Optimization Strategies of Bayesian Modeling Algorithms for Multilingual Teaching Systems in Southeast Asian Universities

In recent years, language courses are highly respected in colleges and universities, but there are still many deficiencies in the cultivation of comprehensively developed composite language talents [1-2]. In order to better improve the cultivation efficiency and quality of language talents and cultivate more practical language talents, colleges and universities need to carry out a certain degree of reform of the current language teaching strategy to improve students’ practical ability [3-4].

Human language learning can be divided into two main categories, the learning of native language and the learning of non-native language, the latter can be subdivided into second language (in the target language environment) and foreign language (in the non-target language environment) learning according to the different learning environments [5-6]. In the post-methodological era, different linguistic theories can often be found behind each of these pedagogical concepts. This is very different from the simple correspondence between a teaching method or technique and a theory or idea (e.g., sentence drills versus structuralist ideas), which was common in the previous one-dimensional era [7-9]. The most closely related theory in this regard, which emphasizes the importance of context in teaching and learning, can be traced back to Himes’s communicative competence in language, that is, the learner’s ability to use language appropriately, which is the representative theoretical basis of the language-as-usage model of teaching and learning [10-12]. All other studies that focus on the importance of context in language use can be seen as an extension of this foundation [13].

The central concern of language teachers is, what to teach? How to teach? The results of language ontology research in linguistics, numerous teacher training programs, reference books and teaching-related scholarly articles have led most teachers to feel that they are largely able to answer these two core questions [14-16]. According to the practice of language teaching over the years, different schools of teaching and learning have developed different teaching systems under the influence of various factors (including institutions, philosophies, regions, traditions, cultures, etc.), and each teacher generally answers the question of “how to teach” by himself/herself in the system to which he/she belongs [17-19]. Although these answers may look different on the surface, they are essentially structural [20], in which a small part of the three language subsystems, namely, the phonological system, the grammatical system, and the semantic system (or vocabulary in practice), is singled out as the teaching goal according to a certain concept, answering the question of “what to teach”. The question of “what to teach” is answered. This is the great contribution of structuralism and language ontology research to language teaching, a contribution that has been with us since the days of chalk and blackboard [21-24].

The study uses the “multi-knowledge point cognitive state tracking module” to extend the traditional BKT model, so that the model can simultaneously track the cognitive state of students on multiple knowledge points, considering the exponential explosion of algorithmic complexity faced by the problem, the introduction of genetic algorithms to optimize the model, the use of EM algorithms for parameter optimization, and then the use of “Multiple Knowledge Points Answer Prediction Module” to predict students’ performance based on the answer questions and their current cognitive state. The GA-BKT model is compared with the standard BKT model on the KDD dataset, and four evaluation indexes, namely, accuracy, AUC, root-mean-square error, and loss rate, are selected to explore the knowledge tracking performance of the model. On this basis, two parallel classes are selected to design controlled experiments to verify the effectiveness and reasonableness of the multi-knowledge Bayesian knowledge tracking method based on genetic algorithm in terms of three dimensions, namely, knowledge state tracking accuracy, learning effect, and students’ satisfaction, taking the math course of a Southeast Asian university with multilingual teaching as an example.

2

Bayesian optimization model based on multilingual teaching and learning

In smart education, Bayesian knowledge tracking models have been widely studied for their good interpretability. The traditional Bayesian knowledge tracking model is only for student question scenarios in a single knowledge point. However, in real-world scenarios, students often answer questions that examine multiple knowledge points at the same time, and their mastery of these multiple knowledge points will affect their performance simultaneously. To address this problem, this chapter proposes a multi-knowledge point Bayesian knowledge tracking method based on genetic algorithms, known as GA-BKT. It is mainly used in the multilingual teaching system in Southeast Asian universities.

