=Paper=
{{Paper
|id=None
|storemode=property
|title=Econometric Analysis on the Site "Lesson Pulse"
|pdfUrl=https://ceur-ws.org/Vol-1000/ICTERI-2013-p-374-384-ITER.pdf
|volume=Vol-1000
|dblpUrl=https://dblp.org/rec/conf/icteri/Weissblut13
}}
==Econometric Analysis on the Site "Lesson Pulse"==
https://ceur-ws.org/Vol-1000/ICTERI-2013-p-374-384-ITER.pdf
Econometric Analysis on the Site “Lesson Pulse”
Alexander J. Weissblut
Kherson State University, 1, 40 rokiv Zhovtnya Street, 73000, Kherson, Ukraine
veits@ksu.ks.ua
Abstract. In this article the site “Lesson pulse” is considered, as the tool allow-
ing the teacher to receive the objective information on a course and results of a
lesson in a mode online. However adequate interpretation for results of such in-
terrogations is impossible, while we will not separate true students from others.
Besides, interpretation for results of interrogations and the decision-making,
grounded on it, demands to realize, what exactly this concrete group means by
clearness of an explanation, objectivity of the marks etc. For anonymous inter-
rogations it means necessity of correlation and regression analysis for their re-
sults and an estimation of the statistical significance of the received results. So
it means necessity of econometric analysis.
Keywords. Factor, statistical, econometric, analysis, correlation, decision-
making
Key terms. Research, Management, Model, KnowledgeManagementProcess,
KnowledgeManagementMethodology, MathematicalModeling
1 Introduction
In this article the site “Lesson pulse” is considered, as the tool allowing the teacher to
receive the objective information on a course and results of a lesson in a mode online.
It allows for the student or the pupil at any moment to react to a lesson course, having
answered one or several questions, for example:
1. Is it interesting to you at a lesson?
2. Is it accessible (clear) an explanation?
3. Are you tired? Whether arranges you the rate of an explanation?
4. There are at you questions to the teacher?
5. Whether the marks are objective?
(Formulations of questions are defined by the teacher). As a result of an average of
these responses the site produces on the monitor screen the data about a lesson state,
its "pulse" in a mode online. At any moment the teacher can ask to answer all simul-
taneously such or more profound groups of questions (their examples are given be-
low). So, he can measure the “lesson pulse” just at this moment. Such interrogations
Econometric Analysis on the Site “Lesson Pulse” 375
do not demand computer auditorium by all means: they can be carried out on one
tablet, and then results can be transferred to a site.
However adequate interpretation for results of such interrogations is impossible,
while we will not separate true students, for which educational process is a consider-
able part of their life, from those, who would prefer to keep far away from it. Besides,
interpretation for results of interrogations and the decision-making, grounded on it,
demands to realize, what exactly this concrete group means by clearness of an expla-
nation, lesson atmosphere, objectivity of the marks etc. For anonymous interrogations
it means necessity of correlation and regression analysis for their results and an esti-
mation of the statistical significance of the received results. So it means necessity of
econometric analysis.
1. All groups of questions considered further have been chosen in result of "brain-
storming" where students of fourth year study of the Faculty of physics, mathemat-
ics and informatics at the Kherson state university acted as experts. This expert in-
terrogation has been constructed by a technique of " six hats of thinking ” E. Bono
[1], which provides the maximal openness and relaxedness of participants. In all
cases the opinion has unanimously been expressed, that the given set of questions
is full and fair.
2. Then students of speciailties “physics”, “mathematics”, “informatics” and “pro-
gram engineering” of the Kherson state university have been interviewed under
such essential requisites. The respondents estimate each question from 0 (at firm
“no”) up to 10 (at firm “yes”). He arbitrarily sets a name of the folder containing
his interrogation (i.e. his key). The volunteer – a participant of interrogation – col-
lects all folders in one main folder and sorts them here (i.e. shuffles). Only after
that the main folder was transferred to the teacher: this simple and open procedure
guaranteed to participants anonymity of interrogation. Alternative and technically
simpler variants are answers to the site and to a tablet: the variant choice is defined
by a kind of interrogation and level of trust of an audience to the interviewing
teacher.
3. Results of interrogation then are transferred to a site “Lesson pulse”, which is real-
ized in language PHP and uses database MySQL (see [2]). The queries realizing
now on the site give out results of the econometric analysis of interrogation. They
include the plural correlation analysis of factors and an estimation of the statistical
importance of the received results with use of criteria Student and Fisher (see [3]).
The site interface is oriented to the user, generally speaking, nothing knowing
about the econometric analysis.
