyzes the accuracy and credibility of the experimental conclusions through unit root test and maximum information entropy and other methods and indicators. According to the theory of complex dynamic systems, this paper designs an oral English teaching experiment for EFL learners. The basic flow of the experiment is shown in Figure1.Figure 1
Experimental process of oral English teaching for EFL learners.


### 3.3. Data Processing and Error Analysis of Experimental Results

In this experiment, the processing of audio data detected by EFL learners speaking English is mainly characterized by peak values of audio signal output and maximum information entropy. The data processing process can be carried out by related software tools, and the calculation formula of the maximum information entropyMX is shown in the following equation:(17)MX=12log2e+log22πσ2=12log22πeσ2.When performing error analysis on experimental result data, the first thing to determine is the error function. There are three main types of error functions: passing error function, global error function, and mean square error function. A large number of studies have found that the mean square error function combines the advantages of the other two error functions, so this paper chooses the mean square error function calculation for error analysis. The calculation formula of mean square errorMSE is shown in the following equation:(18)MSE=1MN∑i=1N∑j=1My^ij−yij.


## 3.1. Objects

The research object of this paper is the development of spoken English of EFL learners from the perspective of complex dynamic system theory. According to the theory of complex dynamic systems, this article provides students with oral English teaching resource selection and plans for oral English learning from three aspects: daily communication needs, practical work needs, and their own interests and hobbies for EFL learners’ oral English learning. In order to study the effect of the oral English learning method based on the complex dynamic system theory proposed in this paper, this paper sets up a control experiment of oral English teaching for EFL learners. The experiment is divided into an experimental group and a control group. The experimental group uses the learning method based on the complex dynamic system theory to learn oral English, and the control group does not use the learning method formulated in this research to learn oral English. The experimental group and the control group, respectively, choose EFL learners who voluntarily participate in this experiment with similar oral English proficiency. The experimental group and the control group each have 20 EFL learners. The research period for the development of oral English in this experiment is six months.


## 3.2. Experimental Design of Oral English Teaching

In this experiment, EFL oral English learners who are nonnative English speakers from various universities are selected. Among these learners, there are 24 English majors, 16 non-English majors, 18 boys, and 22 girls. According to the university majors and oral English level of the EFL learners who voluntarily participated in the research and refering to these EFL learners, including in-class and extracurricular learning time, oral English use and communication, and learning attitude, conduct research for multiple impact indicators. In the course of the experiment, it mainly detects and records the personal basic situation of the tested EFL learners, the situation of oral English learning, the situation of oral English performance, and the use of oral English. Then, according to the complex dynamic system theory, these experimental data are processed and analyzed. The specific analysis content and steps are described in the above method introduction. After analyzing the experimental data and drawing the relevant conclusions of the experiment, this paper verifies and analyzes the accuracy and credibility of the experimental conclusions through unit root test and maximum information entropy and other methods and indicators. According to the theory of complex dynamic systems, this paper designs an oral English teaching experiment for EFL learners. The basic flow of the experiment is shown in Figure1.Figure 1
Experimental process of oral English teaching for EFL learners.


## 3.3. Data Processing and Error Analysis of Experimental Results

In this experiment, the processing of audio data detected by EFL learners speaking English is mainly characterized by peak values of audio signal output and maximum information entropy. The data processing process can be carried out by related software tools, and the calculation formula of the maximum information entropyMX is shown in the following equation:(17)MX=12log2e+log22πσ2=12log22πeσ2.When performing error analysis on experimental result data, the first thing to determine is the error function. There are three main types of error functions: passing error function, global error function, and mean square error function. A large number of studies have found that the mean square error function combines the advantages of the other two error functions, so this paper chooses the mean square error function calculation for error analysis. The calculation formula of mean square errorMSE is shown in the following equation:(18)MSE=1MN∑i=1N∑j=1My^ij−yij.


## 4. Discussion on the Experiment of Oral English Teaching for EFL Learners

### 4.1. EFL Learners’ English Performance Level before the Experiment

In this study, we conducted statistics on junior English majors in a university in this city and selected students with little difference in English performance. A total of 40 EFL Efficient Oral English learners who participated in the experiment were selected. They were divided into two groups, namely the experimental group and the control group, each with 20 people. The English scores, CET-4 scores, CET-6 scores of some EFL learners who participated in the experiment, and the English listening and speaking scores tested before starting the experiment are shown in Table2.Table 2
English performance level of EFL learners before the experiment.
NumberABCDEFGroupingExperimentControlExperimentControlExperimentControlGenderFemaleFemaleMaleMaleFemaleMaleMajorEnglishEnglishComputerComputerPhysicsChemistryAge192018192120CEE108104116114123127CET-4512523456478NoneNoneCET-6478486NoneNone504511LES81.58368.5728891.5OES7478.56263.58179.5In order to understand the current situation of oral English learning of EFL learners, this article uses questionnaire surveys and other methods to survey and count the methods and attitudes of college oral English learners to oral English learning: mainly from whether you like to speak English, have a strict plan to learn spoken English, the level of spoken English ability, self-recognition of one's spoken English ability, willingness to communicate in English, and attitudes towards complex dynamic system theory in spoken English learning, etc. The survey is shown in Figure2. The survey found that although most oral English learners are more interested in oral English learning, they are not very willing to communicate in English.Figure 2
Spoken English learning of EFL learners.


