This paper was edited by Subhas Chandra Mukhopadhyay.
The effective learning requires putting down various associations of new ideas to old ones to integrate some innovative thoughts. The learners must change the associations among the things they already know, or even reject some longheld attitude about the world. The choice to the essential reformation is to deform the new information to fit their old ideas or to reject the new information entirely. Learners come to the classroom with their own ideas, some may be correct and some may not be, concerning roughly each topic they are expected to come across. If their perception and misunderstanding are unnoticed or discharged out of control, it affects the learning of a learner. The learners must be encouraged to build up new observation by seeing how such observation helps them make better sense of the world. The objective of this research paper is to put down the fundamentals of learning that promotes effective learning in an instructorled virtual classroom and to analyze the learners’ learning performance using the Discriminant Analysis, a data mining technique. The Discriminant Analysis uses statistically significant determinants to predict learners’ learning in a classroom.
The environment of a learner could be distinguished by synchronous and asynchronous learning, also the level of communication between learnerlearners, learnerinstructor, learnercontent, and learnerinstructional media (
Asynchronous learning has an advantage in offering unlimited access to class contents or materials anytime and anywhere. A responsive plan of course deliverance permits a learner to improve at his/her own speed. The learner not getting immediate answers to their questions on a certain topic is the drawback of asynchronous learning. Also, the learner does not get immediate feedback on their response to class materials and instructional delivery to strengthen their learning (
New York’s Smart School program emphasizes the role of technology integrated into the classroom by enhancing student achievement and practice students to take part in the 21stcentury financial system (
The instructorled virtual classroom is a smart way of teaching and learning environment where learners can work jointly, exchange a few words, monitor and argue the presentation, and employ with learning resources working in a group. The learner’s concentration strengthens in instructorled virtual classrooms as its environment is interactive. The smart instructorled virtual classrooms provide
Immediate feedback.
Access to instructors.
Facetoface interaction.
In smart instructorled virtual classrooms, there is an instructor in the environment with learners when doing or looking at activities. Instructorled virtual classrooms can also be more instructive, provided that a supplementary provides effective knowledge. The class notes are recorded and the important details of the topic are pointed out in an instructorled virtual classroom. The interaction is made through contentrelated discussion topics by the learner. The learner uses text features to discuss the topics with the group. The discussion group helps the learner to get an answer for the posted question. The learner is allowed to take part in the discussion and share their own creative ideas. The learner has the facility to view the lecture on a topic in powerpoint slides. The learner uses programs independently to create an innovative product for the course in applications such as word and excel. The instructor uses multimedia resource that helps the learner to access and view to acquire more ideas. The realtime feedback is provided in such a smart educational environment to engage the learner into effective, proficient, and meaningful learning. This instructorled virtual classrooms use a cognitive approach further to enhance the withstanding ability of any learner. The analysis of learner’s information, such as assessment of academics, attitudes, and behavioral pattern, helps the educational institutes to predict failure rate measuring to reduce the same and to check whether they are using their resources in the right places and producing the right results.
Cognition is a new topic in the field of cognitive science. The basic argument is about the significance of physical experience in sensemaking and learning (
The ability to sustain concentration on a particular object, action, or thought.
The ability to manipulate objects.
The ability to visualize images and scenarios.
Abilities that facilitate goaloriented behavior, such as the tendency to plan and execute a goal.
The ability to withstand distraction and internal advises.
The ability to identify and manage one’s own emotions for good performance.
Learning in an instructorled virtual classroom is done with the help of various methods such as projectbased approach, interactive learning approach, exposition learning approach, contingent assignment, and imaginative empowerment approach. Each approach identifies the learner with different cognitive skills and learning is made with the respective identified approach. Identifying the cognitive skills of each learner and providing learning based on the skill is very difficult. In the instructorled virtual classroom approach, learning is afforded by observing the learner’s cognitive skills. The different cognitive skills are given in
Cognitive skills and related behaviors.
The observation made from each learner is summarized as follows:
A monotonous learner’s keenness is augmented.
An innovative thoughtprovoked outcome is yielded.
Learners engage themselves in group activities voluntarily.
Idea sharing and discussion are done.
Stressfree learning is made.
The upshot of learning is enhanced.
Asking and answering the question.
Later, the prediction and analysis are made with the Discriminant analysis that enhances the performance of each learner.
