Acceso abierto

Research on Precision Teaching Strategies of Civic and Political Education for College Students Driven by Big Data

  
24 mar 2025

Cite
Descargar portada

Introduction

With the continuous growth of national economic strength, education, especially higher education, is facing unprecedented development opportunities and challenges. In order to improve the national economy, higher education must continuously improve its overall development quality, to ensure that the cultivated talents can adapt to and lead the development trend of the new era [1]. In this process, the importance of Civic and Political Education as a key link in the cultivation of talents is self-evident. In order to better serve the overall situation of national economic development and national power enhancement, Civic and political education must break the traditional mode and accurately position and cultivate all kinds of talents.

Precision teaching is based on Skinner’s behaviorist learning theory, which advocates that learning is the role of operational conditions, with fluency as a measure of students’ learning and development indicators, and the development of information technology provides a powerful technical support [2-4]. “Precision” is the essence of refining, perfect, the best; ‘quasi’ is the standard, accurate meaning, the result of the action is completely in line with the actual or expected. Precision teaching can effectively promote the improvement of students’ comprehensive quality, and implement different teaching methods and focuses for different subjects and different education modes [5-7]. It can also effectively improve students’ test scores and professional skills, enhance students’ test-taking ability and skills and knowledge, and improve students’ test scores, which is precisely the meaning of precision teaching [8-9]. Therefore, precision teaching requires teachers to grasp the law, mode and method of the examination, control the key points, test points and hot spots of the examination, study the form and task of the examination, train the skills and techniques of the examination, respond to all changes in order to make students invincible in all levels and types of various kinds of examinations, as well as regulating self-study [10-13]. Precision teaching effectively improves the professional level of teachers. Teaching must be effective, each lesson should have the benefit of each lesson, otherwise it is a waste of class time, through the practice of precision teaching, greatly enhance the professional level and ability of teachers to teach [14].

Contemporary college students are the “aborigines” of the Internet, their values are more diversified, personality characteristics are more distinctive, how to carry out personalized education according to the characteristics of the students, to meet the endogenous motivation of the students’ growth and development, to meet the needs of the national development has become an important breakthrough for the development of innovation in civic education [15-16]. The core role of ideological and political education is to influence students’ ideological concepts and behavioral choices through educational practice, which is deeply rooted in reality and has extremely important practical significance and application value, and its implementation must adhere to the problem-oriented, pay attention to practical results, and continuously promote the innovation of educational content and methods by responding to changes in specific “things”, “times” and “situations”, so as to ensure the accuracy and effectiveness of educational work [17-18]. In this process, accurately grasping the characteristics of “events,” “times,” and “situations” plays an indispensable role in achieving the goals of ideological and political education. Therefore, the study of the precise teaching strategy of college students’ ideological and political education in the era of big data is not only a new opportunity, a new problem and a new challenge for the current ideological and political education, but also a new idea, new channel and new method to solve practical problems.

In this paper, we utilize the Internet of Things (IoT) technology to collect and extract various types of data about students during their school years. The K-means algorithm is used to cluster and analyze student features based on the collected data, in order to construct a student profile. The generated student portraits are integrated into the user-based collaborative filtering algorithm to improve the accuracy of recommending Civic Education resources. By comparing the advantages and disadvantages of Pearson similarity and Jekyll and Hyde similarity, we finally choose to adopt Pearson similarity to calculate the similarity between students. On the basis of the original Pearson similarity calculation method, learning resources weights and scoring differences are integrated to realize the improvement of Pearson similarity, so as to generate the final list of recommended Civic and Political Education resources. The processed data is analyzed by clustering to construct student profiles, and comparative analysis is used to study the superior performance of this paper’s resource recommendation method compared to the deep learning recommendation method. Based on the experimental results, it is argued that the method presented in this paper plays a significant role in achieving precise teaching of Civic and Political Education in colleges and universities.

Construction of student portrait model based on big data
Data acquisition

Data collection is the first step in the construction of student portrait [19], and the data collection stage mainly utilizes the Internet of Things technology to collect and extract all kinds of data of students during their school years, so as to ensure the comprehensiveness, timeliness and accuracy of student data. In this paper, based on the study, life, socialization, and other habits of college students, student data collection is mainly carried out through five characteristic modules. This paper categorizes student data into static and dynamic data. Static data is data that does not change over time or changes more slowly, mostly including basic information data. Dynamic data are data that will change continuously according to students’ behavior, mainly including their learning behavior, consumption records, internships and employment, and interest preference data. The composition of various types of raw data is shown in Table 1.