### 4.2. EFL Learners’ Oral English Development and Ability Testing

In this paper, the fluency, complexity, and accuracy of spoken English of EFL learners are used to test the learners’ oral English proficiency level. During the experiment, some of the learners’ oral proficiency tests and the accuracy of the test data are shown in Table3. WTC represents the average level of learners’ willingness to use English for communicative communication, SD represents the standard deviation of the test data, and F represents that the experiment was carried out at a significant level of 18.76∗.Table 3
EFL learners’ English oral proficiency test scores.
GradesFluencyAccuracyComplexityWTCSDF11160.481.362.542.1618.76∗2970.361.441.152.3418.76∗31380.421.633.262.2718.76∗41250.541.522.332.1518.76∗51040.671.372.282.3718.76∗The data from the survey results in Table2 above are simply processed and drawn into statistical charts so that the level of oral English ability of these learners can be clearly and intuitively seen. As shown in Figure 3, under the significant influence of 18.76∗, the standard deviation of the performance test data in the experiment is in a relatively stable and less fluctuating trend, while the learners’ willingness to use spoken English varies greatly.Figure 3
EFL learners’ English oral proficiency test scores.In the course of the experiment, this article discovers and explores the phenomena of vocabulary and syntactic variation in the development of oral English of EFL learners. The so-called variation of vocabulary and syntax is mainly due to the fact that it is difficult for nonnative speakers to fully conform to the standard pronunciation of spoken English, resulting in murmurs or noises in spoken expressions, and forgetfulness of knowledge and deterioration of ability when they do not use English for a long time. As shown in Table4, this article mainly studies this variation from the vocabulary variation, the absolute difference of spoken recording data, and the recombination distance of spoken audio data.Table 4
Variation data on the development of oral English of EFL learners.
DataLFPTTRMLTGroupingExperimentControlExperimentControlExperimentControl11082277013782219034821723331864568392743368152212185163913291022Average22.273.026.854.218.233.6According to the experimental data statistics in Table4, this article draws the above three indicators into the histogram shown in Figure 4. It can be seen from the figure that most learners have experienced vocabulary variation in oral English learning. Combined with the statistical experimental data in Table 4, it can be found that learners who adopt the learning method formulated according to the complex dynamic system theory have significantly fewer vocabulary variations, indicating that the method of the complex dynamic system theory can effectively reduce the occurrence of vocabulary variation.Figure 4
Variations in the development of oral English of EFL learners.


### 4.3. EFL Learners’ Communication Willingness and Learning Interest

Some scholars have suggested that interest is the best teacher, and a large number of practical studies have shown that strong learning interest and high learning enthusiasm can indeed improve learning efficiency. In order to analyze the interest of EFL learners in oral English learning and their willingness to communicate during the experiment, this article regularly conducts interest interviews and surveys on the learners. The results are shown in Table5.Table 5
Communicative willingness of some learners who participated in the experiment.
DimensionGenderCWLCASelf-CCJohnMale1147866MaryFemale1224568AlanFemale1175461BlakeMale1066378DanFemale1313884According to the investigation and analysis in Table5, this paper analyzes the level of communicative willingness, communicative anxiety, and their self-perception of their English communicative ability in the experimental group and the control group of EFL learners. As shown in Figure 5, this article uses CWL, CA, and Self-CC to represent the above three levels of influencing factors of learners’ communicative willingness.Figure 5
EFL learners’ willingness to communicate in spoken English.


