Where You Sit Matters
How Classroom Seating Might Affect Marks
David Insa
Josep Silva
Salvador Tamarit
Departament de Sistemes Informàtics i Computació
Universitat Politècnica de València
Camí de Vera, s/n
46022 València, Spain
ABSTRACT
In this article we perform a detailed statistical analysis of
a large experiment that was carried out in two engineering schools at Universitat Politècnica de València. The goal
of the study is to quantify how the distance of students to
the professor affects their marks. In the experiment, we
collected and processed data about the exact students’ position in the lecture hall and in the computer lab for two academic years, their changes of position along the course, and
their marks in various degrees, courses, and terms, for both
lectures and practicals. Our experiments provide quantitative data that is analyzed using advanced statistical methods such as ANOVA, the TukeyHSD post-hoc test, and the
Mantel test based on Pearson product-moment correlation
coefficient.
Categories and Subject Descriptors
K.3.2 [Computer and Information Science Education]:
Computer science education, Information systems education
Keywords
Mark; classroom; seat
1.
INTRODUCTION
Many professors often say that their best students use to
sit in the first rows of the classroom while those students
less interested in the course use to sit in the last rows or
in those closer to the exit door. In this paper we validate
these ideas with quantitative statistically-supported data.
We want to answer questions such as: How much does the
distance between the students and the professor affect the
students’ marks? As an average, what is the difference between the marks of the students seated in the first row and
those seated in the, e.g., third row?
The way in which students sit in the lecture hall has
been often ignored, even in methodologies for active learning. This is somehow surprising, because there already exist
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DOI: http://dx.doi.org/10.1145/2899415.2899444
studies that show a clear relation between the position in the
lecture hall and the final mark. Most of these studies have
been done in the context of primary and secondary schools
(see, e.g., [1, 9], or more recently [13]), but there are also
studies applied to the university with the same results [10,
12, 3].
For instance, Giles et al. [4] studied the students’ recall in
relation with their position in the lecture hall, and they concluded that the student’s seating position in the lecture hall
is associated with the level of immediate recall. In educational psychology the potential learning advantages of being
close to the teacher have been already studied:
1. better vision of the blackboard,
2. better hearing of what is being said by the teacher,
3. better attention to what is being said because there are
fewer (or no) people between them and the teacher to
distract them, and
4. greater eye contact with the teacher, which may increase
their sense of personal responsibility to listen to, and take
notes on, what their teacher is saying.
One could think that the relation between the seating position and the marks is not causal, because this relation may
well be a reflection of motivational factors which determine
where students choose to sit rather than of seating position per se [4]. However, some studies were conducted with
the teacher selecting the students’ position: students in the
front, middle, and back rows of the class scored 80%, 71.6%,
and 68.1% respectively on the course exams [10]. This is a
clear indication that it is not simply due to the fact that
more motivated students tend to sit in the front and centre
of the classroom. Instead, the higher academic performance
of students sitting in the front and centre is most likely due
to the fact that there are learning advantages provided by
these seating positions.
Obviously, not all the students are equal. Some of them
are shy or just afraid of the questions that the teacher could
ask them. This feeling makes them sit far away from the
teacher in order to avoid questions. For other students, however, sitting far away from the teacher is an opportunity to
chat with classmates when they cannot follow or they are not
interested in a particular lesson. This is also usual among
students who cannot keep their attention over a long period
of time. Other students, contrarily, try to sit as close as
possible to the teacher to avoid the noise and to have, in
this way, a better understanding.
Table 1: Data from the groups of the analyzed courses
Practicals
Lectures
Name
Year
Degree
Groups
Students
Sessions
DSA
◦
2
ACE
2
66
23
AC
2◦
IDE
1
38
24
PRG
1◦
BCE
1
23
28
◦
DRQS
1
MSEFMIS
1
5
12
ATSD
5◦
MCE
1
20
12
GUI
3◦
MCE
2
28
12
AC
2◦
IDE
1
36
12
PRG
1◦
BCE
2
39
10
This paper presents a wide experiment performed over
two academic years in two engineering schools at Universitat Politècnica de València (UPV). The experiment studied
the relationship between the position of all the students in
the classrooms (both the lecture hall and the computer laboratory) and their marks. To the best of our knowledge,
this is the widest study of this kind performed at university
schools, and it analyzes relations not studied before. In particular, we introduce a novel methodology, which roughly
consists in studying the marks associated to chairs (instead
of to students). The analysis of the collected data, as described below, proves the fact that a student’s position really
influences their marks. Similar studies can be found in [7,
14] for primary and secondary schools; and in [11, 12, 6] for
the university, although with a reduced sample of students.
The rest of the paper describes the experiment and its
results. Section 2 presents the experiment and its context.