Student information data

Serial number Feature category Corresponding data
1 Basic information data Name
Gender
Date of birth
Contact telephone
Race
2 Learning behavior Attendance rate
Test results
Contest award
Scholarship award
3 Consumer record Student loan application
Cartoon consumption record
4 Employment Internships data
Employment data
5 Interests and hobbies Second class score
Community participation
Data processing

The data obtained through data collection comes from different data sources. Data integration is the process of integrating data from multiple sources and storing them uniformly in one database. Raw data from different databases use different field names for the same attributes of students, and this paper uses unified fields to describe student information, as shown in Table 2. For fields such as “award level” and “award category”, this paper uses data conversion to convert “high” to 90-100 points, “medium” to 60-80 points, and below 60 points to “low”. The rest of the quantification is the same.

Students’ characteristics categories and related fields

Serial number Feature category Field
1 Basic information data Name
Gender
Date of birth
Contact telephone
Race
Majors
Admission time
2 Learning behavior Weighted average grade
Winning grade
Prize category
Scholarship amount
3 Consumer record Student loan record
Consumption amount
Consumption frequency
Cartoon amount
4 Employment Internship position
Internship date
Employment position
Employment date
5 Interests and hobbies Second class score
Community participation
Data normalization

In this paper, K-means mean clustering is used for model construction [20], and before the cluster analysis, the data need to be normalized, and the data with different magnitudes are converted to the range of [0, 1], in order to eliminate the magnitude difference, improve the convergence speed of the algorithm, and facilitate the comparison of data with different characteristics. In this paper, linear function transformation method (1) is used for normalization: X=XXminXmaxXmin

Where Xmax is the maximum value in the feature data set, Xmin is the minimum value in the feature data set, X is the data after the quantization process, and X′ is the data after the normalization process. In this paper, all the quantized data are converted to the range of [0, 1] by normalization according to equation (1), and are processed in the K-means clustering algorithm.

Student Portrait Modeling

In this paper, clustering algorithm for unsupervised classification is used for student portrait clustering analysis. According to the steps of K-means algorithm, the value of K is set first. Taking K = 4 as an example, 4 data points are selected as initial clustering centers. Then each data point is assigned to the closest cluster center, and these points assigned to the same cluster center form a cluster. The calculation of the distance metric is performed based on the Euclidean distance as shown in equation (2): d(xi,ci)=i=1n(xikcjk)2

where xi is the data point, cj is the cluster center, and k denotes the kth feature.

For each cluster, find the centroid of all data points in the cluster, the centroid is the mean of all data points in a cluster in each feature dimension, as shown in equation (3): cj=1|Cj|xCjx

where cj is the new center of the jnd cluster, Ci is the set of all data points in the jth cluster, |Ci| is the number of data points in the jth cluster, and x denotes a data point in the jth cluster.

In this paper, the elbow method is used for the selection of K values and the sum of error squares SSE is used to measure the quality of the clustering results. SSE denotes the sum of squares of the distances between all data points and the clustering centers of the clusters to which they belong, which is calculated as: SSE=j=1κxi cjd(xi,cj)2

where K is the number of clusters, xi is the data point, and cj is the clustering center.

Recommendation of Civic and Political Education Resources Based on Students’ Portraits

This section mainly introduces the user-based collaborative filtering algorithm [21], and adds the student portrait to improve the accuracy of the recommendation, the specific process steps are as follows:

Construct the user-item scoring matrix, since this paper realizes the recommendation of Civic and Political Education resources, the user stands for the student, and the item stands for the learning resource which is the Civic and Political Education course, so the first step is to construct the student-learning resource matrix.

Calculate the similarity between all students according to the student-learning resource matrix, and find the set of students with similar interests to the current students, which is an important step of the user-based collaborative filtering algorithm, and the next step of this paper will focus on the calculation of student similarity.

Based on the student similarity obtained in the second step, predict the students’ ratings (degree of interest) for the Civic and Political Education course, and generate a recommendation list according to the level of ratings, integrate the student profiles to calculate the fit between learning resources and students, and generate the final list to recommend to the target students.