2.1

Genetic algorithms

Genetic Algorithm (GA), as an intelligent algorithm for global search and optimization based on the mechanism of biological hereditary evolution, uses genetic operators to mimic the hereditary characteristics of organisms by completing the search for the optimal solution with the mechanisms of selection, crossover, and mutation in the hereditary and evolution of organisms. The traditional solution to optimization problems mainly consists of two categories: numerical method and analytical method, but due to the complexity of the problem, the traditional solution method can not solve the problem well, while the genetic algorithm is not constrained by the specific problem, and can solve the complex problem, which provides a new way of thinking for solving these problems. Genetic algorithm is mainly composed of the following four points.

2.1.1

Variable representation

Coding is the process of representing each possible point in the search space of a problem as a feature string of a certain length. A feature string is an individual or chromosome, and an individual is represented by a string, and when coding a multivariate problem, a single variable corresponds to a component of the entire string, which is also called a gene or genetic factor, and all the individuals make up the population.

2.1.2

Adaptation function

Fitness is a measure used to distinguish between good and bad degree of superiority of population survival, fitness is calculated by fitness function, the algorithm in the search of evolution is only based on the fitness function and the fitness value of each individual to carry out the search. The fitness function is determined by the algorithm’s ability to quickly and accurately complete the search for the optimal solution.

The fitness function should be designed according to the following guidelines: 1)

The design should be reasonable so that it can accurately reflect the advantages and disadvantages of the corresponding solutions.

2)

The design should be simple, reduce the complexity in time and space, and improve the computational efficiency.

3)

The designed fitness function is generalized.

If the objective function is the maximum value solution problem, there are: (1) $F (x) = {\begin{matrix} C_{\max} + f (x), f (x) < C_{\max} \\ 0, O t h e r \end{matrix}$

where C_max is the maximum estimate of the objective function f(x), f(x) is the objective function, and F(x) is the fitness function.

If the objective function is a minimum value solution problem, there is: (2) $F (x) = {\begin{matrix} f (x) - C_{\min}, W h e n f (x) > C_{\min} \\ 0, O t h e r \end{matrix}$

where C_min is the maximum estimate of the objective function f(x), f(x) is the target function, and F(x) is the fitness function.

2.1.3

Genetic operators

The eugenic and hereditary process of modeling biological evolution in genetic algorithms is accomplished through three basic operational operators: selection, crossover, and mutation. 1)

Selection

Before performing the selection operation, the fitness is first calculated. The fitness of individuals in a population and its distribution determine the selection probability of each individual in the alternative set. The operator chosen in this paper is the proportional fitness distribution, also known as roulette selection.

The magnitude of the likelihood of offspring retention is determined by calculating the probability of each individual’s fitness. If an individual i, whose fitness is f_i, is selected, the probability of its selection is expressed as: (3) $p_{i} = \frac{f_{i}}{\sum_{i = 1}^{u} f_{i}} (i = 1, 2, \dots \dots, u)$

Where, p_i is the probability of an individual being selected, u is the size of the population, and f is the fitness of the individual.

From the above equation, it can be seen that the greater the probability of fitness, it can be selected multiple times, and the easier the genetic factor is to expand in the population. 2)

Crossover

Crossover operation is the process of generating two new individuals through partial gene crossover of the chromosomes of two paternal pairs according to certain principles. There are different crossover methods such as single-point crossover, multi-point crossover and uniform crossover, which are commonly used, and there are different crossover forms for different situations. Crossover operation of the parent individual in the good genes inherited to the offspring of individuals, crossover after the bad performance can be eliminated in the subsequent selection process. The crossover operator is the essence of the difference from other optimization algorithms, and plays a great role in the global search of genetic algorithms.

3)

Mutation

After the crossover operation, the mutation operator is a small probability of individual string of certain genes in the population changes, in the expansion of population diversity at the same time on the premature convergence of the algorithm to play a limiting role. The mutation operation is commonly used as a binary mutation.

