# Consistency of Zhejiang Provincial College Entrance Examination Questions and Curriculum Standards Based on Knowledge Map Construction

Authors: Xiaoyu Zhong; Weiqun Wang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Students’ scores on the advanced placement exercise test are an important guide to the development of personalized instructional tutoring. Traditional exercise test systems only counts the total value of students’ scores in each question and cannot analyze students’ different levels of mastery of each aspect of knowledge and intelligence, which limits the accuracy of teaching and tutoring. By introducing the cognitive diagnosis theory, we designed and implemented a personalized online college entrance examination exercise test system, which realizes the functions of test management, course management, group paper management, and learning reports. Based on the college entrance examination score record and knowledge point correlation matrix, we can analyze the students’ knowledge mastery status comprehensively.


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## Body

## 1. Introduction

Since the 1990s, humanity has entered a new process of development. To inherit human civilization, education is an important way, and it is equally an important factor in the development of nations [1]. Many countries have carried out educational reforms in order to enhance their competitiveness in the world. Educational reforms have been carried out in many countries in order to enhance their influence on the process of world competition, to meet the new demand for talents from all walks of life, and to adapt to the knowledge economy [2–4]. The purpose of education reform in many countries is to enhance their influence in the process of global competition, to meet the new demand for talents, and to adapt to the advent of the knowledge economy. For example, the United States, the United Kingdom, Japan, and other countries have made changes in curriculum-based academic assessments [5].In the United States, the United Kingdom, Japan, and other countries, changes have been made in the academic evaluation based on the curriculum standards [6]. The U.S. is one of the countries that have revised the existing education system.In addition, each country has gained some experience and achieved certain research results. The U.S. is committed to achieving a “holistic” approach to education in order to dominate the world’s competition and seize the power of global discourse [7–9].The U.S. is committed to achieving “total excellence” in education. President Biden’s signing of No Child Left Behind (NCLB) was a landmark start to curriculum reforms in the United States. This was followed by the release of Levin’s report—Our Future, Our Teachers [10]. The Chinese Ministry of Education released reports of documents on teachers and the education policy, such as the Every Student Succeeds Act. It states the purpose of teacher education reforms and provides policy support [11, 12].New national curriculum standards were issued in the UK, and the implementation of the new curriculum standards in the country have begun. From then on, the UK stepped into a new era of educational reforms. There was a change in the core of the educational reforms in the UK. It began with the promulgation of the Importance of Teaching and Learning [13, 14].The Rainbow Project in Japan was introduced at the beginning of the twenty-first century. This program focuses on educating students to grasp the basics, to develop sound-minded students, and to teach students to think independently and learn on their own. Students will have different personalities and will be able to survive in the international society by protecting their individual development [15].Since educational reforms are being implemented in various countries, it is important to align curriculum standards with educational assessment, which is fundamental to the implementation of the new curriculum reforms. Therefore, the issue of consistency between academic assessment and curriculum standards has become a popular study worldwide [16–19]. As mentioned above, some developed countries in Europe and the United States, led by the United States, have discussed academic assessment based on curriculum standards and conducted research on the alignment of the two.With the passage of time and based on various national education reforms, China has also carried out a series of education reforms. The new curriculum reform has introduced a series of new curriculum reforms. The new curriculum reform has introduced a series of related laws and regulations. This provides legal protection for the implementation of basic education [20, 21].Until now, one of the most important tests during the academic period of students has been the college entrance examination, which is still an important criterion for admission to universities. Every year in June, China conducts college entrance exams to assess the learning of high-school students [22]. It has a broad and far-reaching impact on the society as a whole. The college entrance exam is not only an overall assessment of students’ high-school education but also a reflection of how well the curriculum reforms are being implemented. It is also the main basis for measuring the strength of school teachers and their professionalism. Teachers’ teaching activities are also influenced by the test content and the cognitive level of the college entrance examination.Based on the full implementation of the new curriculum reform, the evaluation system has changed accordingly, as mentioned in the outline: “To establish an evaluation system that enables students to develop comprehensively, continue to reform and improve the examination system [23].”The contributions of this paper are as follows:(1)
By introducing cognitive diagnosis theory, we designed and implemented a personalized online college entrance examination exercise test system, which realizes the functions of test question management, course management, test paper management, test management, learning situation reports, and so on(2)
We designed the incidence matrix based on the score records of the college entrance examination and knowledge points to recommend the precursor knowledge points of the current knowledge points(3)
We used the developed exercise recommendation platform as the experimental environment to evaluate the performance effect by comparing the results of the knowledge points automatically recommended with the knowledge points manually recommended by experts


