Design and Implementation of a Computational Model for the Enhancement of College Students’ Independent Learning Ability Supported by Big Data

The hierarchical structure of independent learning indicators for college students is shown in Figure 1. The scale mainly consists of two parts: the dynamic subscale and the strategy subscale, and the final questions are 70 questions analyzed through item analysis. The motivation subscale includes six factors: learning self-efficacy, learning intrinsic goal, learning sense of control, learning extrinsic goal, learning sense of meaning, and learning anxiety. The strategy subscale includes 6 factors: general approach, asking for help with learning, scheduling and summarizing learning, assessing learning, and managing learning. Self-efficacy has 6 items, each of which is a reflection of college students’ self-efficacy, and is mainly concerned with the specific manifestation of college students’ perceptions of competence and self-confidence in the learning process. Self-efficacy is measured as SE, and the ratio of the total score of this item to the total score of the questionnaire is recorded as S_SE.

Figure 1.

The college students’ self-learning index hierarchy

Intrinsic goals have 8 items. Intrinsic goals are part of the motivation subscale, which is part of the personal psychological domain. Intrinsic goals are labeled as IG, and the ratio of the sum of the scores of this item to the total score of the questionnaire is labeled as S_IG.

Sense of Learning Control has seven items that reflect the judgment of college students. Sense of Learning Control is labeled as LC, and the ratio of the sum of the scores of this item to the total score of the Self-Directed Learning Questionnaire for college students is labeled as S_LC.

Learning Extrinsic Goals has 3 items, which are related to the goals set by college students in order to compete. It can make it easier for us to enjoy the joy of success. Increase our confidence. Learning Extrinsic Goal is recorded as LEG, and the ratio of the sum of scores of this item to the total scores of the questionnaire of Independent Learning Questionnaire for college students is recorded as S_LEG.

Sense of Learning Significance (LSM) has 2 items, which are the extent to which college students understand the role of learning. The sense of learning significance is recorded as LSM, and the ratio of the sum of scores of this item to the total score of the questionnaire of the Independent Study Questionnaire for college students is recorded as S_LSM.

Learning Anxiety has 4 items and is a psychological condition in which students worry about things related to learning. Learning Anxiety is labeled as LA, and the ratio of the sum of the scores of this item to the total score of the questionnaire is labeled as S_LA.

There are 12 general methods, which are general study methods that students often use to solve study-related problems.The general method is labeled as GM, and the ratio of the sum of the scores for this item to the total score of the questionnaire is labeled as S_GM.

There are nine items of study help, reflecting the difficulties encountered by college students and the need for assistance from others.Learning Help is labeled as LH, and the ratio of the sum of the scores for this item to the total score of the Self-Directed Learning Questionnaire is labeled as S_LH.

There are seven items in the study plan arrangement for college students to design their own study activities in a coordinated way. The Learning Plan Arrangement is labeled as LP, and the sum of the scores of the Independent Study Questionnaire and the total score of the questionnaire is labeled as S_LP.

Learning summary has 5 items, which is a reflection of college students’ reflection on their own learning. The summary of learning is called LS, and the sum of this item’s scores and the total score of the questionnaire is referred to as S_LS.

Assessment of Learning has three items, which are mainly for students to evaluate the process and results of learning activities. Learning evaluation is labeled as LE, and the sum of the scores of the questionnaire and the total score of the questionnaire is labeled as S_LE.

Learning management has four items, which are the adjustment and arrangement of learning activities by university students. Learning management is labeled as LM, and the sum of the scores for this item and the total score of the questionnaire is labeled as S_LM.

The questions related to the factors in the questionnaire were slightly improved to align with the characteristics of big data collection. Independent learning of university students is mainly collected for a specific consecutive period of time for an individual as the basic information for the assessment of the student’s learning ability during this period. Therefore, the time period of collection was one academic year ago, and the collection was carried out every 2 weeks, with the total number of information collected for one individual being 26.