### 4.4. Comparative Analysis of Oral English Learning of EFL Learners before and after the Experiment

In the six-month oral English learning experiment research, this article comprehensively analyzes the oral English learning situation of EFL learners surveyed before the experiment and the experimental statistical data. As shown in Table6, this article compares and analyzes the content of the learners’ oral learning before and after the experiment, that is, the selected oral learning resources, the personality tendency of learning, and the subjective feelings and experiences during the learning process. It can be seen that after the learners have adjusted their learning methods through the experiments of complex dynamic system theory, they have enhanced the planning of oral English learning, with richer learning content and more prominent personality tendencies.Table 6
EFL learners’ oral English ability and learning interest before and after the experiment.
DimensionBefore experimentAfter experimentTPSubject content11.134 ± 2.21311.438 ± 3.064−0.3580.724Subjective feelings9.216 ± 1.7349.766 ± 2.478−0.8230.418Personality tendency11.396 ± 3.16511.976 ± 3.987−0.5670.576Speaking ability61.25 ± 4.5878.64 ± 8.360.0270.618Communicative willingness78.64 ± 4.37112.34 ± 5.870.0360.594Using the results of the survey and comparative analysis in Table6 in the form of scatter diagrams, you can more intuitively see the changes in the learning situation of EFL learners.As shown in Figure6, it can be seen that the significance level of the statistical quantity T of the T test of the experimental data is below 0.05, indicating that the experimental results are highly reliable. And through this experiment, the oral English learning method adjusted according to the theory of complex dynamic system has an obvious promotion effect on the improvement of EFL learners’ oral ability.Figure 6
Learning interest and subjective feelings of EFL learners.


## 4.1. EFL Learners’ English Performance Level before the Experiment

In this study, we conducted statistics on junior English majors in a university in this city and selected students with little difference in English performance. A total of 40 EFL Efficient Oral English learners who participated in the experiment were selected. They were divided into two groups, namely the experimental group and the control group, each with 20 people. The English scores, CET-4 scores, CET-6 scores of some EFL learners who participated in the experiment, and the English listening and speaking scores tested before starting the experiment are shown in Table2.Table 2
English performance level of EFL learners before the experiment.
NumberABCDEFGroupingExperimentControlExperimentControlExperimentControlGenderFemaleFemaleMaleMaleFemaleMaleMajorEnglishEnglishComputerComputerPhysicsChemistryAge192018192120CEE108104116114123127CET-4512523456478NoneNoneCET-6478486NoneNone504511LES81.58368.5728891.5OES7478.56263.58179.5In order to understand the current situation of oral English learning of EFL learners, this article uses questionnaire surveys and other methods to survey and count the methods and attitudes of college oral English learners to oral English learning: mainly from whether you like to speak English, have a strict plan to learn spoken English, the level of spoken English ability, self-recognition of one's spoken English ability, willingness to communicate in English, and attitudes towards complex dynamic system theory in spoken English learning, etc. The survey is shown in Figure2. The survey found that although most oral English learners are more interested in oral English learning, they are not very willing to communicate in English.Figure 2
Spoken English learning of EFL learners.


## 4.2. EFL Learners’ Oral English Development and Ability Testing

In this paper, the fluency, complexity, and accuracy of spoken English of EFL learners are used to test the learners’ oral English proficiency level. During the experiment, some of the learners’ oral proficiency tests and the accuracy of the test data are shown in Table3. WTC represents the average level of learners’ willingness to use English for communicative communication, SD represents the standard deviation of the test data, and F represents that the experiment was carried out at a significant level of 18.76∗.Table 3
EFL learners’ English oral proficiency test scores.
GradesFluencyAccuracyComplexityWTCSDF11160.481.362.542.1618.76∗2970.361.441.152.3418.76∗31380.421.633.262.2718.76∗41250.541.522.332.1518.76∗51040.671.372.282.3718.76∗The data from the survey results in Table2 above are simply processed and drawn into statistical charts so that the level of oral English ability of these learners can be clearly and intuitively seen. As shown in Figure 3, under the significant influence of 18.76∗, the standard deviation of the performance test data in the experiment is in a relatively stable and less fluctuating trend, while the learners’ willingness to use spoken English varies greatly.Figure 3
EFL learners’ English oral proficiency test scores.In the course of the experiment, this article discovers and explores the phenomena of vocabulary and syntactic variation in the development of oral English of EFL learners. The so-called variation of vocabulary and syntax is mainly due to the fact that it is difficult for nonnative speakers to fully conform to the standard pronunciation of spoken English, resulting in murmurs or noises in spoken expressions, and forgetfulness of knowledge and deterioration of ability when they do not use English for a long time. As shown in Table4, this article mainly studies this variation from the vocabulary variation, the absolute difference of spoken recording data, and the recombination distance of spoken audio data.Table 4
Variation data on the development of oral English of EFL learners.
DataLFPTTRMLTGroupingExperimentControlExperimentControlExperimentControl11082277013782219034821723331864568392743368152212185163913291022Average22.273.026.854.218.233.6According to the experimental data statistics in Table4, this article draws the above three indicators into the histogram shown in Figure 4. It can be seen from the figure that most learners have experienced vocabulary variation in oral English learning. Combined with the statistical experimental data in Table 4, it can be found that learners who adopt the learning method formulated according to the complex dynamic system theory have significantly fewer vocabulary variations, indicating that the method of the complex dynamic system theory can effectively reduce the occurrence of vocabulary variation.Figure 4
Variations in the development of oral English of EFL learners.