The main parameters of the genetic algorithm are the population size N (i.e., the number of individuals in the population), the maximum number of algebraic iterations M, the crossover probability P_c, and the mutation probability P_m. The setting of these parameters is determined according to the actual problem, and there is no uniform regulation. If the population size N is too small, the problem of incomplete search and premature convergence will occur, and if the population size N is too large, the number of samples is too large, the computational volume increases and the computational speed is slow, so it is not possible to reasonably arrive at an accurate solution. A crossover probability P_c that is too large leads to a higher probability that a well-adapted string will be corrupted, and a crossover probability P_c that is too small can cause the search to stop. Mutation probability P_m is too large to cause the search of the algorithm to be close to random search while mutation probability P_m is too small to cause insufficient diversity of individuals and make the algorithm’s performance decrease. So the parameter settings should be obtained based on experimental debugging.

2.1.4

Decommissioning guidelines

The convergence of genetic algorithm is heuristic, there is no strict convergence criterion, the current commonly used basis for judging convergence is through the number of calculations whether to reach the maximum number of iterations, the optimal solution in a certain time number of times within the scope of the conditions to determine whether the algorithm reaches convergence.

2.2

BKT model

Bayesian Knowledge Tracking (BKT) model is a tracking model that constructs the learner’s knowledge level in terms of the latent variables of the learner’s mastery of the knowledge point and the observed variables of the performance results of answering the questions, which can predict the mastery of the learner’s current state of the knowledge point and his/her future performance by observing the learner’s past learning state.

Bayesian knowledge tracking models are in essence a special kind of Hidden Markov Model. In the process of constructing the BKT model, the BKT model divides all the knowledge content to be learned into a series of several knowledge nodes connected by a hierarchical relationship, divides the learner’s answer to each knowledge point into corresponding performance nodes, and the mastery of each node is represented by a set of binary variables (“mastered,” “not mastered”), and the transfer process between the nodes is irreversible. Where K is the knowledge node of learning, Q is the performance node of answering questions, 1 means that the node state is “mastery”, 0 means that the node state is “not mastered”. The next node in the model depends only on the learner’s previous series of knowledge node states and performance node states. Therefore, the BKT model can be used to observe the learners’ knowledge node status in multilingual teaching in Southeast Asian universities and track the learners’ current series of different knowledge node statuses to predict their mastery of the next knowledge node and the performance of the current performance node in answering questions.

The BKT model is used to analyze the process of learners’ mastery of knowledge nodes in multilingual teaching, to observe the relationship between the states of each node, and to train the model parameters on a series of data sequences of learners’ positive and incorrect answering results, and with reference to the Conditional Probability Table CPT a Bayesian formula for the current learner’s learning performance can be obtained, and the learner’s learning in the next knowledge node can be inferred.

2.3

GA-BKT model

The overall framework of the multi-knowledge Bayesian knowledge tracking method based on genetic algorithms is shown in Fig. 1, which mainly includes three modules: multi-knowledge cognitive state tracking module, multi-knowledge answer prediction module, and model parameter optimization module.

2.3.1

Problem description

Given I set of students ${S^{i}}$ , i ∈ {1, 2, …I}; Q set of knowledge points ${K C_{q}}$ , $q \in {1, 2, \dots Q}$ ; I set of scores for students’ answers to exercise $Q_{t}^{i}$ in T time ${a_{i}^{t}}$ , $i \in {1, 2, \dots I}$ , t ∈ {1, 2, …T}. The set of knowledge points examined in Exercise $Q_{t}^{i}$ is set ${K C_{i n}} \subset {K C_{q}}$ , and the correct answer to the question is set ${Y_{t}^{i}}$ . The multi-knowledge point knowledge tracking task is to analyze the students’ historical answer data to dig out the students’ mastery level of multiple knowledge points as well as the change trend, and then further predict the students’ performance in answering the question $Q_{t + 1}^{i}$ in the future moments $a_{t + 1}^{i}$ , and the prediction should be as close as possible to the students’ real performance.

