Exploration and Practice of Blended Teaching Reform of Higher Vocational Applied Mathematics Courses Empowered by Digital Technology
Online veröffentlicht: 17. März 2025
Eingereicht: 04. Nov. 2024
Akzeptiert: 19. Feb. 2025
DOI: https://doi.org/10.2478/amns-2025-0335
Schlüsselwörter
© 2025 Xiaoling Zhou et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
With the continuous development of modern science and technology level, China’s comprehensive strength has been increasing, in which mathematical knowledge and thinking play a very big role, and gradually become a key indicator of national scientific and cultural literacy. Mathematics courses in higher vocational colleges and universities not only play the role of auxiliary courses, but also the cornerstone of many professional courses, which is directly related to the students’ professional knowledge and future career planning [1-2]. Although higher vocational colleges and universities apply some modern teaching methods and approaches to mathematics teaching, the actual results achieved are poor, not essentially change the traditional teaching methods, not to mention a good solution to the problems that exist in traditional teaching [3-5]. At the same time, along with the rapid development of information technology, many new teaching modes relying on the Internet, for higher vocational colleges and universities mathematics teaching reform has brought a new opportunity to promote the smooth implementation of mathematics teaching reform.
The traditional teaching mode teaching content is boring, the knowledge is narrow, and the new teaching mode also exists in the lack of face-to-face communication between teachers and students, students’ self-discipline is poor and other problems [6-7]. The combination of the two to form a blended teaching mode, effectively extracting the advantages of offline and online teaching, has gradually become the main direction of educational reform in the context of the Internet [8-10]. In the blended teaching mode, higher vocational colleges and universities should not only pay attention to the classroom teaching effect of teachers, but also master the learning status of students, so as to promote the benign development of classroom teaching [11-12]. This requires teachers to rationally plan the classroom teaching content, strengthen the guidance and inspiration of students, and also requires students to actively participate in classroom teaching activities, give full play to the students’ creative consciousness and subjective initiative, and then ensure that the blended teaching mode to achieve good results [13-15].
With the gradual deepening of the reform of modern teaching informatization, the application of blended teaching mode in the teaching of mathematics in higher vocational colleges and universities is of great practical significance. Krismadinata, U. V. et al. examined the conditions for the development of the blended learning mode in vocational education, which requires not only consideration of the level of development of the blended learning mode itself, but also consideration of its adaptability to the field of vocational education, and then from the conditions, planning, implementation, and improvement stages to gradually realize blended learning reforms [16]. Lee, J. et al. developed an instructional design model for the flipped learning model in teaching and learning in higher education, which provides systematic guidance for teachers or instructional designers to create personalized blended learning classrooms, and the study proved that the mathematics classrooms supported by the proposed model significantly improved the maturity of students’ mathematical perspectives, the quality of their reflections, and their satisfaction [17]. Fitri, S. et al. investigated teachers’ and students’ attitudes towards blended learning using the Moodle cloud learning demonstration in a math classroom, and the results showed that blended learning significantly improved students’ motivation, comprehension, and learning outcomes, and gained unanimous support from both teachers and students [18]. Sukma, Y. et al. showed that critical thinking skills in mathematics education is one of the required competencies for students and blended learning is a type of learning that integrates technology and education and has great potential for developing critical thinking skills in students [19]. Aldalalah, O. M. A. et al. analyzed the effect of blended learning model on students’ mathematical cognition and metacognitive thinking skills and found that the blended teaching model was able to improve the students’ mathematical cognition and metacognitive thinking skills, and it was more effective in helping the students who had lower mathematical cognition and metacognitive thinking [20]. Darma, I. K. et al. conducted a study on blended learning applied mathematics textbooks that can improve students’ mathematical problem solving skills, developed a first draft of the textbook using Thiagarajan and Semmel’s 4- D model, and experimentally verified the effectiveness of the proposed blended mathematics textbook in improving students’ problem solving skills [21]. Lyakhova, S. et al. studied student experiences in face-to-face versus online format math courses and found that students participating in online courses had stronger self-regulation strategies than students participating in face-to-face courses, suggesting that the ability to self-regulate in a blended learning model will have an impact on student learning in math courses [22].