In a projectbased method, the learners are grouped into seven teams with four members in each team. All the team members are instructed to select a topic from microprocessor and microcontroller subjects. The teams were given one month’s time to get ready with their own topics. Each team used different materials to explain their concepts. The materials used by the teams are charts, newspaper content, information from internet sources, cardboard work, and reallife examples to explain the microprocessor working along with the instructions and instruction set. The cognitive skills observed at the end of the work from each team are synthesis, intelligence, reasoning, evaluation, and application. The percentage of skills observed from each team is analyzed and grouped under a grade.
Ifthen rules were formed as follows:
If skill percentage> = 90 then Grade = ‘A’
If skill percentage> = 80 then Grade = ‘B’
If skill percentage> = 70 then Grade = ‘C’
If skill percentage< = 50 then Grade = ‘D’
Grade ‘A’ has the highest percentage and the maximum team members came out with a good explanation on their topics given in
Cognitive skill percentages for grade.
In teambased work, the learners are grouped and given different topics for each team in softwaretesting subject. The time duration for preparing the topic is 45 minutes and the presentation is 15 minutes to each team. In total, there were ten teams with two or three members in each team. The learners enjoyed preparing, discussing among them, and working together preparing materials. The presentation of each team was more creative and realistic. The outcomes from the students are as follows:
Increased interest.
Cleared doubts.
Equally shared in doing.
The cognitive skills are observed and analysis was made for each team.
In a creative empowerment approach, the students were grouped into four teams. Each team was provided with a specialized topic on “how a final product undergoes various testing before releasing it.” The learners were very much enthusiastic in proceeding with their work. They themselves implemented their own ideas in various levels of testing. The upshot of this method was:
Increased creative skills.
Came out with their own ideas.
Different implementation methods.
Diverse styles in presenting.
Sound understanding in the technological approach.
In this approach, the learners were made to act, listen, view, and ask question immediately. This approach was applied to learners for objectoriented programming and computer network subjects. The findings of this approach were:
Active participation.
Improved listening capability.
Knowing the models effortlessly.
Questioning the abilities enhanced.
Better communication between the learner and facilitator.
In a presentationlearning approach, the learner as well as the facilitator were made to present content using powerpoint slides or multimedia presentation softwares. The learner was able to study about the working principles and their simulation in a real way. The simulation and presentation were for mobile communication and programming paradigm subjects. The learners’ individual cognitive skills were analyzed. The learners were educated to be aware of the concept in detail. The learner’s cognitive processes influence the nature of what is learned. People learn new information more easily when they can relate it to something they already know.
Analysis of learning with various approaches.
It was found that the cognitive skill named evaluation has 90.4% in
Overall percentage of cognitive skills when applied with various learning approaches in an instructorled virtual classroom.
There are various data mining algorithms such as decision tree, Naive Bayes, Rule induction, Supervised Learning, Apriori algorithm, and Association rule analysis. This paper scrutinizes the Discriminant analysis that is a very powerful data mining technique.
The learners’ data sets collected in the current research study pertain to the different subjects pursued by the learners of engineering graduates from Dr. G. U. Pope College of Engineering. Learners’ performances in the respective subject prerequisites were collected from the departmental records of result summaries pertaining to three passedout batches of computer science and engineering discipline.
Discriminant analysis is a statistical technique to classify objects based on a set of measurable object’s feature (
Fisher’s Linear Discriminant Analysis is based on the idea of searching for a linear combination of variables that best separates the target classes. Normally, we seek a direction w such that:
“Pooled” is the total, all points contributing. The effectiveness of the discrimination is assessed by calculating the Mahalanobis distance between two groups. If the distance is greater than 3, then the probability of misclassification is reasonably undersized:
Last, a new point is classified by projecting it onto the maximally separating direction and classifying it as C1 if:
The variances appear along the diagonal and covariances appear in the offdiagonal elements given as follows:
The variancecovariance matrix is created as follows:
Suppose X is an n x k matrix holding ordered sets of raw data:
Start with the raw data of matrix X, create a variancecovariance matrix to show the variance within each column and the covariance between columns.
Transform the raw scores from matrix X into deviation scores for matrix x.
Compute x’x, the k x k deviation sums of squares and crossproduct matrix for x.
Then, divide each term in the deviation sums of squares and crossproduct matrix by n to create the variancecovariance matrix. That is:
The learner’s cognitive skills are observed during the lecture time and learning in the instructorled virtual classroom is done using cognitive methods. The learner is assessed using the internal assessment test and the attendance in the classroom.
Discriminant analysis for performance.
Sample summary  Sample size  Internal 1 mean  Internal 2 mean  Attendance mean 