2 The Analysis of Interrogations on Results of Lesson
and Feedback
Results of interrogation about lesson and interrogation Feedback are, of course, abso-
lutely various depending on a lesson, a teacher, an audience etc. However the correla-
376 A. J. Weissblut
tion analysis of factors led to similar outcomes (at 20% a significance level by crite-
rion of Student). Everywhere below we use the interrogations of 421 groups (special-
ity “mathematician”), having typical species (fig. 1).
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5 6 7 8 9 10 11 12 13
-0,2
-0,4
-0,6
Fig. 1. Histogram for distribution of correlation coefficients Q1
Here is the histogram for distribution of correlation coefficients between answers
to a question “Whether the lesson was pleasant to you?” and following factors:
1. Whether it is accessible (clear) an explanation?
2. Whether arranges you the rate of an explanation?
3. Are you tired at a lesson?
4. Lesson atmosphere: is it comfortable, is it pleasant to you at a lesson?
5. Is the statement filled enough by examples?
6. Objectivity of the marks, which have been put down at a lesson.
7. Are you having some questions to the teacher?
8. Do you still want a lesson on this theme?
9. Have you prepared for this lesson?
10. Are you intending to continue studying at home?
11. Accordance of a lesson to tasks of independent (home) work.
12. Is it interesting to you at a lesson?
13. Have you taken out something useful at a lesson or are sorry about spent time?
The most significant factors had appeared (in decreasing order) 1 (0.91), 4 (0.87),
12 (0.83), 13 (0.75) 5 (0.63), 9 and 11 (0.59). Objectivity of marks is only further
(0.51) and inverse correlation – 0.39 for 7 specifies that for the majority the good
lesson is such after which does not remain questions to the teacher (fig.2).
Here is the histogram for distribution of correlation coefficients between answers
to a Feedback question “Whether the teacher is pleasant to you?” and following fac-
tors:
1. Whether lessons were pleasant to you?
2. Estimation by student of the knowledge received at lesson.
3. Is it accessible (clear) an explanation?
Econometric Analysis on the Site “Lesson Pulse” 377
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-0,2
-0,4
Fig. 2. Histogram for distribution of correlation coefficients Q2
4. How much are accessible (clear) and authentic answers to questions of students?
5. The explanation is filled enough by examples.
6. Using of various approaches at training.
7. Whether the teacher aspires to interest, motivate students?
8. Lessons atmosphere: is it comfortable, is it pleasant to you at a lesson?
9. Availability of the teacher, his inclination to listen to students, to conduct discus-
sions with them.
10. Knowledge of a subject by the teacher.
11. Insistence (regular and frequent enough control of knowledge).
12. Punctuality (comes in time at lessons).
13. Possession of an audience (students do not sleep and do not make too much noise
at lessons).
14. Objectivity in estimation of the student by the teacher. Whether criteria of esti-
mation in all subgroups are identical?
15. Accordance of a lesson to control tasks.
The most significant factors appear (in decreasing order) 8 (0.92), 7 (0.85), 6
(0.775), 4 (0.75), 9 (0.72), 3 (0.675), 13 (0.58).
Only further with factor of correlation 0.51 follows 1 - whether lessons were pleas-
ant to you. And major factors of estimations of the teacher and lesson are considera-
bly differing. Further the histogram of differences between factors of correlation for
questions “Whether the teacher is pleasant to you?” and “Whether lessons were pleas-
ant to you?” is resulted.
The factors much more essential at an estimation of a teacher, than a lesson are 6
(using of various approaches at training) and 7 (whether the teacher aspires to interest,
motivate students). On the contrary, at an estimation of a lesson it is much more es-
sential factors 14 (accordance of a lesson to control tasks) and 10 – insistence (regular
and frequent enough control of knowledge): probably, according to students, insis-
tence it is good for lesson and it is not so good for the teacher.
378 A. J. Weissblut
0,6
0,4
0,2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
-0,2
-0,4
-0,6
Fig. 3. Histogram for distribution of correlation coefficients Q3
Certainly, the correlation matrix contains decomposition on factors also for each of
15 questions. So it is found out that 5 (the explanation is filled enough by examples)
is most closely connected with 15 (accordance of a lesson to control tasks); 3 (are you
tired at a lesson) with 7 (presence of questions to the teacher); 13 (possession of an
audience) with 14 (objectivity in estimation of the student).
It is interesting to compare 12 (is it interesting to you at a lesson) with 13 (have
you taken out something useful at a lesson) from interrogation about results of the
lesson (fig.4).