In this paper, based on the content and teaching characteristics of higher vocational mathematics, a BOPPPS blended mathematics teaching strategy based on intelligent Q&A technology is designed by using the BOPPPS model and combining the named entity technology. The intelligent Q&A module is constructed through the process of constructing the knowledge graph and question module, inputting the question’s word segmentation preprocessing, named entity recognition, intent recognition, and matching with the knowledge graph to return the answer, and the intelligent Q&A function based on the knowledge graph is realized. After the model is used in a vocational high school for applied mathematics teaching experiments, learning scores are collected and analyzed, and side-by-side comparisons are made to verify the teaching effect.
Between the blended teaching at each stage of the definition continues to develop, and different scholars have a variety of views on this, but are different understanding of the word “blended”, some scholars believe that blended teaching is the use of resources and activities suitable for the development of current students in the appropriate time and learning environment, so that students form the ability to adapt to the development of the moment, and thus optimize the teaching method. It is an optimized way of teaching and learning. It is a form of teaching that combines teacher teaching and student learning. Blended learning is a form of teaching that combines different teaching philosophies. Other scholars believe that blended teaching is based on the network environment, providing students with course information resources to make up for the lack of classroom learning, providing online learning resources, which is a combination of online and offline teaching form [23].
To this end, the concept of blended teaching is defined, blended teaching using a combination of online and offline a form of teaching, but not for the two a simple patchwork, but a kind of organic combination, in the technical level, is the combination of information technology and the traditional board; in the conceptual level, is the combination of the teacher-led and the students’ main body; in the level of teaching methods, is the combination of different forms of teaching, the combination of online resources and the advantages of offline classroom, each other. At the level of teaching method, it is the combination of different teaching forms, combining the advantages of online resources and offline classroom, complementing each other, making the rational application of all kinds of teaching resources, and achieving the optimal solution of the input and output of the teaching process.
The BOPPPS instructional model originated from teacher skills training in Canada and consists of six modules: introduction, learning objectives, pre-test, participatory learning, post-test, and summarization, and the initials of the above six basic elements are linked together to form the BOPPPS instructional model [24]. The BOPPPS teaching model is centered on goal attainment and breaks down the teaching process into six modules that can be adapted to the needs of the curriculum and the characteristics of the students.The model focuses on participatory learning, aiming to involve every student in the classroom and increase the interaction between teachers and students, so as to achieve the goal of understanding and mastering knowledge.
The concept of effective teaching is an important prerequisite for influencing teachers’ effective teaching practice and researchers’ studies on effective teaching strategies, evaluation, and standards. The definition of the concept of effective teaching reflects the position, viewpoints and methods of researchers, and is the focus of research debates, which is related to the positioning of effective teaching, the fundamental attributes, and is the primary criterion for clarifying the connotation and extension of effective teaching.
First of all, higher mathematics refers to the public mathematics foundation courses commonly offered in higher vocational colleges and universities. Its main content is higher mathematics, including calculus, spatial analytic geometry, series and differential equations, and other aspects of the subject.However, according to the requirements of the attributes of each specialty, sometimes it also contains the preliminary knowledge of linear algebra, probability theory and mathematical statistics, etc. respectively. Universally speaking, any major in higher vocational colleges and universities should offer higher vocational mathematics, on the one hand, higher vocational mathematics is a cultural foundation course, which is conducive to improving the cultural quality of students; on the other hand, higher vocational mathematics is the professional foundation course of many majors, which is conducive to the study of subsequent professional courses. In terms of specificity, the requirements of various professions for cultural quality are not consistent, and the use of their respective subsequent professional courses are not the same, so the requirements of different professions for higher vocational mathematics courses are not consistent. Secondly, teaching as an activity of teachers to teach students to understand the objective world, is the process of pursuing and promoting the development of students, and the specific form of teaching is changing and developing and colorful. Teaching is a part of education and the basic way, which is commonly referred to as teaching or the main features of teaching.However, teaching is concrete and linked to certain times, places, and conditions. Teaching is an activity in which teachers teach and students learn, and it is a process in which students master cultural and scientific knowledge and skills, develop their abilities, enhance their physical fitness, and form their ideological and moral character under the guidance of teachers. Higher vocational mathematics teaching refers to all teaching-related activities or behaviors and their processes for higher vocational mathematics courses, including teaching elements such as teaching materials, teaching processes such as teaching preparation and teaching implementation, and teaching procedures such as extracurricular assignments and extracurricular tutoring. Of course, the teaching of mathematics in higher vocational education has its own special aspects, such as the selection of teaching means and teaching methods, as well as examination and evaluation and other aspects are worth studying. Of course, there is no doubt that the specific content of teaching is different. Finally, it is the effective teaching of higher vocational mathematics.
