Colleges and universities are an important place for higher education. The level and quality of education and teaching are important indicators to measure an university. To improve the quality of education has become the primary task of college. It is the basic form adopted by many colleges and universities to continuously evaluate their education and teaching of the school, and use the evaluation results to improve teaching management and service, so as to promote the improvement of teaching quality[1]. The basic requirement of teaching evaluation is to evaluate and judge the teaching process and teaching effect according to the teaching content and objectives, and serve the teaching decision-making. It is necessary to formulate a relatively complete evaluation system, involving the evaluation content, standards, methods, indicators, application of results and the relationship between various links[2].

Although the teaching evaluation rules has been established for a long time, its implementation is affected by various subjective and objective factors. The scientificity and practicability of the evaluation results need to be improved for the following reasons:

Firstly, the unequal relationship between evaluation subjects. Teachers and students are the core subjects of evaluation, but in most cases, the relationship between teaching and learning is unequal, and the teacher led teaching method occupies the main form. Although students participate in the whole teaching process, their evaluation to teachers and teaching process can best reflect the teaching level and effect in theory. However, student's evaluation is often affected by his personal factors (such as learning attitude, course nature, examination results, personal relationship between teachers and himself, teacher management methods, etc.), and the evaluation is uncertainly objective and fair[3]. In addition, there are similar situations among teaching managers, decision makers, supervisors and teachers.

Secondly, the main form of evaluation is result evaluation. Most teaching evaluation is to evaluate the teaching effect with the examination results after finishing courses or examination. This is called result evaluation. Although the result evaluation also reflects the teaching level to a certain extent, it can not provide effective information during teaching. At the same time, only the observation and assessment results can not completely reflect the real state and teaching quality of teaching and learning, which is particularly obvious in the courses related to practice and art, such as music, sports, dance, painting and so on [4].

Thirdly, The evaluation indicators are not comprehensive enough and the evaluation feedback delay. Most colleges and universities use information systems to assist teaching and collect relevant data through the systems, the collected data can be used as the basis for teaching evaluation. However, many real-time data cannot be obtained through similar information systems, such as students’ interest and learning attitude, classroom teaching activity, teachers’ clarity and accuracy of classroom expression, which need to be collected by questionnaires lately, Thus, it is affected by human subjective factors. Moreover, students’ extracurricular learning behavior also belongs to an important part of the teaching process, but it can not be perceived by the system, resulting in one-sided evaluation of students’ learning process [5].

With the popularization of Internet of things, face recognition, 5G, boundary computing and other technologies, it is possible to collect and analyze people's data on campus insensitively. In order to build an objective and reasonable teaching evaluation model in colleges and universities, we proposes a teaching evaluation model based on accompanying data acquisition and mathematical analysis, which collects the data generated and associated with daily teaching behavior in real time, and analyzes and displays it with the help of big data tools. It is hoped to improve the evaluation method of higher education by using big data intelligent technology

In order to obtain as much teaching related data as possible, it is necessary to summarize some columns of data such as classroom teaching, teaching management, teaching service, before and after class, teaching design and assessment scheme, especially the relevant data that may be generated in each segment of the teaching process. The data acquisition is insensitively and no affection to normal teaching activities.

In Colleges and universities, there are dozens or even hundreds of commonly used information systems, such as educational administration management, student management, personnel management, online learning, etc. These systems usually store structured data, perform independent functions respectively, and are integrated and shared through task management and data exchange. This kind of data is usually to obtain relatively easier. According to the functional categories, these information systems can be divided into teaching, scientific research, management, service and so on. Due to the overlapping and interleaving relationship of data between systems, in order to avoid data conflict, it is necessary to define authoritative data sources, which are called metadata [6]. Table 1 is for various data and metadata relationships.