## 2. Related Work

The exploration of assessment models based on changes in curriculum standards has become a popular study in the United States and in some developed countries. The U.S. has proposed the NAEP, an educational progress assessment mechanism, for assessing educational progress, with the National Education Data Center of the Department of Education taking responsibility [24, 25].A study of the consistency between middle- and high-school examination questions and the curriculum standards was conducted. For example, in [26], the consistency between middle-school chemistry examination papers and the curriculum standards in Changchun was analyzed from both quantitative and qualitative perspectives with the help of the SEC consistency analysis model. In [27], a study was conducted to analyze the differences between the chemistry curriculum standards and the chemistry test questions in the 2004–2009 Shanghai middle-school examinations with the help of SEC consistency analysis and to explore the trends of the changes. In [28], a preliminary study on the consistency of Chinese chemistry examination questions and curriculum standards was conducted in four aspects—knowledge categories, depth of knowledge, breadth of knowledge, and balance of knowledge distribution—drawing on Weber’s model. In [29], from a quantitative perspective, SEC analysis was used to explore the degree of agreement between chemistry test questions and curriculum standards in the last three years of the Jiangxi provincial secondary school examination, and the results showed that there was good agreement between the content of the chemistry test questions and curriculum standards in the last three years of the Jiangxi provincial secondary school examination. The framework of the consistency analysis as well as the methods is presented in [30]. In [2], the authors studied the consistency between junior high-school physics and curriculum standards in Ireland and China. In [3], the authors investigated the consistency between the 2014 national college entrance examination chemistry paper and curriculum standards with the help of Weber’s model. The authors of [4] analyzed the consistency between high-school chemistry-teaching activities, college entrance examination papers, chemistry curriculum standards at the high-school level, and curriculum components that have a significant impact on students in Jiangsu and Jiangxi. In [5], the authors analyzed the consistency between the two components of the Chinese mathematics examination and the curriculum standards through Weber’s analysis model. In [6], four years of high-school entrance examination chemistry questions from Sichuan Province were selected as research materials, and the degree of congruence between the questions and the curriculum standards was investigated with the help of the SEC model. In [7], the SEC consistency analysis model was chosen to investigate the agreement between the test questions of the chemical reaction principles category and the curriculum standards by selecting four years of Zhejiang college entrance examination chemistry test questions as the research material. Weber’s model was used to investigate the agreement between the Beijing advanced level examination mathematics (science) papers and the compulsory modules of the curriculum standards [8]. In [21], the authors adopted a combination of quantitative and qualitative methods to select four years of geography examination papers in Fujian Province as research materials; explored the match between them and the geography curriculum standards; and analyzed the current situation, changing trends, and main influencing factors of the consistency between them.


## 3. Related Concepts

### 3.1. Course Standards

Curriculum standards have different meanings in different countries. The National Science Education Standards in the United States specify that curriculum standards are the basis for evaluating the quality of teaching and learning and that the quality of the functioning of the educational system, the quality of teachers’ teaching, the quality of students’ learning abilities, and the quality of what students learn are measured on the basis of curriculum standards. Whether for schools, localities, or the state, the basis for the evaluation implemented by educators is based on this standard [4]. In 1990, in the Dictionary of Education, a famous Chinese scholar Gu Mingyuan argued that the definition of curriculum standards should be “a programmatic document that determines the level of the curriculum, the structure of the curriculum, and the model of the curriculum at a certain stage” [1] and that each learning content, the cognitive level, and the development of the curriculum of each school period should be specified in detail in the curriculum standards.In summary, based on the new concept of curriculum reforms and with reference to the views of other scholars, this study will define that chemistry curriculum standards are programmatic documents issued by the state that reflect the students’ knowledge. Curriculum standards are the minimum requirements in terms of content topics, cognitive levels, and student performance in the process of learning chemistry, including activities, assessments, and development of material.


### 3.2. Consistency

Columbia state in the State Standards and Evaluation Consistency Guide defines consistency as follows: “Consistency refers to the degree of similarity between two or more things that are similar to each other and also refers to matching the branches of the whole so that they work well” [4]. According to the well-known scholar Weber, “Consistency is the degree to which two or more things match, that is, the degree to which the parts or elements of a thing form a harmonious whole and concentrate on a unified concept” [3]. In summary, consistency refers to the degree of similarity between various factors or a better fit between the elements of the whole, and it is attributed to the same goal.The consistency analysis method is a method of analyzing and discerning the degree of agreement between the elements of the curriculum system [14]. Practice has shown that after the implementation of curriculum reforms and the implementation of the new curriculum reform concept, there is a need to maintain a high degree of consistency between curriculum assessment and curriculum standards.


## 3.1. Course Standards

Curriculum standards have different meanings in different countries. The National Science Education Standards in the United States specify that curriculum standards are the basis for evaluating the quality of teaching and learning and that the quality of the functioning of the educational system, the quality of teachers’ teaching, the quality of students’ learning abilities, and the quality of what students learn are measured on the basis of curriculum standards. Whether for schools, localities, or the state, the basis for the evaluation implemented by educators is based on this standard [4]. In 1990, in the Dictionary of Education, a famous Chinese scholar Gu Mingyuan argued that the definition of curriculum standards should be “a programmatic document that determines the level of the curriculum, the structure of the curriculum, and the model of the curriculum at a certain stage” [1] and that each learning content, the cognitive level, and the development of the curriculum of each school period should be specified in detail in the curriculum standards.In summary, based on the new concept of curriculum reforms and with reference to the views of other scholars, this study will define that chemistry curriculum standards are programmatic documents issued by the state that reflect the students’ knowledge. Curriculum standards are the minimum requirements in terms of content topics, cognitive levels, and student performance in the process of learning chemistry, including activities, assessments, and development of material.


## 3.2. Consistency

Columbia state in the State Standards and Evaluation Consistency Guide defines consistency as follows: “Consistency refers to the degree of similarity between two or more things that are similar to each other and also refers to matching the branches of the whole so that they work well” [4]. According to the well-known scholar Weber, “Consistency is the degree to which two or more things match, that is, the degree to which the parts or elements of a thing form a harmonious whole and concentrate on a unified concept” [3]. In summary, consistency refers to the degree of similarity between various factors or a better fit between the elements of the whole, and it is attributed to the same goal.The consistency analysis method is a method of analyzing and discerning the degree of agreement between the elements of the curriculum system [14]. Practice has shown that after the implementation of curriculum reforms and the implementation of the new curriculum reform concept, there is a need to maintain a high degree of consistency between curriculum assessment and curriculum standards.