Here, the researcher puts forward the definition of effective teaching of mathematics in higher vocational: effective teaching of mathematics in higher vocational refers to the effective teaching of mathematics in higher vocational teachers according to the specific teaching content and existing teaching conditions, combined with the learning needs and cultivation objectives of different professions, selecting and applying the appropriate teaching methods and teaching strategies, and making the ability of higher vocational students get due development through careful design, serious organization, reasonable arrangement and correct guidance. The process.
The key to effective teaching of senior mathematics is for senior mathematics teachers to pursue the optimization of the teaching process and constantly reflect on the effectiveness of teaching. It is only when higher vocational students get positive and deep-rooted experiences that teaching can effectively promote the progress and development of higher vocational students and fundamentally improve the quality of teaching that it can be called “effective teaching”. Therefore, through optimizing the teaching process, senior mathematics teachers organically integrate all teaching links together, guide senior students to actively participate in mathematics learning, and obtain excellent cognitive performance, good cognitive structure, positive mathematical learning emotions, a strong sense of efficiency, strong rational thinking, strong mathematical learning ability of the teaching behavior can be identified as the effective teaching of mathematics in higher vocational education.
Under traditional classroom learning strategies, teachers need to spend a lot of time correcting assignments and test questions submitted by students, thus reducing the time spent on Q&A with students. The concept of smart education emphasizes the integration of educational technology, humanistic care, and learner-led learning as a way to improve learners’ learning outcomes and develop their creative and problem-solving abilities. Therefore, education technology can be used to automate or assist teachers in correcting students’ homework and test questions, using intelligent algorithms to give feedback based on students’ response patterns and analyzing the correctness of answers, thus saving teachers’ time and improving teaching efficiency.
The Intelligent Q&A module analyzes and answers user questions based on natural language processing. Theoretically, intelligent Q&A is an important development direction of artificial intelligence, natural language processing and other disciplines, and its research covers a variety of fields such as natural language processing, computer vision, knowledge graph and machine learning. The intelligent Q&A module is constructed through the process of constructing the knowledge graph and question module, the word segmentation preprocessing of the input question, the named entity recognition, the intent recognition, and the matching with the knowledge graph to return the answer, and the specific design scheme is shown in Fig. 1.
Design of the intelligent interanswer function
Before recognizing named entities, data preprocessing is required.Upon receiving a question from a user, the question can first be segmented using Jieba, a third-party Python library.
In order to reduce the labor cost, a deep learning based approach is used here and the BI-LSTM-CRF model is chosen for named entity recognition [25].
BI-LSTM-CRF is a deep learning structure that consists of two parts: bidirectional long and short-term memory network (BI-LSTM) and conditional random field (CRF), which can be used for named entity recognition. Compared to the unidirectional LSTM network, BI-LSTM can solve the problem that LSTM can only encode forward utterance information to a certain extent.
LSTM is a special kind of RNN that can learn long term dependent information
LSTM structure
A forget gate selectively forgets information in a cell state by reading the hidden state
New information can be selectively recorded into the cell state by the input gate, which reads the hidden state
The output gate represents the output of the LSTM, which reads the hidden state
BI-LSTM combines forward LSTM and backward LSTM to obtain two different kinds of implicit layer information, sequential and reverse order, of the input sequence, which enables better modeling of sequence information and learning of contextual semantic information.
In the named entity recognition task, BI-LSTM can effectively encode the information in the sentence, better recognize bidirectional semantic dependencies, and improve the accuracy of entity recognition.
The CRF model is a model that uses discrimination to model conditional distributions. It takes into account the influence of neighboring contextual information or states on the prediction and is more suitable for named entity recognition.The output of BI-LSTM for each word is a labeling score.CRF can add some constraints to the final constrained labels to ensure the validity of the predicted labels.The loss function of CRF has two types of scores, the emission score and the transfer score.
1) The emission score can be obtained from the labeling score output from BI-LSTM.