2.3.2

Cognitive State Tracking Module

Students will have two states for each knowledge point, i.e., “mastery” and “no mastery”, so at the moment of t, the overall mastery of students on K knowledge points can be expressed as: $P (L_{t}) = P (c_{t}^{i}, c_{t}^{2}, \dots, c_{t}^{K})$ . Considering the change of students’ cognitive state from the moment of t to the moment of t + 1, it can be written as equation (4): (4) $\begin{array}{rcl} P (L_{t + 1}) & = & P (L_{t}) P (L_{t + 1} | L_{t}) \\ = & P (L_{t}) P (c_{t + 1}^{1}, c_{t + 1}^{2}, \dots c_{t + 1}^{K} | c_{t}^{1}, c_{t}^{2}, \dots c_{t}^{K}) \end{array}$

Assuming that students’ palimpsest states for different knowledge points are independent of each other, the above equation can be adjusted to equation (5): (5) $P (L_{t + 1}) = P (L_{t}) \prod_{i = 1}^{K} P (c_{t + 1}^{i} | c_{t}^{i})$

For the knowledge points examined in the current question, the mastery status of the students can be estimated based on their current answer results. If the students’ current answer results are correct, it is estimated according to equation (6). If the students’ current answers are wrong, the estimation will be made according to equation (7): (6) $P (c_{t}^{i} | a_{t} = 1) = \frac{P (c_{t}^{i}) (1 - P_{i} (S))}{P (c_{t}^{i}) (1 - P_{i} (S)) + (1 - P (c_{t}^{i})) P_{i} (G)}$ (7) $P (c_{t}^{i} | a_{t} = 0) = \frac{P (c_{t}^{i}) P_{i} (S)}{P (c_{t}^{i}) P_{i} (S) + (1 - P (c_{t}^{i})) (1 - P_{i} (G))}$

For knowledge points that are not examined in the current topic, the previous assessment is considered correct for the time being.

Students’ mastery of these knowledge points is changing at different moments, and students may become more familiar with a certain knowledge point by practicing the related topic, while they will gradually forget the knowledge points that have not been tested and practiced, so considering the learning factor and the forgetting factor of the students, the change of students’ mastery state for different knowledge points is shown in Equation (8): (8) $\begin{array}{l} P (c_{t + 1}^{i}) = \\ {\begin{array}{l} P (c_{t}^{i} | a_{t}) (1 - P_{i} (F)) + (1 - P (c_{t}^{i} | a_{t})) P_{i} (T) & i f e x a \min e s t o \\ P (c_{t}^{i} | a_{t}) (1 - P_{i} (F)) & i f n o t e x a \min e d \end{array} \end{array}$

2.3.3

Answer prediction module

Students’ mastery of different knowledge points is different, and an exercise may test multiple knowledge points, so it is necessary to consider the joint influence of multiple knowledge points to predict students’ response performance. The multi-knowledge point prediction score function is shown in equation (9): (9) $P (y_{t} = 1) = \sum_{j \in K C_{i n}} w_{j} [P (c_{t}^{j}) (1 - P_{j} (S)) + (1 - P (c_{t}^{i})) P_{j} (G)]$

$\sum_{j \in K C_{i n}} w_{j} = 1$ of them.

In particular, two different treatment strategies are designed considering that multiple knowledge points jointly influence the final result. 1)

Equal influence strategy: in the absence of redundant information about the difficulty and importance of the knowledge points it is simply assumed that the different knowledge points produce the same result on the question, and that each of the knowledge points examined has the same degree of influence on the exercise, i.e., $w_{j} = \frac{1}{N U M (K C_{i n})}$ , j ∈ KC_in.

2)

Non-equal impact strategy: the question examined more than one knowledge point, taking into account the difficulty and importance of different knowledge points, that different knowledge points for the final answer to the final results of the exercise is a different impact. This influence weight can be brought into the model as a parameter related to the knowledge points and eventually optimized together.

2.3.4

Model parameter optimization module

1)

Introduction of model parameters

The parameters to be optimized are shown below:

$P_{j} (L_{0})$ : The initial mastery state of the students on the jnd knowledge point.