Markov process: When the state of a system (or process) at a certain time t1 is a known condition, the conditional probability distribution of the state of the system (or process) at time t > t1 is independent of the state before time t1, but only related to time t1. In other words, the “future” and the “past” are independent of each other under the condition that the “now” state of the system (or process) is known, and its “future” state does not depend on the “past” state, which is often referred to as Markov or non-after-effect [27].Markovianity is described in terms of a probability distribution function as follows: let the state space of the stochastic process {X(t),t ∈ T} be S if, for any moments of time t, t₁ < t₂ < ⋯ < t_n, n ≥ 3t_i ∈ T, the conditional probability distribution function of X(t_n) under conditions X(t_i) = χ_i, xi ∈ S, and i = 1,2,⋯,n – 1 is exactly equal to the conditional probability distribution function of X(t_n) at time X(t_n–1) = x_n–1, that is: (1) P{ X(tn)≤xn }/X(t1)=x1,X(t2)=x2,⋯,X(tn−1)=xn−1 }=P{ X(tn)≤xn/X(tn−1)=xn−1 },xn∈R

The stochastic process {X(t),t ∈ T} is then said to be Markovian or to have no posteriority, and the process is called a Markov process.

State transfer probabilities: Markov chain properties can be described by state transfer probabilities. For a finite state space, the transfer probability distribution can be expressed as a matrix with (i,j) elements, called the “transfer matrix”: (2) pij=P(Xn+1=i/Xn=j),i,j∈E

The integral of the k-step transfer probability in the discrete state space is the summation, which can be obtained by summing the powers of k over the transfer matrix. If it is a “one-step transfer probability matrix”, i.e., the transfer matrix after a k-step transfer, then it is satisfied: (3) pij(t)1≥0,i,j∈E∑j∈EPij=1,i∈E

Self-directed learning ability prediction models are used to predict the degree of a person’s self-directed learning ability in the next time state for a short period of time a stable learning state.

The basic idea of Markov chain model is to predict the next state of independent learning ability based on the state in the current period. If the current state of independent learning of a student is known, the prediction of independent learning ability in the next time period is based on the prediction model on this basis. In order to get a more stable prediction model, the examination time is set as 4 weeks, during which the analysis and research is carried out to find the state transfer probability matrix.

The state of the next time period T_i+1 is independent of the previous state of time period T_i, and the prediction results are obtained by examining only the state of autonomous learning in the current time period T_i.

The construction process is as follows:

1) Factors affecting college students’ independent learning (IF) are divided into two factors, namely, study motivation (ST) and study strategy (SS), where study motivation (ST) includes study interest (SI), study purpose (SG), teacher’s assessment (TA), learning environment (LE), major choice (PC), and study attitude (SA). Study strategies (SS) included study plan (SP), study style (SW), study reflection (SR), assignment assessment (JA), study content (SC), and self-efficacy (SE). Taking these 12 data as the current learning state of students, and setting the examination period in 4 weeks as n, a total of n independent learning states were collected: {S₁,S₂,⋯,S_n}, i < n, and i indicate the current period, and the independent learning state of S_i predicts the independent learning state of S_i+1, and S_i serves as the base data for the prediction, which is S_i represented in the form of a data vector of the 12 indicators in the calculation.

S_i, S_i+1, S_i+1 are expressed as follows: (5) Si=( S_SIi,S_SJi,S_TAi,S_TAi,S_LEi,S_PCi,S_SAi S_SPi,S_SWi,S_SRi,S_JAi,S_SCi,S_SEi ) (6) Si+1=( S_SIi+1,S_SJi+1,S_TAi+1,S_TAi+1,S_LEi+1S_PCi+1,S_SAi+1,S_SPi+1,S_SWi+1,S_SRi+1S_JAi+1 S_SCi+1,S_SEi+1 ) (7) S′i+1=( S_SI′i+1,S_SJ′i+1,S_TA′i+1,S_TA′i+1,S_LE′i+1S_PC′i+1,S_SA′i+1,S_SP′i+1,S_SW′i+1,S_SR′i+1S_JA′i+1 S_SC′i+1,S_SE′i+1 )

S_i, S_i+1, and S′i+1 are all 1×12 matrices, and P is a 12×12 matrix, which is a state transfer matrix. From equation (4), the predicted value of the student’s independent learning ability can be calculated each time.

To make the model prediction experimental results more credible, students from five different colleges and universities were selected as test subjects. The test data statistics are shown in Table 1.