2) Transfer scores represent the scores transferred from one label to another, and the transfer matrix is usually used to store the scores of all labels transferred to each other to represent the constraints on the labels. The transfer matrix is a parameter of the BILSTM-CRF model, and this transfer score matrix can be randomly initialized before training the model, and all random scores in this matrix will be updated during the training process. With continuous training, these scores will become more and more reasonable, forming reasonable constraints on the labels.
The goal of the model is to maximize the probability of the true path, which is represented in Equation (7). Where
For ease of calculation, logarithmic and negative numbers are taken from Eq. (7) as the loss function, see Eq. (8).
The scores of the real paths can be calculated by summing the launch scores and transfer scores, and the sum of the scores of all paths can be calculated by the dynamic programming method. The BI-LSTM-CRF model is obtained by splicing the BI-LSTM and CRF through the fully connected layer.
In order to be able to answer the questions entered by the user, after clarifying the object asked by the question through named entity recognition, the intent of the question needs to be clarified, which is also known as intent recognition. Due to the small size of the dataset oriented in this paper, in order to improve the efficiency of intent recognition, a template-based approach is used here for this purpose. The types of questions are mainly categorized into the following two broad categories:
1) Types of “relationships”, such as “mathematically conditional on”, “occurrence”, “subordination”, “Alias”, etc. The purpose is to obtain the entity at the other end of the spectrum that is associated with the entity identified in the problem. 2) “Attribute” types such as “distribution”, “characteristics”, “color”, “degree”, etc. The purpose is to obtain the specific values of the attributes of the entities identified in the problem.
The two types of questions are standardized here to form a question template.
In order to investigate whether the BOPPPS hybrid teaching model based on intelligent question and answer technology can improve students’ academic performance, learning interest, independent learning ability, learning engagement and learning efficacy in applied mathematics courses, a semester-long teaching experiment was conducted in a higher vocational institution.
Before the teaching experiment, a questionnaire survey was conducted on the students, and two classes with similar learning bases were randomly selected as the experimental and control classes for the teaching experiment. The same teacher implemented the BOPPPS teaching model based on the intelligent question and answer technology in the experimental class, while the control class used the original teaching model to carry out the teaching activities of the course.
After completing the teaching experiment, learning scores were collected and analyzed for horizontal comparison to verify the teaching effect. The questionnaire was used to collect the teaching satisfaction and teaching effect of the students in the experimental class using the BOPPPS teaching mode based on intelligent question and answer technology.
The experimental and control classes adopted the BOPPPS teaching method, which is based on intelligent question and answer technology, and the original teaching method, respectively, to complete the learning tasks of their semester course projects. During the teaching period, the teaching progress of the experimental class and the control class is the same; the teaching evaluation of the control class is composed of the midterm test (50%) and the final exam (50%). The teaching evaluation of the experimental class is composed of 50% process evaluation and 50% summative evaluation.Statistics on the academic performance of the experimental class and the control class in the applied mathematics course were analyzed by using SPSS software to analyze the academic performance of the two classes.
The pre and post-test scores of the control class are shown in Table 1. The highest and lowest scores on the pre-test were 76.94 and 50.11, respectively. For the post-test, the scores were 77.32 and 56.29.
The comparison of the students’ academic performance
| School number | Pretest score | Aftertest score | Total score |
|---|---|---|---|
| 1 | 73.05 | 75.98 | 74.515 |
| 2 | 60.14 | 70.96 | 65.55 |
| 3 | 58.42 | 75.02 | 66.72 |
| 4 | 55.73 | 66.52 | 61.125 |
| 5 | 75.74 | 67.59 | 71.665 |
| 6 | 61.49 | 61.21 | 61.35 |
| 7 | 57.92 | 58.95 | 58.435 |
| 8 | 52.16 | 59.26 | 55.71 |
| 9 | 52.59 | 56.29 | 54.44 |
| 10 | 66.63 | 75.85 | 71.24 |
| 11 | 73.25 | 77.32 | 75.285 |
| 12 | 62.11 | 74.22 | 68.165 |
| 13 | 57.28 | 76.71 | 66.995 |
| 14 | 76.94 | 59.58 | 68.26 |
| 15 | 50.11 | 58.06 | 54.085 |
| 16 | 57.61 | 67.51 | 62.56 |
| 17 | 64 | 67.07 | 65.535 |
| 18 | 62.43 | 57.44 | 59.935 |
| 19 | 56.56 | 57.15 | 56.855 |
| 20 | 51.42 | 71.33 | 61.375 |
The experimental class scores are shown in Table 2. The highest and lowest scores on the pre-test were 76.91 and 50.94, respectively. For the posttest, the scores were 95.65 and 79.35.