The first step is to construct the Student-Learning Resource Matrix Pmn, assuming that the set of students is U = {u1, u2, ⋯, ui, ⋯um−1, um} and the set of learning resources is I = {i1, i2, ⋯, ij, ⋯in−1, in}. From this, it can be seen that the number of students is m and the number of learning resources is n. The scoring matrix Pmn is shown in Table 3.

Student - Learning resource scoring matrix

i1 i2 ij in−1 in
u1 s11 s12 s1j s1n−1 s1n
u2 s21 s22 s2j s2n−1 s2n
ui si1 si2 sij sin-1 sin
um−1 sm−11 sm−12 sm−1j sm−1n−1 sm−1n
um sm1 sm2 smj smn−1 smn

Where sij indicates the rating of student i on the Civics teaching resources j, and when sij = 0, it means that student i has not had any behavior on the learning resources j.

In this paper, we mainly obtain the ratings through explicit and implicit ways, among which, the implicit way is mainly obtained through the students’ historical information in the learning system, including the length of viewing, browsing records, evaluation system, and course collection, etc. The specific scoring criteria are shown in Table 4.

Student learning behavior scoring criteria

Learning behavior Grading criteria Symbol representation
Browse 1 ω1
Evaluation 3 ω2
Learning 2 ω3
Collect 4 ω4
Grade 1-5 ω5

From Table 4, Student i‘s rating of Learning Resource j can be calculated using Equation (5): sij=ω1+ω2+ω3+ω4+ω5

Next, we introduce the method of solving the similarity between students Currently, there exist many methods for calculating the similarity between vectors, and this paper focuses on some of the commonly used methods, as shown below.

Pearson similarity

Pearson similarity by the student’s ratings on all learning resources to do normalization, each rating in the student vector minus the average of all the ratings of the student, eliminating the impact of different rating criteria, Pearson is the modified cosine similarity, mainly used to represent the linear correlation between the two datasets, the calculation formula is shown in (6): sim(u,v)Pearson=iCw(swsw¯)(swsv¯)iCw(swsw¯)2iCw(swsv¯)2

In Equation (6), u and v represent different students and the similarity between these two is calculated, where Cuv denotes the intersection of the learning resources of student u and student v, sui denotes the rating of student u on learning resource i, and s¯u denotes the mean of the ratings of all the learning resources of student u, and for student v as well.

Pearson similarity can directly and efficiently calculate the correlation between two users and reduce the influence of the difference in ratings between different users, but the approach also has some defects, that is, it does not fully take into account the influence of the number of course resources of public ratings of students on the calculation of similarity.

Jaccard similarity

In addition to the calculation of similarity mentioned above, the application of Jaccard similarity is also very wide, it is a kind of index used to measure the degree of similarity between two sets, which indicates the proportion of the same elements in two sets to all the elements, and the calculation formula is shown in (7): sim(u,v)Jaccard=|N(u)N(v)||N(u)N(v)|

In Equation (7), N(u) represents the set of all learning resources ever rated by student u, N(v) represents the set of all learning resources ever rated by student v, the numerator represents the set of all learning resources ever rated by student u and student v together, and the denominator represents the set of all learning resources ever rated by student u and student v respectively.

In this paper, we decided to use Pearson to calculate the similarity between students and improve it on this basis, and the improvement method is described in the next section.

Table 5 shows an example of a matrix of students’ ratings of learning resources, which is used as an example to analyze the degree of similarity between students calculated through Pearson similarity.

Student - Learning resource scoring matrix

Resource A Resource B Resource C Resource D
Student A 3 2 1 4
Student B 0 5 5 0
Student C 1 2 1 3
Student D 2 4 2 1
Student E 3 4 1 2

As can be seen from Table 5, a total of five students’ ratings of four kinds of Civic and Political Education course resources are included, and there are two common resources between Student A and Student B, while there are four common resources between Student A and other students, so theoretically the similarity between Student A and Student B is lower than that with other students, but the results are found to be unreasonable by Pearson similarity calculation. Therefore, in this paper, we consider the weight of common learning resources between two students, which is calculated by formula (8): weight(u,v)=com(u,v)sum(u,v)