1
0,8
0,6
0,4
Interesting
0,2 Useful
0
1 2 3 4 5 6 7 8 9 10 11 12
-0,2
-0,4
Fig. 4. Histogram for distribution of correlation coefficients Q4
As we see, from the student’s point of view, it is interesting and it is useful is not
the same. So 4 (lesson atmosphere) correlates with the factor interesting much more,
while factor 5 (is the statement filled enough by examples) with 11 (accordance of a
lesson to tasks of independent (home) work).
Econometric Analysis on the Site “Lesson Pulse” 379
3 The Analysis of Interrogations about the Factors Influencing
a Lesson
Unlike interrogations about results of lesson and Feedback results of interrogations
about factors of influence on a lesson course are close enough in different groups. The
histogram for distribution of interrogation requisites on the relation to lesson (in 421
group) is below (fig. 5).
10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Fig. 5. Histogram for distribution of correlation coefficients Q5
Here:
1. Is study pleasant to you? Is it interesting to you?
2. Whether you believe that education is “road to the future”?
3. Is your speciality pleasant to you?
4. Is the program of training for your speciality satisfying you?
5. Whether satisfies you teaching level at the university?
6. Whether on own will you have chosen university and a speciality?
7. Would you like to change the speciality or to receive additional higher education?
8. Whether your attendance of lessons is regular?
9. Do you regularly prepare homework?
10. Whether there were at you conflicts to teachers?
11. Were you afraid of an exception of university?
12. Do you wish to take part in scientific work, in Olympiads on your speciality?
13. Whether often to you fellow students address for the help in lessons?
14. Do you wish to enter postgraduate study after training end?
15. What’s the time you spend for preparation for lessons (on the average hours per
day)?
And further similar results of interrogation on external factors (fig. 6):
380 A. J. Weissblut
10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
Fig. 6. Histogram for distribution of correlation coefficients Q6
Here:
1. Close dialogue with teachers.
2. Accessibility of the Internet at university.
3. Readiness of an auditorium for a lesson (working capacity of projectors, com-
puters, the software; comfort of an auditorium).
4. Presence of enough points for the centralized feeding.
5. Accessibility of contacts to the future employers.
6. Accessibility of summer improvement.
7. Participation in scientific work.
8. Teaching level at the university.
In a correlation matrix under all these factors there are only few factors which cor-
relations are close to 1. These are factors:
1. Whether your attendance of lessons is regular with factors
(a) do you regularly prepare homework (0.87)
(b) teaching level at the university (0.84)
(c) participation in scientific work (0.63)
(d) have you prepared for this lesson (0.59)
(e) accessibility of summer improvement (– 0.5)
2. Do you regularly prepare homework with factors
(a) whether your attendance of lessons is regular (0.87)
(b) teaching level at the university (0.815)
(c) have you prepared for this lesson (0.66)
(d) participation in scientific work (0.56)
(e) accessibility of summer improvement (– 0.52)
Econometric Analysis on the Site “Lesson Pulse” 381
3. Teaching level at the university with factors
(a) whether your attendance of lessons is regular (0.843)
(b) do you regularly prepare homework (0.815)
(c) whether on own will you have chosen university and a speciality (0.65)
(d) have you prepared for this lesson (0.59)
(e) participation in scientific work (0.56)
(f) accessibility of summer improvement (– 0.55)
Besides them correlation factors above 0.7 appear still only twice: between factors
whether there were at you conflicts to teachers and were you afraid of an exception
of university (0.85); and between factors participation in scientific work and is
the program of training for your speciality satisfying you (0.74). Occurrence in
such line the factor teaching level at the university is, probably, the best compli-
ment for Faculty of physics, mathematics and informatics of the Kherson state univer-
sity for all its history. Our main task is to use the mental orientation, fixed thus in the
correlation analysis of factors, for separating true students, for which educational
process is a considerable part of their life, from those, who would prefer to keep far
away from it. Using already cited data and the following table 1
Table 1. Correlation analysis of factors
Factor Average value Root-mean-square deviations
Teaching level at the university 702 2.17
Regularly attendance of lessons 8.85 2.3
Regularly prepare homework 8.4 2.6
We choose as a differentiating sign between groups the factor regularly prepare
homework. In this case mutual correlations of defining sign are closer to 1; and the
dispersion is more, that testifies about more variability of respondents under this fac-
tor. Besides, among others selected it more corresponds to such sign on common
sense.
4 Results of Interrogations about Lesson and Feedback on
Subgroups
To the selected differentiating sign among 20 respondents of group 421 the 12 par-
ticipants is allocated, who for a question do you regularly prepare homework have
answered with 10 or 9 points. The additional subgroup consists of 8 respondents.