P_j(T): Learning rate of students’ cognitive state of the jth knowledge point.

P_j(F): The forgetting rate of the students’ cognitive state of the jth knowledge point.

P_j(S): The failure rate of the jth knowledge point.

P_j(G): The rate of guessing on the jth knowledge point.

w_j: The degree of influence of the jth knowledge point on the current topic.

2)

Chromosome coding method and operator selection

Each set of parameters is coded into a chromosome as an individual in the population, and the parameters include $P (L_{0})$ , P(T), P(S), P(G), P(F) and w, all of which contain the physical meaning of probability or weight. Therefore, it is straightforward to choose the “real number coding method”, i.e., each gene in the chromosome has consecutive values and is restricted to a value range of 01, which satisfies the needs of the model. Knowing that the number of knowledge points is K, each individual in the population is represented by a vector of length 5*K or 6*K.

For the selection operation, the tournament selection strategy is used, and the “analog binary crossover operator” and “polynomial mutation operator” are selected for the crossover operator and mutation operator, respectively.

3)

Population Diversity Strategy

The parameters are optimized in traditional BKT using Expectation Maximization (EM) algorithm, which fits the data step by step through iterations. In order to increase the population diversity, dominant genes are introduced at the same time. The work in this chapter considers the operation of parameter optimization in traditional BKT and encodes the good genes it produces into chromosomes that are added to each generation of the population. Specifically, the following operations are added to each iteration of the genetic algorithm:

Step 1: Using the EM algorithm, one EM iteration is performed on the training data without considering the differences between the knowledge points (constructing a single-knowledge point environment) to get a set of parameters for a single knowledge point.

Step 2: The parameters of single knowledge point after one step of EM iteration are randomly perturbed to generate the parameters of K knowledge point and constructed into the chromosome of an individual according to the encoding.

Step 3: Add the constructed n individuals to the current population, and continue crossover, mutation and selection operations to generate the next generation population.

2.4

Experimental results and analysis

2.4.1

Test data sets

The dataset for this study comes from an online educational system called Bridge to Algebra, which was one of the competition datasets from the 2010 International Knowledge Discovery and Data Mining Competition (KDD). This dataset is a record of the steps of each question completed by students in a math classroom, as recorded by the system. During the process of answering a question, students can request a hint from the system when they encounter difficulties, but after requesting a hint, the question will be marked as incorrect. The Bayesian knowledge tracking model in the system calculates the probability that a student has mastered a knowledge point, and when this probability reaches 0.95, the system will not continue to examine this knowledge, which means that the student will not encounter a question that examines this knowledge point again.

2.4.2

Evaluation indicators

In this study, four commonly used model evaluation metrics are selected to evaluate the GA-BKT model, which are accuracy rate, AUC, root mean square error and loss rate.

Accuracy rate, which is used to indicate the ratio of the number of correctly predicted samples to the total number of samples in a given test dataset. The range of accuracy is 0-1, so a higher value of accuracy means a better model.

AUC is the size of the area under the ROC curve, which is a curve consisting of points (TPR, FPR) connected together, while AUC is the area under the ROC curve, and a value of AUC between 0.5 and 1 indicates that the model outperforms the random classifier.

Root Mean Square Error (RMSE) represents the mean of the square root of the error between the predicted and true values.The smaller the value of RMSE, the better the fit of the model.

Loss rate is a very important indicator in neural network training. The smaller the loss value, the better the model training.

2.4.3

Analysis of results

1)

Accuracy

The training of the GA-BKT model and the standard BKT model resulted in the prediction accuracy of the two models being shown in Fig. 2.The GA-BKT model has a higher improvement in accuracy than the standard Bayesian knowledge tracking model, and the model is more effective.The accuracy of the GA-BKT model and the BKT model at the time of training up to 40 steps is 0.803 and 0.747, respectively.Therefore, the GA-BKT model can more accurately determine the knowledge mastery level of students in multilingual teaching.