## 4. Research Materials

This study will explore the content dimension and cognitive depth from a quantitative perspective in the last three years in Hunan Province. It is hoped that this study will help explore the alignment of the questions in the last three years of the scientific examination with the curriculum standards of general high-school chemistry.


### 4.1. General High-School Chemistry Curriculum Standards

In this study, the “General High-School Chemistry Curriculum Standards (Experimental Draft)” of Zhejiang Province was selected as one of the study materials. “The content to be mastered by high-school students and the objectives to be achieved for each topic are clearly defined in the curriculum standards” [47]. The study will analyze the alignment between the chemistry test questions in the college entrance examination and the curriculum standards, thus reflecting the implementation status of the curriculum standards in Hunan Province. The study will investigate the distribution of the content of the curriculum standards in the chemistry test questions of the college entrance examination so as to provide a reference for the proposition researchers.


### 4.2. Zhejiang Provincial College Chemistry Entrance Examination Test

The research material of this paper is the science synthesis chemistry test questions of Zhejiang Province from 2018 to 2021, and the method takes a knowledge mapping to construct a model, takes a quantitative test on the science synthesis chemistry test questions of Zhejiang Province from 2018 to 2021, and uses the SEC model to analyze the coincidence between the test questions and the curriculum standards in the three years so as to illustrate the proposition of the science synthesis chemistry test questions of Hunan Province in the last three years.


## 4.1. General High-School Chemistry Curriculum Standards

In this study, the “General High-School Chemistry Curriculum Standards (Experimental Draft)” of Zhejiang Province was selected as one of the study materials. “The content to be mastered by high-school students and the objectives to be achieved for each topic are clearly defined in the curriculum standards” [47]. The study will analyze the alignment between the chemistry test questions in the college entrance examination and the curriculum standards, thus reflecting the implementation status of the curriculum standards in Hunan Province. The study will investigate the distribution of the content of the curriculum standards in the chemistry test questions of the college entrance examination so as to provide a reference for the proposition researchers.


## 4.2. Zhejiang Provincial College Chemistry Entrance Examination Test

The research material of this paper is the science synthesis chemistry test questions of Zhejiang Province from 2018 to 2021, and the method takes a knowledge mapping to construct a model, takes a quantitative test on the science synthesis chemistry test questions of Zhejiang Province from 2018 to 2021, and uses the SEC model to analyze the coincidence between the test questions and the curriculum standards in the three years so as to illustrate the proposition of the science synthesis chemistry test questions of Hunan Province in the last three years.


## 5. Strategies for Advanced Placement Courses Based on Knowledge Mapping

Regarding the recommendation of exercises, this study makes full use of the antecedent and subsequent relationships of knowledge points and recommends them in the following two directions:(1)
Based on the knowledge map, we recommend toward the antecedent knowledge points of the current knowledge points. This allows learners to consolidate the basic knowledge points they have not yet mastered and to build a good foundation for learning the current knowledge points.(2)
Based on the knowledge map, we recommend the subsequent knowledge points to the current knowledge points. This can guide learners to learn the next knowledge point efficiently based on mastering the current knowledge point to enhance learning efficiency.In the process of the study, the system calculates the probability of students mastering the current knowledge point based on the knowledge tracking model proposed in the previous section combined with the results of learner exercise tests. For the knowledge points that have not yet been mastered, the knowledge map is used to find their precursor knowledge points and recommend the corresponding exercises to the learners to achieve the purpose of personalized recommendation.