Average  5  54  51.2  89 
Good  11  78  77  90.54545455 
Poor  5  19.4  25.2  73.8 
Discriminant function analysis undergoes two steps: (1) testing the significance of a set of discriminant functions and (2) classification. The first step is computationally identical to MANOVA. There is a matrix of total variances and covariances. Similarly, there is a matrix of pooled withingroup variances and covariances. The two matrices are compared via multivariate F tests in order to determine whether or not there are any significant differences between groups. First, it performs the multivariate test, and, if statistically important, proceeds to see which of the variables have considerably different means across the groups. Once group means are found to be statistically considerable, classification of variables is undertaken. DA automatically determines some best possible combination of variables so that the first function provides the most overall discrimination between groups, the second provides second most, and so on. Once the discriminant functions are determined, groups are differentiated; the utility of these functions can be examined via their ability to correctly classify each data point to their a priori groups. Classification functions are derived from the linear discriminant functions to accomplish this use. Different classification functions are used and equations exist that are best suited for equal or unequal samples in each group.
Classification matrix.
Classification matrix  Average  Good  Poor  Correct 

Average  5  0  0  100 
Good  3  8  0  72.7272727 
Poor  1  0  4  80 
Matrix of variance and covariance.
Matrix of vars and covars  PA 1  PA 2  Attendance 



PA 1  126.5  243.5  96.5 
PA 2  243.5  472.7  178 
Attendance  96.5  178  100.5 


PA 1  258  163.6  10.4 
PA 2  163.6  152.2  7 
Attendance  10.4  7  22.27273 


PA 1  237.8  190.4  126.85 
PA 2  190.4  268.7  107.8 
Attendance  126.85  107.8  92.2 


PA 1  224.289  187.31  55.41111 
PA 2  187.311  249.31  67.4 
Attendance  55.4111  67.4  55.19596 
In
Summary classification.
Correct  81.0% 
Base  52.4% 
Improvement  60.0% 
Statistical distance of each observation to the mean vector.
The learners’ performance in the instructorled virtual classroom is analyzed using Discriminant analysis and the classification is made with Mahalanobis distances.
Comparison of the final outcome with periodical assessment.
From the implementation result, it is identified that learning with cognitive skills produces a good outcome with 96.4%. The dropout ratio of the learner gets reduced with this enhanced learning approach.
Summary statistics.
Variable  Categories  Frequencies  % 

Predicted performance  Average  68  34.171 
Good  62  31.156  
Poor  69  34.673 
Summary statistics (validation).
Variable  Categories  Frequencies  % 

Predicted performance  Average  0  0.000 
Good  0  0.000  
Poor  1  100.000 
Sum of weights and prior probabilities for each class.
Class  Sum of weights  Prior probabilities 

Average  68.000  0.342 
Good  62.000  0.312 
Poor  69.000  0.347 
Mahalanobis distances.
Class  Average  Good  Poor 

Average  0  1,526.947  1,257.661 
Good  1,526.947  0  2,554.130 
Poor  1,257.661  2,554.130  0 
Generalized squared distances.
Class  Average  Good  Poor 

Average  2.147594  1,529.279  1,259.779 
Good  1,529.094  2.332341  2,556.248 
Poor  1,259.809  2,556.462  2.118397 
Fisher distances.
Class  Average  Good  Poor 

Average  0  6.580  5.723 
Good  6.580  0  11.082 
Poor  5.723  11.082  0 
Class  Average  Good  Poor 

Average  1  0.021  0.028 
Good  0.021  1  0.006 
Poor  0.028  0.006  1 
In discriminant analysis, Wilk’s lambda (
Wilks’ Lambda test (Rao’s approximation).
Lambda  0.000 
F (observed value)  7.018 
F (critical value)  2.551 
DF1  384 
DF2  10 