The test data in Table 1 are divided into training samples and validation samples according to the ratio of 3:1, and the fitting accuracies of the training samples and validation samples are analyzed and counted, and the specific results are shown in Figure 3. The fitting accuracy of the prediction experiment of college students’ independent learning ability is higher than the prediction accuracy, which is consistent with the actual situation, and the fitting accuracy are more than 88%, indicating that the model in this paper has a better fitting effect, and at the same time, it can accurately predict the independent learning ability of college students.

Figure 3.

The model’s self-learning ability and the prediction accuracy

The fitting errors of the training samples and validation samples are calculated, and the specific results are shown in Figure 4. The fitting and prediction errors of college students’ independent learning ability prediction experiments are controlled within 10%, which fully meets the practical requirements of college students’ independent learning ability prediction error less than 20%, and obtains very ideal prediction results, and the experimental results prove the effectiveness of the prediction model of college students’ independent learning ability designed in this paper.

Figure 4.

The autonomic learning ability of the model and the prediction error

In order to test the superiority of the Markov chain-based prediction model of college students’ independent learning ability designed in this paper, the same test data are used under the same test platform to compare and analyze with the prediction models of independent learning ability based on BP neural network (Model 1) and based on Random Forest (Model 2), and the fitting and prediction accuracies of their training and validation samples are respectively as shown in Figure 5. Comparing the prediction accuracy of the three models, it can be found that the average prediction accuracy of college students’ independent learning ability based on Markov chain, BP neural network and random forest is 0.874, 0.813, 0.861 respectively, which indicates that the model designed in this paper solves the problem of large prediction error of college students’ independent learning ability, and can accurately reflect the changing law of college students’ independent learning ability, and verifies the superiority of the prediction model of college students’ independent learning ability in this paper. The superiority of the prediction model for the independent learning ability of college students.

Figure 5.

Model fitting precision and prediction accuracy contrast

The modeling efficiency of college students’ independent learning ability becomes an important evaluation index of the superiority of the model. The statistical total time of modeling college students’ independent learning ability is shown in Figure 6. From the total time of modeling college students’ independent learning ability, it can be seen that the average values of the total time of modeling college students’ independent learning ability based on Markov chain, BP neural network and random forest are 21.15s, 27.43s and 34.74s respectively.The total time spent modeling college students’ self-directed learning ability in this paper is significantly less and more valuable for practical application.

Figure 6.

Comparison of the prediction efficiency of autonomous learning ability

The study selected two groups of students from university A, one experimental group (N=40) and the other control group (N=40), which were comparable in terms of their independent learning ability, grade level and major before the experiment. A 4-week experimental cycle was set. The experimental group used the Markov chain-based prediction model of college students’ independent learning ability to provide students with personalized guidance on improving their learning ability, and provided each student with customized learning and improvement suggestions based on the model’s prediction results. The control group did not use the prediction model, but provided regular study guidance and resources. 4 weeks later, students in both groups were tested again on their independent learning ability to assess the changes in their ability. According to the data collection method proposed in the previous section, and according to the hierarchical structure diagram of college students’ independent learning indicators, the overall pre-post analysis of college students’ ability improvement and the pre-post analysis of each dimension were conducted. The assessment method is based on a Likert scale, with “1~5” indicating “strongly disagree~strongly agree” respectively.

Using SPSS19.0 paired samples t-test, the evaluation of the level of independent learning ability of students in the experimental group is shown in Figure 7. Pre- and post-test variance analyses of learning motivation and learning strategies were conducted, and the p-values were 0.003 and 0.001, respectively, which were less than 0.01. It indicated that the students in the experimental group had a significant improvement in their independent learning ability after using the Markov Chain-based prediction model of college students’ independent learning ability.

Figure 7.

Evaluation of independent learning ability of the experimental group

The evaluation of the level of independent learning ability of the students in the control group is shown in Figure 8. The pre- and post-test variance analysis of learning motivation and learning strategies showed p-values of 0.131 and 0.215, respectively, which were not significantly different. It indicates that the independent learning ability of college students using conventional study guides and resources is not significantly improved.

Figure 8.

Control group autonomous learning ability level evaluation

Pre- and post-test analyses were conducted for the experimental group on each indicator under the dimensions of learning motivation and learning strategies.