### 5.1. Recommended Strategies for Antecedent Knowledge Points

The main task of the knowledge graph-based precursor knowledge point recommendation is to find out the basic knowledge points of the learner’s current learning knowledge points and recommend exercises to guide the learner to consolidate the basic knowledge points.Before executing the exercise recommendation algorithm, the system generates a sequential knowledge point A by default, or learners can select a knowledgeable point according to their mastery of the subject. The recommendation algorithm recommends an exercise to the learner and calculates the probability of the learner’s mastery of knowledge point A using the student knowledge mastery probability model [18].As shown in Figure1, if the probability model concludes that the learner has not mastered knowledge point A, the knowledge graph in the knowledge model can be matched to obtain the set of base knowledge points of the compound knowledge point A and the set of its precursor knowledge points.Figure 1
Diagram of the start of the exercise recommendation.In the process of recommending knowledge point A’s subknowledge pointai (i = 1, 2,...,n) and precursor knowledge point cj (j = 1, 2,...,m) to students, we first determine whether knowledge point A is an initial knowledge point, and if it is an initial knowledge point, we generate knowledge point A’s subknowledge point ai and stores it in Java’s Arraylist. Otherwise, the algorithm will give a knowledge list in HashSet according to the order of edge weights in the knowledge graph and recommend the precursor knowledge point cj or subknowledge point ai of knowledge point A corresponding to the largest edge in this order to the learner, as shown in Figure 2 of the model of knowledge point A.Figure 2
Model diagram of knowledge point A.Depending on the knowledge point selected by the learner or generated by default, the algorithm can recommend exercises to the learner in two cases:(1)
If the default generated knowledge intelligence is a metaknowledge pointai of a compound knowledge point A, then the algorithm will recommend the exercises related to the compound knowledge point A to the learner. Then, after the learner completes the exercises, the algorithm stops if the knowledge tracking result shows that the learner’s probability of mastering the compound knowledge point A has exceeded the threshold (0.8). If the result of the knowledge tracking shows that the probability of the learner mastering the compound knowledge point A did not exceed the threshold (0.8), then the algorithm will recommend other subknowledge points ai of knowledge point A that the learner has not mastered in the order of their weights and recommend the exercises of ai to the student until the learner has completely mastered the subknowledge points of the compound knowledge point. If the learner has mastered all the subknowledge points of the compound knowledge point A, the result of knowledge tracking is still unsatisfactory, and if the compound knowledge point A has the precursor knowledge point cj, the precursor knowledge point cj is recommended to the learner, and the operation is carried out according to the processing method in equation (2). If the compound knowledge point A has no precursor knowledge intelligence, the subknowledge points of A will be recommended until the learner’s learning effect is satisfactory.(2)
If the system generates a precursor knowledge pointcj of knowledge point A by default, the algorithm will recommend the exercises of the precursor knowledge point cj to the learner. Then, using the knowledge tracking model, the probability P of the learner mastering the precursor knowledge point cj is calculated, and a threshold p is set for the probability. Then, the relationship between the probability P and the threshold p is divided into two cases ① and ②:(1)
If P >p, the learner has mastered the compound knowledge point cj. In this case, the system will generate an exercise for the compound knowledge point A and use the knowledge tracking model to calculate the learner’s mastery of knowledge point A [15]. The algorithm is finished. If the learner still has not mastered knowledge point A and there are other precursor knowledge points cj for that knowledge point, it further recommends other precursor knowledge points cj for that knowledge point based on the ranking of the weight of the precursor knowledge points and then proceeds as in equation (2).(2)
If P <p, it means that the learner has not mastered the compound knowledge point cj. For such a case, the precursor knowledge points of knowledge point cj are searched until the probability of the learner mastering knowledge point cj reaches the threshold, and then knowledge tracking is performed for the mastery of knowledge point A. If the probability of the learner mastering knowledge point A reaches the threshold, then the algorithm terminates. If the learner’s probability of mastering knowledge point A does not reach the threshold, then the algorithm recommends other prior knowledge points cj of knowledge point A to the learner.


### 5.2. Recommended Strategies for Subsequent Knowledge Points

The recommendation strategy of subsequent knowledge points based on the knowledge graph mainly pushes the subsequent knowledge points that learners currently master well, which is consistent with the traditional form of classroom teaching; in the traditional classroom, after learners master a certain knowledge point, the teacher will arrange the next knowledge point for learning, and the precursor example diagram of knowledge points is shown in Figure3.Figure 3
Example diagram of the precursors of a knowledge point.Suppose the learner is found to have mastered the compound knowledge point F in the actual operation of the algorithm after testing, then the system finds the knowledge graph to get the successor knowledge pointDi (i = 1, 2, ..., p) of the compound knowledge point F. If there is no successor knowledge point of the compound knowledge point F, the algorithm ends. Then, the base knowledge points of knowledge point Di are obtained by matching the knowledge graph, and the backward recommendation algorithm is executed for knowledge point F.In the execution flow of the algorithm, F is considered asc1. Depending on how many antecedent knowledge points Di has to be analyzed during the execution of the algorithm, it is handled in two cases:(1)
If knowledge pointDi has a unique precursor knowledge point, then the algorithm will present the learner with the exercises corresponding to the subknowledge point di1 of knowledge point Di in the process of running. Knowledge tracking is performed on the learning process of the learner to examine the degree of mastery of the learner in pushing the compound knowledge point Di. If the probability of the learner mastering the knowledge point calculated according to the knowledge tracking model exceeds a threshold value, the recommendation algorithm ends. If the learner has not mastered knowledge point Di according to the knowledge tracking model, the algorithm continues to recommend the next subknowledge point di2 to the intimacy of the learner’s knowledge points until the probability of the learner mastering knowledge point Di is higher than the threshold, and the recommendation strategy is shown in Figure 4.(2)
Knowledge pointDi has other precursor knowledge points, and the other precursor knowledge points of Di are to be obtained first. Here, the algorithm is divided into two cases according to the students’ mastery of it:Figure 4
Recommendation strategy for subsequent knowledge points.If the student has mastered all the precursor knowledge points of the compound knowledge pointDi, then the algorithm processes them as in equation (1).If the learner has not mastered all the antecedent knowledge points, then the algorithm selects the antecedent knowledge pointc1 that the learner has not mastered, generates a copy of the exercise corresponding to knowledge point c1, and performs knowledge tracking on the completion of the learner’s exercise to examine its mastery of knowledge point c1, at which the following needs to be considered:(a)
The probability that the learner has mastered the knowledge pointc1 is above the threshold:If the probability of the learner mastering other precursor knowledge points of knowledge pointDi is higher than or equal to the threshold, the exercises corresponding to the subknowledge points of knowledge point Di are presented to the learner, and the strategy of equation (1) is followed.If the probability of the learner mastering other precursor knowledge points of knowledge pointDi is lower than the threshold, other knowledge points that have not yet been mastered are recommended to the student, and the strategy of algorithm (2) is followed.(b)
If the probability of mastering knowledge pointc1 is lower than the threshold, then the precursor knowledge point recommendation strategy is performed for the knowledge point until knowledge point c1 is mastered.