0.001 
alpha  0.05 
The test interpretation is H0: the mean vectors of the 3 classes are equal, Ha: at least one of the mean vectors is different from another. As the computed
The test interpretation is H0: the mean vectors of the 3 classes are equal, Ha: at least one of the mean vectors is different from another. As the computed p value is lower than the significancelevel alpha = 0.05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha. The risk to reject the null hypothesis H0 while it is true is lower than 0.02% in
Pillai’s trace.
Trace  1.992 
F (observed value)  7.610 
F (critical value)  2.310 
DF1  384 
DF2  12 

0.000 
alpha  0.05 
The test interpretation is H0: the mean vectors of the 3 classes are equal, Ha: at least one of the mean vectors is different from another. As the computed p value is lower than the significancelevel alpha = 0.05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha. The risk to reject the null hypothesis H0 while it is true is lower than 1.14% in
Hotelling–Lawley trace.
Trace  596.480 
F (observed value)  7.256 
F (critical value)  3.923 
DF1  384 
DF2  6 
P value  0.011 
alpha  0.05 
The test interpretation is H0: the mean vectors of the 3 classes are equal, Ha: at least one of the mean vectors is different from another. As the computed
Roy’s greatest root.
Root  426.213 
F (observed value)  13.319 
F (critical value)  3.691 
DF1  192 
DF2  6 

0.002 
alpha  0.05 
Eigenvalue.
F1  F2  

Eigenvalue  426.213  170.267 
Discrimination (%)  71.455  28.545 
Cumulative %  71.455  100.000 
Bartlett’s test for eigenvalue significance.
F1  F2  

Eigenvalue  426.213  170.267 
Bartlett’s statistic  1125.651  516.894 

0.000  0.000 
Eigenvalue is a ratio between the explained and unexplained variation in a model. For a good model, the eigenvalue must be more than one. In discriminant analysis, there is one eigenvalue for each discriminant function.
The bigger the eigenvalue, the stronger is the discriminating power of the function. The eigenvalue for the obtained results is 426.213 that has the strongest discriminating power of the function (
Canonical correlations.
F1  F2 
0.999  0.997 
Chart of the eigenvalue.
Group centroids are the mean discriminant scores for each group in the dependent variable for each of the discriminant functions specified in
Functions at the centroids.
F1  F2  

AVERAGE  −1.441  17.951 
GOOD  27.354  −8.465 
POOR  −23.159  −10.085 
Outcome of predicted performance with Bartlett’s test.
In
Observations (axes F1 and F2: 100.00%).
Confusion matrix for the training sample.
From/to  AVERAGE  GOOD  POOR  Total  % correct 

AVERAGE  68  0  0  68  100.00 
GOOD  0  62  0  62  100.00 
POOR  0  0  69  69  100.00 
Total  68  62  69  199  100.00 
Confusion matrix for the validation sample.
From/to  AVERAGE  GOOD  POOR  Total  % correct 

AVERAGE  0  0  0  0  0.00 
GOOD  0  0  0  0  0.00 
POOR  0  0  1  1  100.00 
Total  0  0  1  1  100.00 
Confusion matrix for the crossvalidation results.
From\to  AVERAGE  GOOD  POOR  Total  % correct 

AVERAGE  23  26  19  68  33.82 
GOOD  16  36  10  62  58.06 
POOR  5  8  56  69  81.16 
Total  44  70  85  199  57.79 
The proposed work identifies cognitive skills of each learner with their associated behavior and learning is made in the instructorled virtual classroom. The learners’ learning skills are improved and the thinking capacity of each learner is increased. The different views of the learner make every learner to easily understand the concept by improving the concentration of the learner. The performance measure of each learner is predicted using the discriminant analysis. The information obtained subsequent to the execution of the data mining technique probably will help the instructor as well as the learners. The performance report of the learner also helps to improve the result of the learner. This performance enhancement will also help the entire learner to get placement in various trades according to the norm. The educational institution gets benefited with the proposed system for their even and victorious running of the organization. The solution provided using the Discriminant Algorithm predicts the performance of a learner correctly filling the error gap to produce a sound enough result.
Centroids (axes F1 and F2: 100.00%).