Whether there correspond such subgroups to required division into true students and
the others? Below there is the histogram for average results of interrogation about
lesson on the allocated subgroups (fig. 7).
382 A. J. Weissblut
12
10
8
Prepare
6
Don't prepare
4
2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Fig. 7. Histogram for distribution of correlation coefficients Q7
So, the factors considerably different in subgroups (in decreasing order of modules
of differences between average values in subgroups) are:
2 Whether it is accessible (clear) an explanation? (7.92 – 4.25 = 3.67)
1 Whether the lesson was pleasant to you? (7.1 – 4.38 = 2.72)
12 Accordance of a lesson to tasks of independent (home) work. (9.91–7.5 = 2.41)
6 Is the statement filled enough by examples? (9.41 – 7 = 2.41)
10 Have you prepared for this lesson? (8.75 – 6.5 = 2.25)
13 Is it interesting to you at a lesson? (7.92 – 5.87 = 2.05)
14 Have you taken out something useful at a lesson? (9.1 – 7.4 = 1.7)
5 Lesson atmosphere (7.66 – 1.25 = 1.41)
9 Do you still want a lesson on this theme? (3.66 – 2.65 = 1.01)
The averages of additional group are more only twice, there are:
4 Are you tired at a lesson? (6.5 – 7.62 = – 1.12)
3 Whether arranges you the rate of an explanation? (5.5 – 6.37 = – 0.87)
Last result is strange at first sight, but steady for all groups and it is easy to explain
this phenomenon psychologically: as less adjusted the student for study, the more he
would like acceleration, faster course of time.
Further there are similar results for interrogation Feedback (fig. 8).
12
10
8
Prepare
6
Don't prepare
4
2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Fig. 8. Histogram for distribution of correlation coefficients Q8
Econometric Analysis on the Site “Lesson Pulse” 383
Here the factors considerably different in subgroups are:
5 The explanation is filled enough by examples (9.17 – 6.37 = 2.8)
6 Using of various approaches at training (6.36 – 4 = 2.36)
16 Accordance of a lesson to control tasks (8.9 – 6.87 = 2.03)
4 How much are accessible (clear) and authentic answers? (7 – 5.25 = 1.75)
9 Lesson atmosphere (6.36 – 4.85 = 1.51)
The obtained data corresponds to a hypothesis about required division into groups,
anyway they don’t contradict it.
5 The Latent Division in Group
The site “Lesson pulse” offers also division of group into classes with a given value
of mutual correlation: between two respondents from one class it is possible to find a
chain of respondents of this class so, that the correlations of answers between con-
secutive respondents of this chain not less than the given value. Such division into
subgroups allows finding out distinctions in the group, which is not appreciable di-
rectly.
At mental interrogation about factors of influence on lesson and the set minimum
level of mutual correlation 0,6 in test group 421 splitting into 3 classes has turned out:
from 4, from 5 and from basic subgroup of 11 respondents. Let's compare averages of
the basic class to averages of the first and second subgroups under those factors in
which appreciable differences have come to light.
1. Is the program of training for your speciality satisfying you?
2. Would you like to change the speciality or to receive additional higher education?
3. Do you wish to take part in scientific work, in Olympiads on your speciality?
4. Do you wish to enter postgraduate study after training end?
5. Participation in scientific work.
6. Readiness of an auditorium for a lesson.
7. Accessibility of summer improvement.
8. Accessibility of contacts to the future employers.
12
10
8
Class 1
6 Class 2
Main class
4
2
0
1 2 3 4 5 6 7 8
Fig. 9. Histogram for distribution of correlation coefficients Q9
384 A. J. Weissblut
Respondents from classes 1 and 2 much less than the basic group are satisfied by
the program of training of the speciality (point 1). They would like to change the spe-
ciality or to receive additional higher education essentially more than the basic group
(point 2). Their difference is the sharpest comes to light in point 3: unlike the basic
group they at all do not wish to take part in scientific work or in the Olympiads on the
speciality. So, apparently, the speciality for them has lost now appeal. Respondents
from a class 2 does not interest in the postgraduate study (point 4), however they do
not against scientific work (point 5). The main thing, they have the most interest in
contacts to employers (point 8). Apparently, it is search of the application out of the
speciality. Respondents from a class 1 are focused differently: they have a little inter-
est in scientific work and employers (points 5 and 8), but they wish to enter post-
graduate study (point 4).
References
1. De Bono, E.: Six Thinking Hats. Penguins Books (1997)
2. PHP Book, http://www.phpreferencebook.com (2012)
3. Hansen, B. E.: Econometrics. Textbook, http://www.ssc.wisc.edu (2012)