### 5.3. Compound Knowledge Point Default Subknowledge Point Recommendation Strategy

In the process of recommending exercises to learners, how to recommend subknowledge points of compound knowledge points to learners is based on learners’ mastery of the knowledge points. In this study, the learners’ past learning records are analyzed, and if the learners want to consolidate what they have learned, the system sets a higher threshold of knowledge points and recommends some more difficult subknowledge points to the learners.In this study, the average of learners’ knowledge mastery probability is used as the threshold of knowledge points so as to measure which knowledge points are weakly mastered by the target learners and which are better mastered by the learners, and the system will recommend the weakly mastered knowledge points to the learners. In the experiment, a vectorsi is selected as the probability of learners’ knowledge points, and the knowledge points to be recommended by the target learner S are obtained. If the probability of mastering Ki is less than or equal to the threshold value, the subknowledge is added to the list of weakly mastered knowledge points αsi; otherwise, the subknowledge is not processed. The above-mentioned procedure is repeated until all the subknowledge points are compared with the threshold value, and the list of weak knowledge points is finally obtained.


## 5.1. Recommended Strategies for Antecedent Knowledge Points

The main task of the knowledge graph-based precursor knowledge point recommendation is to find out the basic knowledge points of the learner’s current learning knowledge points and recommend exercises to guide the learner to consolidate the basic knowledge points.Before executing the exercise recommendation algorithm, the system generates a sequential knowledge point A by default, or learners can select a knowledgeable point according to their mastery of the subject. The recommendation algorithm recommends an exercise to the learner and calculates the probability of the learner’s mastery of knowledge point A using the student knowledge mastery probability model [18].As shown in Figure1, if the probability model concludes that the learner has not mastered knowledge point A, the knowledge graph in the knowledge model can be matched to obtain the set of base knowledge points of the compound knowledge point A and the set of its precursor knowledge points.Figure 1
Diagram of the start of the exercise recommendation.In the process of recommending knowledge point A’s subknowledge pointai (i = 1, 2,...,n) and precursor knowledge point cj (j = 1, 2,...,m) to students, we first determine whether knowledge point A is an initial knowledge point, and if it is an initial knowledge point, we generate knowledge point A’s subknowledge point ai and stores it in Java’s Arraylist. Otherwise, the algorithm will give a knowledge list in HashSet according to the order of edge weights in the knowledge graph and recommend the precursor knowledge point cj or subknowledge point ai of knowledge point A corresponding to the largest edge in this order to the learner, as shown in Figure 2 of the model of knowledge point A.Figure 2
Model diagram of knowledge point A.Depending on the knowledge point selected by the learner or generated by default, the algorithm can recommend exercises to the learner in two cases:(1)
If the default generated knowledge intelligence is a metaknowledge pointai of a compound knowledge point A, then the algorithm will recommend the exercises related to the compound knowledge point A to the learner. Then, after the learner completes the exercises, the algorithm stops if the knowledge tracking result shows that the learner’s probability of mastering the compound knowledge point A has exceeded the threshold (0.8). If the result of the knowledge tracking shows that the probability of the learner mastering the compound knowledge point A did not exceed the threshold (0.8), then the algorithm will recommend other subknowledge points ai of knowledge point A that the learner has not mastered in the order of their weights and recommend the exercises of ai to the student until the learner has completely mastered the subknowledge points of the compound knowledge point. If the learner has mastered all the subknowledge points of the compound knowledge point A, the result of knowledge tracking is still unsatisfactory, and if the compound knowledge point A has the precursor knowledge point cj, the precursor knowledge point cj is recommended to the learner, and the operation is carried out according to the processing method in equation (2). If the compound knowledge point A has no precursor knowledge intelligence, the subknowledge points of A will be recommended until the learner’s learning effect is satisfactory.(2)
If the system generates a precursor knowledge pointcj of knowledge point A by default, the algorithm will recommend the exercises of the precursor knowledge point cj to the learner. Then, using the knowledge tracking model, the probability P of the learner mastering the precursor knowledge point cj is calculated, and a threshold p is set for the probability. Then, the relationship between the probability P and the threshold p is divided into two cases ① and ②:(1)
If P >p, the learner has mastered the compound knowledge point cj. In this case, the system will generate an exercise for the compound knowledge point A and use the knowledge tracking model to calculate the learner’s mastery of knowledge point A [15]. The algorithm is finished. If the learner still has not mastered knowledge point A and there are other precursor knowledge points cj for that knowledge point, it further recommends other precursor knowledge points cj for that knowledge point based on the ranking of the weight of the precursor knowledge points and then proceeds as in equation (2).(2)
If P <p, it means that the learner has not mastered the compound knowledge point cj. For such a case, the precursor knowledge points of knowledge point cj are searched until the probability of the learner mastering knowledge point cj reaches the threshold, and then knowledge tracking is performed for the mastery of knowledge point A. If the probability of the learner mastering knowledge point A reaches the threshold, then the algorithm terminates. If the learner’s probability of mastering knowledge point A does not reach the threshold, then the algorithm recommends other prior knowledge points cj of knowledge point A to the learner.