In Equation (8), com(u, v) denotes the number of all learning resources that have been jointly rated by student u and student v, and sum(u, v) denotes the number of all learning resources that have been rated by each of student u and student v. The similarity between two students and the number of public learning resources are proportional to each other, but weight(u, v) doesn’t take into account the impact brought by the differences in the rating criteria between students, so this paper, on the basis of the weights of the learning resources, takes into account the the influence brought by the difference in scoring, and the formula is defined as shown in (9): dif(u,v)=exp(iCw|suisvi|com(u,v)×|su¯sv¯|)

In Equation (9), Cuv denotes the intersection of the learning resources of student u and student v, which is the common learning resource, com(u, v) denotes the number of elements in the set of Cuv, sui denotes the rating of student u on the learning resource i, and su¯ denotes the mean value of the ratings of all the learning resources of student u, and for student v as well.

In this paper, the final student similarity calculation method is formed by integrating the Pearson similarity, learning resource weights, and rating differences, and the formula is shown in (10): sim(u,v)=sim(u,v)Pearson×weight(u,v)×1dif(u,v)

The k nearest neighbors with the highest similarity to student u are obtained by Pearson similarity, and then the ratings of student i on learning resources i are predicted by the ratings of these k similar students on learning resources i, and then the top N course resources with high predicted ratings are recommended to the students, as shown in the formula in (11): Pui=s¯i+vVsim(u,v)×(svis¯i)vVsim(u,v)

In Equa si¯ 4 denotes the mean value of student’s ratings on resource i, V is the set of the top K students who have the highest similarity with student u, sim(u, v) is the similarity between student u and student v, and svi denotes student v‘s ratings on learning resource i.

Since the similarity between different students and student u is not the same, sim(u, v) is used as a weight to indicate the degree of influence on student u, and the mean score is introduced in Eq. (11) in order to eliminate the effect of the difference in ratings between different students.

The learning resources in the obtained initial screening recommendation list are fit to the students to get the final recommendation results, and the fit is calculated as shown in Equation (12): ψui=tTru,t×δi,t

In Eq. (12), ru, I denotes the behavioral weight accumulated by student u on top of tag t, and δi, I denotes the feature weight of tag t in learning resource i, by which the final recommendation list is obtained.

Portrait construction and resource recommendation analysis
Student Portrait Construction
Student Profiling Based on K-Means Clustering

In this section, experiments are conducted based on the student data processed in the previous section, and the K-means clustering algorithm is used to cluster the features of students, mainly analyzing the learning behavior features, consumption record features, and hobby features in the student data.

Learning behavior features clustering analysis

In this paper, based on the K-means algorithm for clustering analysis of students’ learning behavior characteristics, a total of students were divided into 3 groups, the corresponding eigenvalues of the clustering center of each group and the corresponding number of students in each group accounted for as shown in Table 6. The proportion of students in Group I is 32.71%, and the weighted average score of students in this group is the highest at 89.74, and the award levels and award categories are also high-level awards, with a total of five scholarships. As a whole, Category I students show excellent learning behaviors, so they can be labeled as “exceptional students.” Regarding the civic education of this category of students, it is important to focus on guidance and give this category of students the highest degree of space for independent study. The highest percentage of students in category II is 43.94%, and the weighted average score of students in this category is 64.12, and the level and category of awards are lower level awards, as well as 2 scholarships in their academic studies. This group of students exhibits the characteristics of competent academic behavior and can therefore be labeled as “competent students.” Regarding the Civic and Political Education of this group of students, it is necessary to help them on the basis of guidance and assist them in finding suitable learning methods to enhance the effectiveness of their Civic and Political Education. Category III students accounted for 23.35% of the total, with a weighted average score of 43.28, and have never won any awards and scholarships at any level. This category of students requires focused attention and can therefore be labeled as “Students of Focus”. To give full play to the function and role of ideological education for this group of students, schools and teachers need to devote their main efforts to raising the ideological awareness of this group of students and transforming the misconceptions they may have.