2)

AUC

The AUC curves of the two models are shown in Figure 3. During the complete training process of both models, as the training continues, the final AUC value of the GA-BKT model is higher than that of the standard Bayesian knowledge tracking model, by 0.047. Therefore, the GA-BKT model is better than the Bayesian knowledge tracking model.

3)

Root Mean Square Error

Figure 4 shows the root mean square error values of the two models. The root mean square error is used to measure the difference between the predicted value and the actual value, and the smaller the value of the root mean square error, the better the model’s effectiveness. As the training continues, the final root mean square error values of the GA-BKT model are lower than those of the standard Bayesian knowledge tracking model, which are 0.413 and 0.353, respectively, and thus the GA-BKT model fits better.

4)

Loss value

The Loss values of the two models are shown in Fig. 5.The GA-BKT model has a higher Loss value at the beginning of the training, however, as the training continues to occur, the Loss value decreases rapidly and finally converges to about 0.43, and is lower than the standard Bayesian knowledge tracking model, the model training is more effective.

3

Analysis of the application and effectiveness of multilingual teaching

In this chapter, we test the effectiveness of the model in the actual multilingual teaching process based on the previously constructed multi-knowledge point Bayesian knowledge tracking method based on genetic algorithms.

3.1

Application objects

In this study, 98 undergraduate students in a multilingual teaching system in a university in Southeast Asia were selected for this application activity in a mathematics course, and the principle of random assignment was used, with Class I as the experimental group (48 students) and Class II as the control group (50 students). Class I was taught using the multi-knowledge Bayesian knowledge tracking method based on genetic algorithm constructed in this study, while Class II was kept in line with the usual independent learning. In addition to the fact that the two classes were roughly the same in terms of number, the instructors of the two classes were exactly the same, and to the greatest extent possible, the learning progress, learning content, and learning resources used were also the same, thus eliminating the influence of irrelevant factors on the results of the study as much as possible.

3.2

Application design

The Bayesian knowledge tracking-based learning model dynamically models the question-answering sequences generated by learners during the online learning process, tracks learners’ knowledge status in real time, and predicts learners’ future question-answering performance. For teachers, it can grasp the students’ knowledge status in real-time, which provides a basis for them to summarize and reflect on their teaching, as well as to carry out targeted teaching in the future. For students, they can clearly see their own knowledge mastery, which provides direction for their personalized learning and improves their learning efficiency.

After tracking the learners’ knowledge status, this study needs to collect relevant data to analyze the effectiveness of the model, including the accuracy analysis of the tracking results of the learners’ knowledge status, the analysis of the personalized learning effect, and the analysis of the satisfaction of the model application. Therefore, this study adapted and designed a questionnaire on the accuracy of Bayesian knowledge tracking to assess learners’ knowledge status, and a satisfaction questionnaire on the application of the model in light of practical needs.

An 8-week application activity was conducted and a survey was conducted to analyze the students in a class after the activity. By using data processing software such as SPSS 25, the data from the questionnaire filled out by Class I, as well as the data from the pre-test and post-test of the control group of students in Class I and Class II were organized and analyzed, and certain conclusions were drawn.

3.3

Effectiveness analysis

3.3.1

Knowledge status tracking accuracy analysis

In order to verify the accuracy of the Key Bayesian knowledge tracking model in evaluating the learners’ knowledge status, the learning support system generates the latest learners’ individual knowledge mastery report at the end of each knowledge level post-test in the 2nd-7th week of the course, and the students in the first class fill out the survey questionnaire truthfully according to their actual mastery of the knowledge points, so as to obtain the data for evaluating the accuracy of the learners’ knowledge status tracking results. During the implementation of the model, the accuracy of knowledge status tracking results was evaluated for learners a total of six times.