## 5.2. Recommended Strategies for Subsequent Knowledge Points

The recommendation strategy of subsequent knowledge points based on the knowledge graph mainly pushes the subsequent knowledge points that learners currently master well, which is consistent with the traditional form of classroom teaching; in the traditional classroom, after learners master a certain knowledge point, the teacher will arrange the next knowledge point for learning, and the precursor example diagram of knowledge points is shown in Figure3.Figure 3
Example diagram of the precursors of a knowledge point.Suppose the learner is found to have mastered the compound knowledge point F in the actual operation of the algorithm after testing, then the system finds the knowledge graph to get the successor knowledge pointDi (i = 1, 2, ..., p) of the compound knowledge point F. If there is no successor knowledge point of the compound knowledge point F, the algorithm ends. Then, the base knowledge points of knowledge point Di are obtained by matching the knowledge graph, and the backward recommendation algorithm is executed for knowledge point F.In the execution flow of the algorithm, F is considered asc1. Depending on how many antecedent knowledge points Di has to be analyzed during the execution of the algorithm, it is handled in two cases:(1)
If knowledge pointDi has a unique precursor knowledge point, then the algorithm will present the learner with the exercises corresponding to the subknowledge point di1 of knowledge point Di in the process of running. Knowledge tracking is performed on the learning process of the learner to examine the degree of mastery of the learner in pushing the compound knowledge point Di. If the probability of the learner mastering the knowledge point calculated according to the knowledge tracking model exceeds a threshold value, the recommendation algorithm ends. If the learner has not mastered knowledge point Di according to the knowledge tracking model, the algorithm continues to recommend the next subknowledge point di2 to the intimacy of the learner’s knowledge points until the probability of the learner mastering knowledge point Di is higher than the threshold, and the recommendation strategy is shown in Figure 4.(2)
Knowledge pointDi has other precursor knowledge points, and the other precursor knowledge points of Di are to be obtained first. Here, the algorithm is divided into two cases according to the students’ mastery of it:Figure 4
Recommendation strategy for subsequent knowledge points.If the student has mastered all the precursor knowledge points of the compound knowledge pointDi, then the algorithm processes them as in equation (1).If the learner has not mastered all the antecedent knowledge points, then the algorithm selects the antecedent knowledge pointc1 that the learner has not mastered, generates a copy of the exercise corresponding to knowledge point c1, and performs knowledge tracking on the completion of the learner’s exercise to examine its mastery of knowledge point c1, at which the following needs to be considered:(a)
The probability that the learner has mastered the knowledge pointc1 is above the threshold:If the probability of the learner mastering other precursor knowledge points of knowledge pointDi is higher than or equal to the threshold, the exercises corresponding to the subknowledge points of knowledge point Di are presented to the learner, and the strategy of equation (1) is followed.If the probability of the learner mastering other precursor knowledge points of knowledge pointDi is lower than the threshold, other knowledge points that have not yet been mastered are recommended to the student, and the strategy of algorithm (2) is followed.(b)
If the probability of mastering knowledge pointc1 is lower than the threshold, then the precursor knowledge point recommendation strategy is performed for the knowledge point until knowledge point c1 is mastered.


## 5.3. Compound Knowledge Point Default Subknowledge Point Recommendation Strategy

In the process of recommending exercises to learners, how to recommend subknowledge points of compound knowledge points to learners is based on learners’ mastery of the knowledge points. In this study, the learners’ past learning records are analyzed, and if the learners want to consolidate what they have learned, the system sets a higher threshold of knowledge points and recommends some more difficult subknowledge points to the learners.In this study, the average of learners’ knowledge mastery probability is used as the threshold of knowledge points so as to measure which knowledge points are weakly mastered by the target learners and which are better mastered by the learners, and the system will recommend the weakly mastered knowledge points to the learners. In the experiment, a vectorsi is selected as the probability of learners’ knowledge points, and the knowledge points to be recommended by the target learner S are obtained. If the probability of mastering Ki is less than or equal to the threshold value, the subknowledge is added to the list of weakly mastered knowledge points αsi; otherwise, the subknowledge is not processed. The above-mentioned procedure is repeated until all the subknowledge points are compared with the threshold value, and the list of weak knowledge points is finally obtained.


## 6. Experimental Evaluation of Recommended Knowledge Graph-Based High-Stakes Exam Exercises

### 6.1. System Performance Evaluation of the Recommended High-School Exam Exercises

In this study, the exercise recommendation platform developed by the author was chosen as the experimental environment, and the recommendation algorithm was combined with the recommendation algorithm of previous similar studies. The algorithm evaluation method uses precision, recall, and F-value to evaluate the knowledge point. Accuracy is a criterion to measure the accuracy of the system knowledge point recommendation, which can be expressed as the ratio of the correct knowledge points recommended to the total knowledge points recommended. Recall rate is a criterion used to evaluate the comprehensiveness of knowledge point recommendation, which can be expressed as the ratio of recommended correct knowledge points to the actual existing knowledge points. F-value is a measure of the overall evaluation index of the system knowledge point recommendation [19].This study uses the method of comparing the results of automatically recommended knowledge points with those of manually recommended knowledge points by experts to evaluate the above-mentioned indicators. There are a large number of knowledge points to be recommended in the system, and in the process of conducting experiments, a common starting knowledge point is selected uniformly for the experts and the system. Then, according to the system’s recommendation strategy, the system recommends a list of knowledge points according to the learners’ mastery of the knowledge points and compares this list with the list of knowledge points recommended by the experts to calculate the accuracy, recall, and F-value. In order to verify more accurately, the validation is repeated twice during the experiment.The experts evaluated by the system are all excellent teachers from front-line teaching positions with rich teaching experience in the subject and can accurately grasp the learning status of learners, and these conditions can ensure the accuracy and reliability of the manual knowledge point recommendations.Knowledge points recommended by the system and those manually extracted by experts were compared one by one for accuracy, recall, and F-value of the knowledge point recommendations, through which Table1 is obtained.Table 1
Recommendation system knowledge point recommendation result evaluation.
FrequencyAccuracyRecallF-value10.860.710.8720.750.680.72The experiments show that the recommendation algorithm used in this study has a high accuracy rate. The low recall rate indicates that the sample of knowledge points is too small and less comprehensive and there is still a need to improve the recommendation details of the recommendation algorithm. However, in general, the sex of the system can meet the needs of small sample scenarios. The next section analyzes and evaluates the experimental effect of the recommendation algorithm.


