Design of college education evaluation based on accompanying data acquisition and mathematical analysis

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.

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.

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.

Figure 2

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.

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.

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.

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 = (χ₁, χ₂, χ₃…χ_m) is used to evaluate the quality of teachers’ classroom teaching, where χ₁ indicates the compliance of teaching content, χ₂ indicates the standardization of writing, χ₃ indicates content integrity, and so on. It is definition: (1) H=M2∑i=1m(xi−x¯)2, M=∑k=1iak(xm+1−k−xk) {\rm{H}} = {{{M^2}} \over {\sum\nolimits_{i = 1}^m {{{\left({{x_i} - \bar x} \right)}^2}}}},\,{\rm{M}} = \sum\limits_{k = 1}^i {{a_k}\left({{x_{m + 1 - k}} - {x_k}} \right)}

When the data sample is large enough, it can be proved that lim∞ H=1 \mathop {\lim}\limits_\infty \,H = 1 , that means the assumed normal distribution is valid [11].

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: (2) X=[x11…x1m⋮⋱⋮xn1…xnm] {\rm{X}} = \left[{\matrix{{{x_{11}}} & \ldots & {{x_{1m}}} \cr \vdots & \ddots & \vdots \cr {{x_{n1}}} & \ldots & {{x_{nm}}} \cr}} \right]

There is defination: (3) Xi*=Xi−E(Xi)varXi, i=1,2,…,p X_i^* = {{{X_i} - E\left({{X_i}} \right)} \over {\sqrt {{var}{X_i}}}},\,\,i = 1,2, \ldots,p

Where E(X_i) is the mean value of the data i, varX_i is its standard deviation.

The departure variance A, covariance S and positive correlation matrix F of the sample matrix are respectively: (4) A=(aij)=∑j=1n(xj−x¯)(xj−x¯)′ {\rm{A}} = \left({{a_{ij}}} \right) = \sum\limits_{j = 1}^n {\left({{x_j} - \bar x} \right){{\left({{x_j} - \bar x} \right)}^{'}}} (5) S=1n−1A=(sij) {\rm{S}} = {1 \over {n - 1}}A = \left({{s_{ij}}} \right) (6) F=(rij),rij=aijaiiajj=sijsiisjj {\rm{F}} = \left({{r_{ij}}} \right),{r_{ij}} = {{{a_{ij}}} \over {\sqrt {{a_{ii}}{a_{jj}}}}} = {{{s_{ij}}} \over {\sqrt {{s_{ii}}{s_{jj}}}}}

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 (7) λ={λ1,λ1,…λm}, λ1≥λ2≥…λm≥0 \lambda = \left\{{{\lambda_1},{\lambda_1}, \ldots {\lambda_m}} \right\},\,{\lambda_1} \ge {\lambda_2} \ge \ldots {\lambda_m} \ge 0

The corresponding eigenvectors are: (8) vi=(v1i, v2i,…vmi)′, i=1,2,…m {v_i} = \left({{v_{1i}},\,{v_{2i}}, \ldots {v_{mi}}} \right)',\,\,i = 1,2, \ldots m

The contribution degree αi=λi/∑j=1mλj {\alpha_i} = {\lambda_i}/\sum\limits_{j = 1}^m {{\lambda_j}} is defined to illustrate the importance of this data in the evaluation indicator. When the value ∑1pαk \sum\limits_1^p {{\alpha_k}} is greater than or equal to the specific gravity threshold ρ(0<ρ≤ 1), it can be considered that the top P datas calculated are enough to constitute the evaluation indicator. If ρ= 0.95, to take the evaluation indicator composed of the top P datas would be 95% reliability.

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: (9) X=(xij), i=1,2,3…m, j=1,2,3…n {\rm{X}} = \left({{x_{ij}}} \right),\,{\rm{i}} = 1,2,3 \ldots {\rm{m}},\,{\rm{j}} = 1,2,3 \ldots {\rm{n}}

Standardize the matrix: (10) xij=xij/xmax {x_{ij}} = {x_{ij}}/{x_{max}}

x_max is the maximum value of the matrix element.

The information entropy of Matrix is (11) Hj=−k∑i=1mpijlnpij, pij=xij∑i=1mxij, k=1ln m {H_j} = - k\sum\limits_{i = 1}^m {{p_{ij}}\ln {p_{ij}},{p_{ij}} = {{{x_{ij}}} \over {\sum\nolimits_{i = 1}^m {{x_{ij}}}}},\,k = {1 \over {\ln \,m}}}

The weight coefficient of evaluation indicator j is: (12) αj=1−Hj∑j=1n1−Hj, 0≤αj≤1, ∑1nαj=1 {\alpha_j} = {{1 - {H_j}} \over {\sum\nolimits_{j = 1}^n {1 - {H_j}}}},\,0 \le {\alpha_j} \le 1,\,\sum\nolimits_1^n {{\alpha_j} = 1}