metadata definition

management data subset | Organization | Personnel system |

financial | Financial system | |

Logistics service | Agile Logistics | |

Land and property | Asset management system, experimental management system | |

Instrument and equipment | ||

major information | Educational administration system | |

Class information | ||

Course information | ||

Faculty data subset | Staff basic information | Personnel system |

Course information | Educational administration system | |

Scientific research information | Scientific research management system | |

Tutor information | Student management system | |

Teaching management data subset | Teaching plan | Educational administration system |

Curriculum information | ||

Online course resources | E-learning | |

Student course selection | Educational administration system | |

Classroom information | ||

Experimental course | ||

Laboratory | Experimental management system | |

Teaching evaluation | Teaching evaluation system | |

Student management data subset | Student status | Educational administration system |

Student registration | ||

Score | ||

Admissions | Enrollment system | |

Freshman enrollment | Freshman enrollment system | |

Graduate departure | School leaving system | |

Student payment | Financial system | |

Aid financially | Student management system | |

Accommodation | ||

Reward and punishment | ||

Students’ mental health | ||

Student employment | Student employment system |

The metadata is united and shared through data bus and data exchange center. After extraction, verification and transform, the basic data from the data source enters the sharing data center to form a metadata table. The standardized data can be pushed back to each information system in the form of synchronization, association and sharing, so as to realize the standardization and accuracy of the data of the information system. The logical relationship is shown in Figure 1.

Another kind of data exists not in the form of records and tables, but in file or raw format, which is called unstructured data or semi-structured data. The common file formats include pictures, audio, video, long text log, etc. Because of its large capacity of unstructured data files, in order to reduce the storage space and facilitate later retrieval and analysis, it is necessary to extract their key information (such as index, description and feature sets) and store them structurally [7].

Let's Take classroom teaching as an example. During class in the smart classroom, the camera will capture the class state. The smart camera with boundary calculation will execute portrait recognition, then face comparison and face recognition. So as to record the students participating in the class, complete the class check-in function, and save the students’ class state image. The camera will take a complete picture of the class in the classroom. The camera with zoom and pan tilt function will also track and snapshoot the teacher's activities, and automatically synthesize teaching materials in combination with projection and other equipment, so as to facilitate students’ on-demand review after class. Voice recognition system converts the teaching content and interactive dialogue into words. In physical education or dance class, the camera not only can finish face recognition function, but also has the functions of posture capture and behavior recognition, which is convenient to judge whether the students’ movements are standardized. These data are collected in real time automatically.

Many machine's logs are in the form of messages, and its text is very long and different in length. For example, the log of study state in e-learning system records online contents and learning situations of students. Therefore, it is necessary to analyze, decompose and convert the whole record into structured records for storage.

The data types described above can be automatically collected through machines and information systems, while some data can not be obtained through non perceptual way, which requires the cooperation of users. For example, the results of the questionnaire or the data related to personal information need to be authorized or submitted by oneself. When we evaluating the physical condition of students, students are required to submit their own physiological data, or collect them through medical instruments and Internet of things devices on the premise that students know and authorize [8]. In the physical education courses of many colleges and universities, IOT or GPS are used for positioning to complete the measurement and assessment of students’ running and daily exercise, and students are required to actively submit data during exercise [9].

In order to facilitate data analysis, it is necessary to store the data obtained from each channel orderly. Table 2 shows the subjects involved in teaching evaluation and their relationship. We can see that there are several pairs of subjects that need cross evaluation, including mutual evaluation between teachers and students, students and teachers.