### 6.2. Evaluation of the Learning Effect of the Recommendation System on High-School Exams

The purpose of the experiment to evaluate the learning effectiveness of the exercise recommendation system is to investigate whether there is a significant improvement in test scores after learners use the recommendation algorithm for learning.This study develops a corresponding learning platform based on the study of knowledge graph-based exercise algorithms. Learners can log into the learning platform to learn and then practice. In order to verify the effectiveness of the exercise recommendation algorithm, a controlled experiment was designed and set up in this study. The learners who participated in the experiment were divided into two groups—the experimental group and the control group—and in the process of the experiment, the learning performance of each group was recorded separately, and the average performance of the group was calculated. In equation (1), Spa is the mean score of the control group after the experiment, Spb is recorded as the score of the control group before the experiment, and the learning effect of the control group is assessed according to the following equation:(1)Rp=Spa−SpbSpb.IfSea is the average score of the experimental group after learning with the exercise recommendation algorithm and Seb is the average score of the experimental group after learning with the exercise recommendation algorithm, then the score improvement rate of the experimental group is calculated according to the following formula:(2)Re=Sea−SebSeb.The rate of improvement of the learning effect of the exercise recommendation algorithm can be calculated according to the following formula:(3)R=Re−RP.In this study, the above-mentioned formula will be used to evaluate the effectiveness of learners’ learning based on the knowledge graph-based exercise recommendation algorithm.In the course of the experiment, 30 middle-school students were selected to register and log in to the exercise recommendation platform developed in this study to conduct experiments with the knowledge graph-based exercise recommendation algorithm. Fifteen students were randomly selected as the experimental group to practice the exercises recommended by the recommendation algorithm on the platform, and the remaining 15 students were in the control group to study the material independently.On the learning platform, two sets of exercises with the same knowledge and difficulty were selected and named Volume A and Volume B, which contained two compound knowledge points that were antecedents and successors of each other. 20 questions were set in each paper, each with 5 marks, and 5-6 questions were set for each metaknowledge point; the learners were allowed to use these two questions for testing. The pretest and post-test scores for each group of learners were recorded separately; the knowledge mastery of learners in the experimental and control groups was recorded in each instance, and the average of each group was calculated as the result of the experiment. To ensure validity of the experiment, random effects were eliminated in the experiment in conjunction with the actual situation. The test was repeated 10 times in the experiment.Table2 and Figure 5 show the test data of the experimental group and the change in the improvement effect:Table 2
Test results of the experimental group.
Number of testsVolume A scoreVolume B scorePromotion rate168.2178.250.12266.2578.230.14370.2595.780.21469.5686.750.2563.2174.580.14665.2787.560.25775.2885.270.29872.1482.100.07974.2590.780.161070.8795.170.23Figure 5
Comparison of scores of experimental groups.Calculations using the data in Table2 yielded an average experimental lift rate of 19.30% for the experimental group.As shown in Table3 and Figure 6, the test data of the control group and the change in the lifting effect are demonstrated:Table 3
Experimental results of the control group.
Number of testsVolume A scoreVolume B scorePromotion rate167.2175.50.17265.5778.230.13372.7885.780.09468.786.680.08573.5874.580.12665.2587.510.07761.7885.260.12872.2882.180.09974.2490.750.081085.6385.280.19Figure 6
Graph of experimental results of the control group.The experimental average improvement rate for the control group reached 8.12%, as calculated by using the data in Table3. It is clear from the simulation experiments that there is a significant improvement in the scores of learners who use the knowledge graph-based exercise recommendation algorithm. Therefore, the knowledge graph-based learning recommendation is of great significance. It shows that strengthening the practice of basic knowledge can effectively improve the learning effect, and all can get twice the result with half the effort in learning as long as they study hard.