Concretely, in Section 2.1 we explain how the data was collected, and the methodology used to normalize them. Then,
in Section 2.2 we present the statistical results obtained.
Finally, the conclusions and future work are discussed in
Section 3, where we provide an interpretation of the data
and ideas about how to use this information.
2.
THE EXPERIMENT
The experiment has been conducted at the School of Engineering Design and at the School of Computer Science, both
at UPV. It was supported by the Institute of Education Sciences of UPV. Specific details about the experiment are the
following:
• Data Size: 255 students (2160 attendances).
• Programs: Bachelor in Industrial Design Engineering (IDE),
Master in Computer Science Engineering (MCE), Associate degree in Computer Engineering (ACE), Bachelor
in Computer Engineering (BCE), and Master of Software
Engineering, Formal Methods, and Information Systems
(MSEFMIS).
• Courses: Development of Reliable and Quality Software
(DRQS), Data Structures and Algorithms (DSA), Advanced Tools for Software Development (ATSD), Graphical User Interfaces (GUI), Applied Computing (AC),
and Programming (PRG). Table 1 provides additional
information about the courses, including whether each
course corresponds to lectures or practicals, mark, degree, number of groups and students involved in the experiment, and number of sessions.
• Null Hypothesis: There is no relation between the students’ position in the lecture hall and their marks.
In order to ensure the replicability of our study and analyses, and to make public our information to other researchers
for other possible analyses, all the source data, together with
the intermediate and final processed data have been made
publicly available at:
http://www.dsic.upv.es/˜jsilva/sitsandmarks/
2.1
Data collection
Prior to the experiment, we developed a software tool called
AWAD [5]. AWAD allows for automatic data collection and
processing as well as performing online exams. This tool
stores the row and column where each student is sat when
logged in. In those lecture halls without computers, the row
and column were taken manually by the professor. These
data were collected in all lectures and practicals in all sessions. Moreover, at least one official exam was registered
for each course. AWAD combined the final marks with the
other available data to generate a number of reports with
statistics and other calculations that are the basis of more
advanced statistics shown in Section 2.2. One of the biggest
challenges was to obtain statistics not related to individual
students but, on the contrary, associated with the different
physical positions that can be occupied inside classrooms.
To achieve this goal, we designed the experiment in a novel
way (we are not aware of any other experiment, neither in
universities nor in primary or secondary schools, that processes the data in this way): we collected the data linked to
each individual chair of each classroom instead of analyzing
the students. Therefore, the data linked to each chair have
been produced by combining the data collected every time a
student (not necessarily the same one) sat in this particular
chair. All data were later combined to produce extrapolative
results. The data provided by AWAD are the following:
Average mark of a chair: It represents the average mark
a specific chair got in a particular exam. It was obtained
by adding up the marks of all students that occupied
that chair (if the same student occupied the chair several times, their mark was also counted several times)
and then dividing the result by the number of times this
chair was occupied (hence, we get the average mark of
the individual occupation of this chair).1 We can see
specific examples of this in Figure 1. Observe that each
1
Our statistical analysis considers the fact that the sample is
not distributed homogeneously, i.e., one chair could be occupied many times, while other chair could be occupied only a
2.2
Results
The data collected and processed by AWAD have been
further analyzed to extract statistically valid results. In all
cases, we have computed 95% symmetric confidence intervals
and we show the centre of the interval. We have analyzed
the data in two phases. In the first phase, we obtained
individual results for each group. In the second phase, we
combined the data from all groups to obtain global results.
(a) Course: PRG - Group: PL1
Phase 1: The data collected by AWAD were stored in a
database that was later processed using R.2 For each group
we produced a table as those shown in Table 2. These tables
summarize information for each row of chairs in a classroom,
in such a way that the first row in the table corresponds to
the first row in the classroom, the second with the second,
and so on. Column Attendance shows the number of times
that the chairs in each row were used by students that finally
took the exam. Column Mean shows the average mark associated with each row. Column Norm. Mean (Normalized
Table 2: Results obtained by group
(a) Course: PRG Group: PL1
Row
Attendance
1
22
[4.76 5.18
5.61 ]
[0.82 0.89
0.97 ]
2
34
[5.85 6.33
6.80 ]
[1.01 1.09
1.17 ]
3
39
[4.96 5.48
6.00 ]
[0.85 0.94
1.03 ]
4
8
[5.76 6.63
7.51 ]
[0.99 1.14
1.29 ]
5
3
[5.57 6.44
7.31 ]
[0.96 1.11
1.26 ]
(b) Course: GUI - Group: PL5
Figure 1: Two (real) examples of average marks of
chairs in a group
chair (not each student) is labelled with a mark. Observe also that each computer is shared by two students
in the labs. The blank chairs were never occupied by
any student in any session. Lecture halls and labs have a
symmetric and proportional distribution of chairs, thus,
row 2i is twice as far to the professor as it is row i. The
reader should not extract conclusions from these figures,
because they just show unprocessed data from two examples of courses. These data (together with the rest
of courses) are mixed and statistically analyzed in Section 2.2.