Evaluation Subject

Evaluated Subject | Student | Teacher | Supervise | Management | Tools | Environment |
---|---|---|---|---|---|---|

Subject | ||||||

Student | ✓ | ✓ | - | ✓ | ✓ | ✓ |

Teacher | ✓ | ✓ | - | ✓ | ✓ | ✓ |

Supervise | ✓ | ✓ | - | ✓ | ✓ | ✓ |

Management | ✓ | ✓ | ✓ | - | ✓ | ✓ |

We need to design a corresponding analysis topic, package and sort out the data related to the topic, and store the data according to the column storage rules. The evaluation of teaching process is involving the topics of students, teachers, courses and teaching environment. Teaching management evaluation is involving the topics of specialty, training plan, personnel and teachers. The evaluation of teaching conditions is involving assets, teaching environment, teaching tools and themes. The massive educational data can be storaged, calculated and processed by multi-source heterogeneous data module in Hadoop big data platform. The platform consists of data source, data collection, cleaning and integration, distributed data storage, data analysis, visualization and other modules. In terms of data storage, HDFS is used to store unstructured data, HBase and hive are used to store structured data, and Kafka and redis are used to cache data that are often processed and need rapid response. In terms of parallel computing, MapReduce is used for large-scale data set computing, and spark technology is used to realize streaming data processing and memory computing [10]. The design framework of campus data acquisition and analysis platform is shown in Figure 3.

In order to evaluate education and teaching reasonably, we need to design the evaluation indicators based on the existing data, and get the evaluation results through data analysis and calculation. The design of evaluation indicators should meet the requirements of teaching objectives and correctly reflect the teaching quality and level, it should also feed back the existing problems. Each evaluation index has data support and correct calculation method. The quantitative results can be easily obtained through the evaluation model.

We take the evaluation of teachers’ classroom teaching ability as an example to introduce the analysis and application of accompanying data. Table 3 shows the indicators designed for the evaluation of College Teachers’ classroom teaching ability.

evaluation indicators of teacher's classroom teaching ability

Primary Indicator | Secondary Indicator |
---|---|

Content of Courses | The teaching content is correct without scientific errors |

Specification for words, symbols, units and formulas | |

The knowledge content is complete and in line with the teaching objectives | |

Clear knowledge structure and logical level | |

The key points and difficulties are prominent and Enlightening | |

Teaching Method | Adopt heuristic, inquiry and case teaching methods |

Interactive teaching | |

Students-centered teaching | |

The exercises are rich and the number of questions is appropriate | |

Teaching orientation is accurate and adapt to students’ cognitive level | |

Teaching Attitude | Adequate preparation and abundant teaching materials |

Clear expression and standard writing | |

Words and deeds are appropriate and energetic | |

Observe the time and finish classes on time | |

Teaching Skills | Skilled use of teaching tools, good human-computer interaction |

The courseware is fine and artistic | |

Classroom organization and management | |

The teaching scene design is creative, vivid and interesting | |

Teaching Effectiveness | Students are active in class and have a high attendance rate |

Good classroom order | |

Students have a high degree of knowledge acquisition | |

Students’ participation is high and the classroom atmosphere is active |

Because there are many data sources and a large collection range, the data dimensions that can be used to support the evaluation indicators are large too. Especially there may be a certain relationship between various data sets. In order to reduce the calculating cost, we need to find out the key indicators and key data dimensions in a large amount of data.

We assume that the collected data meet the normal distribution, and use a vector X to represent a set of data to be calculated. Each type of data can be regarded as the dimension of a vector. For example, X = (_{1}, _{2}, _{3}…_{m}_{1} indicates the compliance of teaching content, _{2} indicates the standardization of writing, _{3} indicates content integrity, and so on. It is definition:

When the data sample is large enough, it can be proved that

Principal component analysis can be used to choose indicators and data. The principle is to execute orthogonal verification on the vectors so as to find out the uncorrelated vectors, which are called the main components [12]. This chosen vectors have a major impact on the evaluation results. Assuming that there are n evaluation data and dimensions of each indicator is m, the sample matrix is:

There is defination:

Where _{i}_{i}

The departure variance A, covariance S and positive correlation matrix F of the sample matrix are respectively:

The principal component can be obtained by solving the eigenvalue and eigenvector of correlation matrix F. F is actually a sparse matrix. Its characteristic root is defined as

The corresponding eigenvectors are:

The contribution degree

After choosing the evaluation indicators and the datas required, we need to assign weight coefficient to the indicators. Because the evaluation data includes not only the data collected by machines and equipment, but also the mutual scores of various evaluation subjects, the subjective evaluation often has a certain priori. Therefore, combined with subjective and objective evaluation, information entropy is used to calculate the weight coefficient. On the basis of maintaining good subjective orientation, the weight coefficient of each indicator is corrected with objective data [13].