## 6.1. System Performance Evaluation of the Recommended High-School Exam Exercises

In this study, the exercise recommendation platform developed by the author was chosen as the experimental environment, and the recommendation algorithm was combined with the recommendation algorithm of previous similar studies. The algorithm evaluation method uses precision, recall, and F-value to evaluate the knowledge point. Accuracy is a criterion to measure the accuracy of the system knowledge point recommendation, which can be expressed as the ratio of the correct knowledge points recommended to the total knowledge points recommended. Recall rate is a criterion used to evaluate the comprehensiveness of knowledge point recommendation, which can be expressed as the ratio of recommended correct knowledge points to the actual existing knowledge points. F-value is a measure of the overall evaluation index of the system knowledge point recommendation [19].This study uses the method of comparing the results of automatically recommended knowledge points with those of manually recommended knowledge points by experts to evaluate the above-mentioned indicators. There are a large number of knowledge points to be recommended in the system, and in the process of conducting experiments, a common starting knowledge point is selected uniformly for the experts and the system. Then, according to the system’s recommendation strategy, the system recommends a list of knowledge points according to the learners’ mastery of the knowledge points and compares this list with the list of knowledge points recommended by the experts to calculate the accuracy, recall, and F-value. In order to verify more accurately, the validation is repeated twice during the experiment.The experts evaluated by the system are all excellent teachers from front-line teaching positions with rich teaching experience in the subject and can accurately grasp the learning status of learners, and these conditions can ensure the accuracy and reliability of the manual knowledge point recommendations.Knowledge points recommended by the system and those manually extracted by experts were compared one by one for accuracy, recall, and F-value of the knowledge point recommendations, through which Table1 is obtained.Table 1
Recommendation system knowledge point recommendation result evaluation.
FrequencyAccuracyRecallF-value10.860.710.8720.750.680.72The experiments show that the recommendation algorithm used in this study has a high accuracy rate. The low recall rate indicates that the sample of knowledge points is too small and less comprehensive and there is still a need to improve the recommendation details of the recommendation algorithm. However, in general, the sex of the system can meet the needs of small sample scenarios. The next section analyzes and evaluates the experimental effect of the recommendation algorithm.


## 6.2. Evaluation of the Learning Effect of the Recommendation System on High-School Exams

The purpose of the experiment to evaluate the learning effectiveness of the exercise recommendation system is to investigate whether there is a significant improvement in test scores after learners use the recommendation algorithm for learning.This study develops a corresponding learning platform based on the study of knowledge graph-based exercise algorithms. Learners can log into the learning platform to learn and then practice. In order to verify the effectiveness of the exercise recommendation algorithm, a controlled experiment was designed and set up in this study. The learners who participated in the experiment were divided into two groups—the experimental group and the control group—and in the process of the experiment, the learning performance of each group was recorded separately, and the average performance of the group was calculated. In equation (1), Spa is the mean score of the control group after the experiment, Spb is recorded as the score of the control group before the experiment, and the learning effect of the control group is assessed according to the following equation:(1)Rp=Spa−SpbSpb.IfSea is the average score of the experimental group after learning with the exercise recommendation algorithm and Seb is the average score of the experimental group after learning with the exercise recommendation algorithm, then the score improvement rate of the experimental group is calculated according to the following formula:(2)Re=Sea−SebSeb.The rate of improvement of the learning effect of the exercise recommendation algorithm can be calculated according to the following formula:(3)R=Re−RP.In this study, the above-mentioned formula will be used to evaluate the effectiveness of learners’ learning based on the knowledge graph-based exercise recommendation algorithm.In the course of the experiment, 30 middle-school students were selected to register and log in to the exercise recommendation platform developed in this study to conduct experiments with the knowledge graph-based exercise recommendation algorithm. Fifteen students were randomly selected as the experimental group to practice the exercises recommended by the recommendation algorithm on the platform, and the remaining 15 students were in the control group to study the material independently.On the learning platform, two sets of exercises with the same knowledge and difficulty were selected and named Volume A and Volume B, which contained two compound knowledge points that were antecedents and successors of each other. 20 questions were set in each paper, each with 5 marks, and 5-6 questions were set for each metaknowledge point; the learners were allowed to use these two questions for testing. The pretest and post-test scores for each group of learners were recorded separately; the knowledge mastery of learners in the experimental and control groups was recorded in each instance, and the average of each group was calculated as the result of the experiment. To ensure validity of the experiment, random effects were eliminated in the experiment in conjunction with the actual situation. The test was repeated 10 times in the experiment.Table2 and Figure 5 show the test data of the experimental group and the change in the improvement effect:Table 2
Test results of the experimental group.
Number of testsVolume A scoreVolume B scorePromotion rate168.2178.250.12266.2578.230.14370.2595.780.21469.5686.750.2563.2174.580.14665.2787.560.25775.2885.270.29872.1482.100.07974.2590.780.161070.8795.170.23Figure 5
Comparison of scores of experimental groups.Calculations using the data in Table2 yielded an average experimental lift rate of 19.30% for the experimental group.As shown in Table3 and Figure 6, the test data of the control group and the change in the lifting effect are demonstrated:Table 3
Experimental results of the control group.
Number of testsVolume A scoreVolume B scorePromotion rate167.2175.50.17265.5778.230.13372.7885.780.09468.786.680.08573.5874.580.12665.2587.510.07761.7885.260.12872.2882.180.09974.2490.750.081085.6385.280.19Figure 6
Graph of experimental results of the control group.The experimental average improvement rate for the control group reached 8.12%, as calculated by using the data in Table3. It is clear from the simulation experiments that there is a significant improvement in the scores of learners who use the knowledge graph-based exercise recommendation algorithm. Therefore, the knowledge graph-based learning recommendation is of great significance. It shows that strengthening the practice of basic knowledge can effectively improve the learning effect, and all can get twice the result with half the effort in learning as long as they study hard.


## 7. Conclusions

Obtaining students’ real-time cognitive level is a key prerequisite for accurate personalized instruction. In this paper, by introducing knowledge graph construction, we design and implement a recommended high-stakes testing system based on knowledge graph construction. The system takes students’ test data in the system as input, and after cognitive diagnostic modeling and analysis, it obtains students’ current cognitive state, thus providing a decision basis for teachers to target-teaching students and also facilitating students to consolidate and strengthen their knowledge according to their own cognitive level.In the future, we will reconstruct the exercise testing system into a client–server model and improve the flexible support mechanism for various subjective and objective question types.



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