The accuracy of knowledge status tracking results is shown in Table 1. The model was applied at the beginning of the low accuracy (L) accounted for 14.8%, medium accuracy (M) accounted for 27.7%, and high accuracy (H) accounted for 57.5%, although the accuracy of the tracking results was not too high at the beginning, but with the advancement of the math course of multilingual teaching and deepening of the learning, each week’s low accuracy was lower than the previous week’s, and the high accuracy showed a gradual upward trend, and the final statistics of the three levels, the average value of low accuracy is 8.5%, the average value of medium accuracy is 15.7%, and the average value of high accuracy is 75.8%. From this, it can be concluded that the multi-knowledge Bayesian knowledge tracking method based on genetic algorithm has a high accuracy in assessing the knowledge status of learners, and can reflect the knowledge status of learners instantly and accurately.

Table 1.

Accuracy of the knowledge status tracking results

Weeks	Valid number	Evaluation dimension
Weeks	Valid number	L(0-70%)	M(70%-85%)	H(85%-100%)
1	48	14.8%	27.7%	57.5%
2	47	11.8%	22.7%	65.5%
3	48	8.3%	15.9%	75.8%
4	48	6.8%	12.4%	80.8%
5	47	5.2%	9.7%	85.1%
6	48	3.9%	5.8%	90.3%
Average		8.5%	15.7%	75.8%

3.3.2

Analysis of learner learning outcomes

The knowledge level pre-test was administered in week 1 of the model application and there was no significant difference in the knowledge level pre-test scores between the two groups of learners. At the end of each learning activity in weeks 2-7, learners were tested on their knowledge level post-test. Independent samples t-test was conducted on the post-test scores of the tested students using SPSS software, and the post-test scores of the knowledge level of the students in the two classes were analyzed as shown in Table 2. In the first two knowledge level posttests, the average scores of the two classes were not significantly different from each other. There was no significant difference, and the significance was greater than 0.05.

Table 2.

The aftertest results of the knowledge level of the two class students

After test number	Class	Mean	SD	SE	Sig.(Double tail)
p1	Class 1	74.64	7.95	1.44	0.493
p1	Class 2	75.77	7.08	1.24	0.493
p2	Class 1	76.88	7.41	1.03	0.133
p2	Class 2	76.15	7.62	1.19	0.133
p3	Class 1	78.14	6.52	0.94	0.042
p3	Class 2	77.74	7.59	1.05	0.042
p4	Class 1	82.45	5.03	0.82	0.025
p4	Class 2	78.77	6.93	0.95	0.025
p5	Class 1	83.59	4.18	0.84	0.006
p5	Class 2	78.18	6.27	0.93	0.006
p6	Class 1	85.86	3.82	0.75	0.002
p6	Class 2	79.45	4.59	0.89	0.002

With the in-depth application of the Bayesian knowledge tracking model, in the last four knowledge level posttests, the significance of the academic performance of the two classes was gradually significant (p3=0.042, p4=0.025, p5=0.006, and p6=0.002, which were all less than 0.05), and the mean values of the first class were higher than those of the second class. It indicates that by using the Bayesian knowledge tracking model, the students in Class I are able to quickly grasp their knowledge status according to the learning report generated by the learning support system, and accordingly carry out targeted leakage remediation, which not only improves their learning efficiency, but also enhances their learning performance.

3.3.3

Satisfaction analysis

Three dimensions of tracking method utility, tracking report validity, and model application satisfaction were investigated, and five related questions (Q1-Q15) were set for each dimension. The results of students’ satisfaction after the application of Bayesian knowledge tracking model in multilingual teaching are shown in Figure 6. The overall mean value of the utility of the tracking method, M = 4.45, indicates that the tracking method has a certain degree of utility and can be generalized to other learners for continued use. The overall mean values of effectiveness of the tracking report and satisfaction with the application of the model were 4.46 and 4.44 respectively, indicating that the tracking report has some effectiveness and that the learners have a good level of satisfaction with the application of the model.