Experimental student academic achievement chart
| School number | Pretest score | Aftertest score | Total score |
|---|---|---|---|
| 1 | 68.52 | 87.15 | 77.835 |
| 2 | 71.11 | 85.05 | 78.08 |
| 3 | 72.67 | 86.42 | 79.545 |
| 4 | 56.46 | 84.1 | 70.28 |
| 5 | 52.51 | 85.46 | 68.985 |
| 6 | 55.21 | 85.29 | 70.25 |
| 7 | 76.91 | 86.94 | 81.925 |
| 8 | 60.28 | 93.08 | 76.68 |
| 9 | 53.31 | 95.65 | 74.48 |
| 10 | 56.88 | 91.07 | 73.975 |
| 11 | 61.65 | 83.62 | 72.635 |
| 12 | 68.31 | 80.66 | 74.485 |
| 13 | 71.65 | 87.95 | 79.8 |
| 14 | 50.94 | 85.44 | 68.19 |
| 15 | 76.1 | 89.98 | 83.04 |
| 16 | 58.77 | 93.14 | 75.955 |
| 17 | 64.29 | 80.37 | 72.33 |
| 18 | 51.04 | 79.35 | 65.195 |
| 19 | 73.52 | 90.31 | 81.915 |
| 20 | 70.36 | 87.88 | 79.12 |
The table shows that after one semester of study the experimental class had an overall grade point average of 75.235 and the control class had an overall grade point average of 63.99. The experimental class is 11.245 points higher than the control class in terms of the average of total class grades.
Figure 3 shows the distribution of final final grades for the experimental and control classes. It can be seen that the experimental class has a significantly higher distribution of score ranges than the control class, and is higher than the control class in terms of the passing rate and the good rate (80 points or more).
The final distribution of the experimental class and the comparison class
After the teaching practice according to the above process, in order to understand the teaching effect in the implementation of BOPPPS and online-offline hybrid, this paper conducts a questionnaire survey on the experimental class and analyzes it.
In order to obtain feedback information on the teaching effect of the implementation of BOPPPS and online-offline hybrid in junior high school physics teaching, the author designed the “Integration of BOPPPS and online-offline hybrid teaching survey of higher vocational applied mathematics”, which contains the integration of BOPPPS and online-offline hybrid teaching mode of the use of the feeling of using the effect of the use of two dimensions, the questionnaire using the electronic version of the questionnaires issued to the experimental class of students, the issuance of the questionnaire The number of questionnaires is 20, the effective questionnaire is 20, the effective rate is 100%, the questionnaire content composition is as follows.
Feeling of use:
Q1: Do you think that learning with the blended higher vocational applied mathematics teaching with fusion BOPPPS and online and offline will increase your burden? Q2: Do you think the classroom of blending BOPPPS with online-offline blended higher vocational applied mathematics is active? Q3: Do you like and want to continue to use the new model for learning?
Effectiveness of use:
Q4: Do you think the new mode can enhance your interest in learning? Q5: Are you willing to actively participate in the communication and discussion in the classroom during the series of inquiry activities carried out by the higher vocational applied mathematics teacher in the classroom? Q6: Has the integration of BOPPPS and the online-offline blended teaching mode improved your self-learning ability, actively completing learning tasks, pre-study and review? Q7: Has the integration of BOPPPS with the online-offline blended teaching mode improved your ability to apply mathematics in higher education?
Table 3 shows the survey on the feeling of using the blended teaching mode of smart quiz technology and BOPPPS. 75% of the students thought that the blended teaching of able quiz technology and BOPPPS increased their learning burden. However, 85% of the students indicated that they liked and wanted to continue with the Smart Quizzing Technology and BOPPPS blended instruction. The data also showed that 90% of the students recognized the level of activity in the blended instruction classroom.