Define m is number of evaluation indicators, and there are n evaluation parameters corresponding to each indicator. Define the judgment matrix:

Standardize the matrix:

_{max}

The information entropy of Matrix is

The weight coefficient of evaluation indicator j is:

Teaching evaluation is a very important segment in the teaching work of colleges and universities. It is a scientific evaluation and judgment to the teaching process and teaching effect. Reasonable evaluation methods and scientific evaluation models are conducive to promoting the improvement of teaching quality. Using the evaluation mathematical model based on accompany data analysis of the new generation of information technology such as Internet of things and big data, the traditional evaluation method is changed from result, lag and subjectivity to process, real-time and comprehensive, and the evaluation results are more objective and credible.

#### metadata definition

management data subset | Organization | Personnel system |

financial | Financial system | |

Logistics service | Agile Logistics | |

Land and property | Asset management system, experimental management system | |

Instrument and equipment | ||

major information | Educational administration system | |

Class information | ||

Course information | ||

Faculty data subset | Staff basic information | Personnel system |

Course information | Educational administration system | |

Scientific research information | Scientific research management system | |

Tutor information | Student management system | |

Teaching management data subset | Teaching plan | Educational administration system |

Curriculum information | ||

Online course resources | E-learning | |

Student course selection | Educational administration system | |

Classroom information | ||

Experimental course | ||

Laboratory | Experimental management system | |

Teaching evaluation | Teaching evaluation system | |

Student management data subset | Student status | Educational administration system |

Student registration | ||

Score | ||

Admissions | Enrollment system | |

Freshman enrollment | Freshman enrollment system | |

Graduate departure | School leaving system | |

Student payment | Financial system | |

Aid financially | Student management system | |

Accommodation | ||

Reward and punishment | ||

Students’ mental health | ||

Student employment | Student employment system |

#### Evaluation Subject

Evaluated Subject | Student | Teacher | Supervise | Management | Tools | Environment |
---|---|---|---|---|---|---|

Subject | ||||||

Student | ✓ | ✓ | - | ✓ | ✓ | ✓ |

Teacher | ✓ | ✓ | - | ✓ | ✓ | ✓ |

Supervise | ✓ | ✓ | - | ✓ | ✓ | ✓ |

Management | ✓ | ✓ | ✓ | - | ✓ | ✓ |

#### evaluation indicators of teacher's classroom teaching ability

Primary Indicator | Secondary Indicator |
---|---|

Content of Courses | The teaching content is correct without scientific errors |

Specification for words, symbols, units and formulas | |

The knowledge content is complete and in line with the teaching objectives | |

Clear knowledge structure and logical level | |

The key points and difficulties are prominent and Enlightening | |

Teaching Method | Adopt heuristic, inquiry and case teaching methods |

Interactive teaching | |

Students-centered teaching | |

The exercises are rich and the number of questions is appropriate | |

Teaching orientation is accurate and adapt to students’ cognitive level | |

Teaching Attitude | Adequate preparation and abundant teaching materials |

Clear expression and standard writing | |

Words and deeds are appropriate and energetic | |

Observe the time and finish classes on time | |

Teaching Skills | Skilled use of teaching tools, good human-computer interaction |

The courseware is fine and artistic | |

Classroom organization and management | |

The teaching scene design is creative, vivid and interesting | |

Teaching Effectiveness | Students are active in class and have a high attendance rate |

Good classroom order | |

Students have a high degree of knowledge acquisition | |

Students’ participation is high and the classroom atmosphere is active |

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Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network