Cluster analysis of students’ consumption record features

Using K-means algorithm to cluster analysis of students’ consumption characteristics, students are divided into three categories, the corresponding feature values of each type of cluster center and the corresponding number of students in each category are shown in Table 7. The consumption records of students in the first category as a whole show the characteristics of low economic level, so it can be labeled as “low economic level”, and this category of students accounts for 26.42%. The ideological education for this group of students should focus on helping them establish lofty ideals and educate them to realize the improvement of their economic level through their own struggles. At the same time, if necessary, when recognizing and financing poor students, priority can be given to these students. Category II students have a good economic standard and can be labeled as “good economic standard”, accounting for 49.79% of the students. This group of students can be provided with Civic and Political education in accordance with the normal course implementation methods. Category III students labeled as “excellent economic conditions” accounted for 23.81%. From their consumption data, it can be seen that the number of consumption of this type of students is the lowest, but the amount of consumption is the highest, which means that this type of students spend a large amount of money on a single occasion. Civic education for this group of students mainly focuses on helping them establish correct consumption concepts and form good consumption habits.

Cluster analysis of interest and hobby characteristics

The clustering analysis of students’ interests and hobbies features, the results are shown in Table 8. From the table, it can be seen that the K-means algorithm divides students into a total of three categories according to their interests and hobbies, accounting for 13.66%, 59.78% and 26.56% respectively. Students in category I have the lowest second class score of 54.86 and the lowest average number of clubs participation of 3.87 times. These students can be labeled as “students with low interest in extracurricular activities”, and they need to be motivated to establish a sense of comprehensive development through Civic and Political Education. Students in category II have a medium level of participation in extracurricular activities, so they can be labeled as “students with a medium level of interest in extracurricular activities”. Category III students have the highest score of 95.74 in the second classroom, and the average number of times they participate in club activities is 46.71, showing a high interest in extracurricular activities, so they can be labeled as “students with high interest in extracurricular activities”. Civic education for this group of students needs to focus on reminding them to pay attention to balancing the allocation of time for participation in extracurricular activities, avoiding the phenomenon of putting the cart before the horse, and achieving excellent results both inside and outside the classroom.

Learning feature clustering center eigenvalue and proportion

I II III
Weighted average grade 89.47 64.12 43.28
Winning grade 100.00 60.00 0.00
Prize category 95.00 60.00 0.00
Scholarship amount 5.00 2.00 0.00
Proportion/% 32.71 43.94 23.35

Consumption feature clustering center eigenvalue and proportion

I II III
Student loan record 5.00 1.00 0.00
Consumption amount 594.72 1036.84 2394.63
Consumption frequency 128.00 52.00 11.00
Cartoon amount 472.96 746.83 1389.47
Proportion/% 26.42 49.79 23.81

Interests and hobbies feature clustering center eigenvalue and proportion

I II III
Second class score 54.86 72.38 95.47
Community participation 3.87 12.63 46.71
Proportion/% 13.66 59.78 26.56
Evaluation of clustering effects

For the evaluation of the clustering effect, the index adopted in this paper is the contour coefficient. The procedure of calculating the contour coefficient needs to obtain the contour coefficient of each point, and for each point, it is necessary to calculate its intra-cluster dissimilarity and inter-cluster dissimilarity, in which the inter-cluster dissimilarity a(i) is the average of the dissimilarity from point i to other stores in the same cluster, and the inter-cluster dissimilarity b(i) is the minimum value of the average dissimilarity from point i to other clusters. Both intra-cluster dissimilarity and inter-cluster dissimilarity can reflect the cohesion and separation of the clustering model, respectively. The profile coefficient of point i is: S(i)b(i)a(i)max{a(i),b(i)}

The closer S(i) is to 1, the more sensible the clustering of point i is. S(i) The closer to -1, the more point i should be categorized into the other cluster. The closer S(i) is to 0, the closer point i is to the edge of the two clusters.

Finally, the contour coefficients of all points are averaged, which is the total contour coefficient of this cluster analysis.

After calculation, the contour coefficients of this paper’s K-means algorithm on the three features of learning behavior, consumption records and hobbies are shown in Figure 1, where the purple lines indicate the error ranges. From the figure, it can be seen that the contour coefficients of the three features are 0.827, 0.736, and 0.642 respectively. It shows that the clustering of student features using K-means algorithm in this paper is more reasonable.

Figure 1.

The contour coefficient of K-means algorithm

Presentation of student portraits

Constructing a student portrait is to display the behavioral characteristics of students in a visual way. In this paper, we cluster and tag students based on their consumption, life, and performance characteristics, and combine them with their basic information to visualize their characteristics. Figure 2 shows the portrait of a student. Through the visual display of student portraits, it is possible to more intuitively and efficiently understand the characteristics of students’ learning and hobbies, simplifying the process of analyzing students’ needs for personalized recommendation of Civic Education content, and significantly promoting the development of precise teaching of Civic Education in colleges and universities.