The use of the teaching pattern
| Item | Consent number | Proportion | Different number | Proportion | |
|---|---|---|---|---|---|
| Usage perception | Q1 | 15 | 75% | 5 | 25% |
| Q2 | 18 | 90% | 2 | 10% | |
| Q3 | 17 | 85% | 3 | 15% |
Table 4 shows the survey on the effects of using intelligent question and answer technology and BOPPPS blended teaching mode. In the four aspects that the new teaching mode can enhance learning interest, willingness to actively participate in the communication and discussion in class, actively complete the learning tasks, and improve the ability to apply mathematics, the percentage of students’ agreement is 80% or more than 80%.
The use effect of the teaching model is investigated
| Item | Consent number | Proportion | Different number | Proportion | |
|---|---|---|---|---|---|
| Usage effect | Q4 | 18 | 90% | 2 | 10% |
| Q5 | 16 | 80% | 4 | 20% | |
| Q6 | 18 | 90% | 2 | 10% | |
| Q7 | 19 | 95% | 1 | 5% |
The introduction before class is a key step in teaching the BOPPPS model, and a good introduction method can increase learning interest and have an important impact on subsequent teaching. In this study, we adopted the “online + offline double introduction” method to understand the students’ learning status in advance and stimulate their learning interest. Observation in the classroom shows that the students in the experimental class pay attention, actively participate in teaching activities, are good at exploring and thinking, and are highly motivated to learn independently.
Participatory activities form the foundation of the BOPPPS model. In the process of teaching implementation, this study integrates the content of the teaching materials, combines with the development of technology, and designs knowledge-coherent, step-by-step, and diversified participatory activities in phases to meet the learning needs of different students. When all students are actively involved in classroom activities, learning difficulties are solved. Gradually, a good learning environment was formed through confidence, hard work, cooperation, and teacher-student interaction.This study found that the experimental class has a good classroom atmosphere, sufficient learning motivation, a high completion rate of participatory activities, and a better promotion of students’ sustainable development.
BOPPPS model teaching feedback throughout the teaching process, from online pre-test evaluation, classroom participatory activities evaluation to post-test evaluation, can effectively feedback on student learning and teacher teaching quality. Teachers continuously optimize the teaching design and activities based on feedback, so that the teaching meets the needs of students and improves the quality of teaching.In addition, students gain understanding of their own learning situation through feedback, timely checking, and remediation, which improves learning efficiency.
This study also proves that the process feedback ensures the virtuous cycle of the whole teaching mode, and the spiral upward teaching design and learning mode is the source power of students’ cultivation, and the effective “teaching and learning” rapidly improves the vocational competitiveness of higher vocational students.
The rapid development of information technology and artificial intelligence has vigorously promoted “online and offline” hybrid teaching. The organic combination of online and offline is not only the integration of educational resources, but also the integration of teaching links, complementary teaching methods, and upgrading of teaching evaluation, which successfully builds a bridge of teacher-student and student-student interaction, and ensures the effective development of information-based teaching. The efficiency of teaching management and evaluation is improved by this study, reflecting the teaching advantages of the organic combination of online and offline, and providing a solid guarantee for the development of the optimized BOPPPS mode.
In this paper, starting from the effective teaching content of higher vocational applied mathematics, combining the BOPPPS teaching mode with online and offline blended teaching, we designed the BOPPPS blended teaching strategy based on intelligent question and answer technology, and carried out a semester teaching experiment in a higher vocational college. The highest and lowest scores in the pre-test of the experimental class were 76.94 and 50.11 respectively. The scores on the posttest were 77.32 and 56.29. After one semester of study the total grade point average of the experimental class was 75.235 and the total grade point average of the control class was 63.99. The experimental class had a total grade mean of 11.245 points higher than the control class. Observing the interval distribution of final final grade, it can be seen that the interval distribution of scores in the experimental class is significantly higher than that of the control class and is higher than that of the control class in terms of pass rate and good rate (80 or more).75% of the students think that the blended teaching of able quiz technique and BOPPPS has increased their learning load. However, 85% of the students indicated that they liked and wanted to continue with the blended instruction of smart quizzing technology and BOPPPS. The data also showed that 90% of the students recognized the level of activity in the blended instruction classroom. In the four aspects that the new teaching mode can enhance the interest in learning, willingness to actively participate in the communication and discussion in the classroom, taking the initiative to complete the learning tasks, and improving the ability to apply mathematics, the percentage of students’ approval is 80% or more.
This research was supported by the Exploration and Practice of Hybrid Teaching Reform of Applied Mathematics Curriculum in Digital Technology (No.2024GXJK859).