4

Teaching strategies in multilingual classrooms

The previous analysis confirms that the Bayesian knowledge tracking model proposed has a positive impact on multilingual teaching and learning. The multilingual classroom poses certain challenges to teachers’ teaching and development, and teachers need to acquire more diversified knowledge, and in addition to the necessary specialized knowledge and pedagogical knowledge, they also need to be able to develop certain teaching strategies to coordinate the relationship between mathematics teaching and language. Teachers need to provide students with a variety of opportunities (e.g., listening, speaking, reading, writing, and translating) to participate in the whole teaching and learning process and to enhance the overall learning literacy of students.

In a multilingual classroom, teachers can encourage students to defend their positions by presenting opposing arguments. The reasoning behind a position can help students develop critical thinking, even though there is no right answer to some questions. Language shifts in the classroom can enhance students’ intellectual understanding. In order to develop students’ self-confidence and encourage discussion, questions and answers can be asked in students’ mother tongue, and during the summarization stage teachers can rephrase and rewrite the knowledge concepts in English and consolidate the learning process by writing solutions and English terms on the board.

Furthermore, teachers must be aware of the linguistic needs of students in a multilingual classroom. Mathematics teachers in multilingual teaching and learning environments need to possess a proper understanding of linguistic diversity and knowledge teaching: 1)

Teachers should recognize multilingualism as a potential learning resource rather than a barrier to students’ learning of mathematics.

2)

Teachers should be aware of the linguistic structure of the language of instruction and the everyday language of students.

3)

Teachers should pay attention to how students use linguistic expressions in classroom activities such as guessing, reasoning, abstracting, explaining and proving.

4)

Teachers should use appropriate language to respond to learners.

5

Conclusion

This study uses a genetic algorithm to optimize the Bayesian knowledge tracking model and proposes a multi-knowledge point Bayesian knowledge tracking method based on genetic algorithms. Its performance is analyzed through modeling experiments, and the method is applied to multilingual teaching courses in Southeast Asian universities. The main findings of the research are as follows: 1)

By using the KDD dataset to compare with the initial Bayesian knowledge tracking model, according to the experimental results, the GA-BKT model in this paper outperforms the original knowledge tracking model in all evaluation indexes, with higher accuracy and lower loss rate, and the AUC value is 0.047 higher than that of the initial Bayesian knowledge tracking model, which allows for more accurate prediction of students’ knowledge structure.

2)

With the in-depth application of the multi-knowledge point Bayesian knowledge tracking method, the accuracy of knowledge state tracking and the students’ learning effect are significantly improved. At the end of the teaching practice, the high accuracy evaluation of knowledge state tracking accounts for 75.8% overall, and there is a significant difference between the two classes of students’ performance at the 5% level in the last four tests. Meanwhile, the mean scores of students’ evaluations of the practicality of the tracking method, the validity of the tracking report, and the satisfaction of the model application were all above 4.4 points.

3)

The teaching experiment of a multilingual teaching course in a Southeast Asian university shows that the proposed multi-knowledge point Bayesian knowledge tracking method can realize the accurate assessment of learners’ knowledge status, improve learners’ academic performance, and obtain better learner satisfaction. The method provides richer information based on comprehensive statistics and analysis of students’ learning data, enabling teachers and students to get real-time feedback on students’ learning status, and comprehensively assisting the multilingual teaching process.

Sprache:: Englisch

Zeitrahmen der Veröffentlichung:: 1 Hefte pro Jahr
Fachgebiete der Zeitschrift:: Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere

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Optimization Strategies of Bayesian Modeling Algorithms for Multilingual Teaching Systems in Southeast Asian Universities

Chenruixue Luo

Online veröffentlicht: 24. März 2025

Eingereicht: 31. Okt. 2024

Akzeptiert: 22. Feb. 2025

DOI: https://doi.org/10.2478/amns-2025-0730

SchlüsselwörterBayesian, Knowledge tracking, Genetic algorithm, Multiple knowledge points, Multilingual teaching

© 2025 Chenruixue Luo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
Bayesian, Knowledge tracking, Genetic algorithm, Multiple knowledge points, Multilingual teaching