Figure 2.

Student portrait display

Analysis of Recommended Ideological Education Resources
Setting up the experimental environment

A university is selected to provide appropriate Civics teaching resources and collect experimental data. In the collected data, a total of 800 students are engaged in online learning and are provided with 300 kinds of Civic and Political teaching resources. The relevant data of the students are randomly selected as the training set, and the rest of the data are used as the test set for the experiment. P5 microprocessor was selected and C language was used as the development tool. The software used for the experiment is SQL, the operating system is Window10, and the running platform is Visual Studio2022.

For the cleaning of data, Java scripts are used to realize the various cleaning algorithms, commonly used cleaning rules and evaluation methods are encapsulated into each Java script file for Kettle to call. The hyperparameter of the deep neural network of the model is set to 10, and the model is set to have two kinds of samples, positive and negative, which are defined as follows: the samples that can be correctly recognized are positive samples, and vice versa are negative samples. According to the definition, the following indexes can be evaluated: the proportion of samples that can be recognized correctly in the process of recognizing samples is the degree of accuracy, which is calculated by the formula: p=tpn

Where: tp is the positive sample. n is the number of samples. The proportion of positive samples that can be correctly identified in the positive data of the test set is denoted as the recall rate, which is calculated as: r=tptp+fn

Where: fn is the positive sample is misidentified. In order to test the rationalization of the recommended method of this paper, three groups are set up. The group of this paper’s method serves as the experimental group, and the two groups of the deep learning method are the control A group and control B group respectively. The application of recommendation ability is carried out on real data, and the variable parameter is set as the number of Civics teaching resources recommended to students. The recall and precision of different recommendation methods are calculated using different parameters.

Results and analysis

When the parameter takes the value of 1 to 10, the precision degree and recall rate of different groups are calculated, and the specific values are shown in Fig. 3 and Fig. 4. From the experimental results, it can be seen that with the change of parameters, the precision degree of the experimental group stays more stable, the precision degree is above 90.76%, and it has the slowest decay speed among the three groups’ results. Meanwhile, the recall of the experimental group is larger, and the improvement is fast as seen in Fig. 4. When the parameter K=10, the recall rate reaches 91.45%, which is the highest recall rate of the three groups. After many experiments, it has been proved that resource recommendation using the method of this paper can yield results at a significant level, and the gain obtained is better than that of deep learning methods. In real recommendation scenarios, better recommendation results can be achieved.

Figure 3.

Comparison of accuracy results

Figure 4.

Comparison of recall results

In summary, using the resource recommendation method in this paper can improve the timeliness of the recommended content and make accurate recommendations for teaching resources in Civics and Political Science. In the process of students’ search, the student portrait is constructed, matching content is presented to students, enabling students to browse online Civics and Political Science teaching resources, and online Civics and Political Science teaching resources of interest to students are recommended. The cold-start problem is solved by collecting students’ historical behavioral data through their self-selected labels and inputting new feature data into the model. By using the recommended method in this paper, students can use online teaching resources in Civics and Political Science more accurately and improve their learning efficiency.

Conclusion

In this paper, a K-means clustering algorithm is used to classify students’ learning behavior, consumption record, and hobbies into three categories respectively, and provide the corresponding civic education strategy for each category of students. By calculating the profile coefficient of K-means algorithm, the profile coefficient of K-means algorithm is 0.827, 0.736 and 0.642 respectively, which indicates that K-means algorithm clustering results in the research scenarios of this paper are more reasonable, and the clustering results have a high degree of credibility. Based on the clustering analysis results combined with the basic information of the students, the student portrait is visualized, and the student’s characteristic data are presented intuitively. Comparison experiments are conducted between the deep learning recommendation method and this paper’s method, and the results show that the accuracy of this paper’s method in 10 kinds of ideological and political education resources recommendation reaches more than 90%, and when the number of recommendations reaches 10, the recall rate of this paper’s method reaches 91.45%. The experimental results strongly demonstrate the effectiveness of this paper’s method of recommending Civic and political resources by integrating students’ portraits, and its application in Civic and political education can effectively realize the precise teaching of students.