## 4.3. EFL Learners’ Communication Willingness and Learning Interest

Some scholars have suggested that interest is the best teacher, and a large number of practical studies have shown that strong learning interest and high learning enthusiasm can indeed improve learning efficiency. In order to analyze the interest of EFL learners in oral English learning and their willingness to communicate during the experiment, this article regularly conducts interest interviews and surveys on the learners. The results are shown in Table5.Table 5
Communicative willingness of some learners who participated in the experiment.
DimensionGenderCWLCASelf-CCJohnMale1147866MaryFemale1224568AlanFemale1175461BlakeMale1066378DanFemale1313884According to the investigation and analysis in Table5, this paper analyzes the level of communicative willingness, communicative anxiety, and their self-perception of their English communicative ability in the experimental group and the control group of EFL learners. As shown in Figure 5, this article uses CWL, CA, and Self-CC to represent the above three levels of influencing factors of learners’ communicative willingness.Figure 5
EFL learners’ willingness to communicate in spoken English.


## 4.4. Comparative Analysis of Oral English Learning of EFL Learners before and after the Experiment

In the six-month oral English learning experiment research, this article comprehensively analyzes the oral English learning situation of EFL learners surveyed before the experiment and the experimental statistical data. As shown in Table6, this article compares and analyzes the content of the learners’ oral learning before and after the experiment, that is, the selected oral learning resources, the personality tendency of learning, and the subjective feelings and experiences during the learning process. It can be seen that after the learners have adjusted their learning methods through the experiments of complex dynamic system theory, they have enhanced the planning of oral English learning, with richer learning content and more prominent personality tendencies.Table 6
EFL learners’ oral English ability and learning interest before and after the experiment.
DimensionBefore experimentAfter experimentTPSubject content11.134 ± 2.21311.438 ± 3.064−0.3580.724Subjective feelings9.216 ± 1.7349.766 ± 2.478−0.8230.418Personality tendency11.396 ± 3.16511.976 ± 3.987−0.5670.576Speaking ability61.25 ± 4.5878.64 ± 8.360.0270.618Communicative willingness78.64 ± 4.37112.34 ± 5.870.0360.594Using the results of the survey and comparative analysis in Table6 in the form of scatter diagrams, you can more intuitively see the changes in the learning situation of EFL learners.As shown in Figure6, it can be seen that the significance level of the statistical quantity T of the T test of the experimental data is below 0.05, indicating that the experimental results are highly reliable. And through this experiment, the oral English learning method adjusted according to the theory of complex dynamic system has an obvious promotion effect on the improvement of EFL learners’ oral ability.Figure 6
Learning interest and subjective feelings of EFL learners.


## 5. Conclusions

In the six-month experimental study of oral English teaching for EFL learners, this study draws the following conclusions about the influence of complex dynamic system theory on the development of oral English of EFL learners. First, in the process of oral English learning of EFL learners, this article mainly measures the learners’ oral English ability through the fluency, accuracy, and complexity of oral English expression. Experiments have found that there are variations in the development of oral English of these learners. Simply put, there are noises in the learners’ oral vocabulary pronunciation and learners who have not conducted oral communication for a long time experience deterioration in their oral knowledge and ability. Second, the development of oral English ability has unpredictable features such as complexity and dynamics. These features highlight the irreplaceable role of complex dynamic system theory in the development of oral English. Third, from the perspective of complex dynamic system theory, the spoken English learning method proposed in this paper for EFL learners has the characteristics of complex dynamic system theory dynamics and nonlinearity, which can help learners adjust their learning time and learning methods adaptively. EFL learners play an important role in the development of oral English.Based on the results of experimental research and related conclusions and the current problems encountered by EFL learners in the development of oral English, this article proposes the following suggestions to EFL learners of oral English from the perspective of complex dynamic system theory. First of all, choose appropriate and high-quality oral English learning resources based on daily communication, work needs, and hobbies. Each language is a broad and profound cultural essence. Nonnative language learners often cannot learn everything in depth, so they must focus on learning. Secondly, learners should improve their own thinking ability, understand and think about spoken English expression and semantic thought in various situations, and realize the comprehensive development of spoken English semantic understanding and practical communication skills. Finally, the development of spoken English is a process of perseverance and practice. In order to improve one’s own pronunciation standards as much as possible to reduce the variation in the development of spoken language ability, oral communication with other learners, especially native English speakers, should be often conducted through spoken English. In summary, we can find that the theory of complex dynamical systems can play a role in promoting English learning for EFL.Since the learning of spoken English is a long-lasting process, and the research methods in this article are under objective conditions, such as EFL learners’ learning case samples are few, and there are certain accidental errors, the research in this article is still in theoretical research due to its limitations. Level, has not been put into practical application. I hope that in the future, we can conduct in-depth research on the oral English development of EFL learners of different ages, different genders, and different educational backgrounds and majors and apply the theory of complex dynamic systems to the study of various second language learning development including English.



---

*Source: 9965139-2021-06-23.xml*