Times a chair was used: It counts the number of times
that (possibly different) students occupied the chair during the course. Figure 2 contains examples of these counters.
Times a chair was used by students who gave up the
course: It represents the total amount of times a chair
was used by a student who gave up the course (those
that did not take the exam).
few times. As a consequence, our results are presented with
confidence intervals (see Table 2, Figure 3, and Figure 4).
Mean
Total Mean = [5.52 5.80
Norm. Mean
6.09 ]
(b) Course: GUI Group: PL5
Row
Attendance
Mean
–
Norm. Mean
1
0
2
68
[6.92 7.17
7.43 ]
[0.95 0.98
1.02 ]
3
63
[6.80 7.05
7.29 ]
[0.93 0.96
1.00 ]
4
46
[7.56 7.84
8.12 ]
[1.04 1.07
1.11 ]
5
10
[6.73 7.35
7.97 ]
[0.92 1.01
1.09 ]
Total Mean = [7.15 7.30
–
7.46 ]
Mean) represents the average mark of the row with regard
to the average mark of the group. The average mark of the
group is represented with the value 1.0 and it is calculated
adding up the marks of all chairs (regardless of in which row
they are). For instance, in the second row of Table 2(a) we
see that the normalized mean is 1.09 and thus, those students who sat in the second row got marks 9% higher than
the average mark of the group.
Phase 2: In the second phase of the analysis we combined
the information of all individual groups, separately in lecture
and practical groups, to obtain global results that can be
generalized to all groups. In order to obtain statistically
valid global results, we needed to introduce another process
2
R is a programming language for statistical computing. See
https://www.r-project.org/ for details.
(a) Course: PRG Group: PL1
(b) Course: GUI - Group: PL5
Figure 2: Two (real) examples of number of times each chair has been occupied
of normalization because we cannot mix data obtained from
different groups for three fundamental reasons:
1. All marks must use the same scale (e.g., from 1 to 10).
In this way, a mark of 7 would mean the same in all
groups. Hence, we changed all the marks to a mark out
of 10.
2. The marks of different groups cannot be combined or averaged out if these groups have a different average mark.
For instance, groups PRG PL1 and GUI PL5 (Table 2(a)
and Table 2(b)) have, respectively, average marks of 5.80
and 7.30. This means that a mark of 7 points in the second group is a bad—below the average—mark, whereas
in the first group, it is a good mark (far above the average). In order to combine marks from different groups
we normalized the marks regarding to the average marks
of the groups. This is shown in column Norm. Mean
of Table 2, which can be already combined with other
groups.
3. In each group, each mark associated with a chair has a
different confidence level. For instance, the marks from
the chair in row 2, column 8, in the two groups shown
in Figure 1 (PL1 and PL5) are very similar (8.08 and
7.59 respectively). However, if we observe the associated
tables of attendance in Figure 2 we see that 7.59 was
obtained from a sample of 11 attendances (that is, it is a
high confidence data, which has been probably obtained
from several students who sat repeatedly in that chair).
On the opposite side, the mark of 8.08 comes from a
student that sat in that chair only once (and probably
this student sat in another chair the rest of the times).
In consequence, this last figure has a very low confidence
level. In order to compare data with different confidence
levels the computed marks take into account the number
of attendances associated with each mark.
We elaborated two tables that summarize the information
from all groups to obtain conclusions for lecture and practical groups. This division is interesting because in lectures
the interaction with the professor is mainly passive, therefore being close to the professor and the blackboard seems
to be more important than in practical sessions, where autonomous work predominates. This information is shown in
Table 3 and Table 4.
Table 3: Total attendance and normalized marks for
lectures
Row Attendance Normalized Mean Volume
1
127
1.16
19.75%
2
163
1.05
25.35%
3
218
0.88
33.90%
4
135
0.99
21.00%
Total Attendance = 643
Table 4: Total attendance and normalized marks for
practicals
Row Attendance Normalized Mean Volume
1
108
1.14
16.80%
2
226
0.97
35.15%
3
230
0.96
35.77%
4
106
1.06
16.49%
5
51
0.99
7.93%
Total Attendance = 721
These tables show combined information from several
groups for each row of chairs in the classrooms. Here again,
the first row of the table corresponds to the first row in
the classroom, the second corresponds to the second, etc.
Column Attendance shows the summation of attendances in
each row for all groups. Column Normalized Mean represents the normalized mean combining the normalized means
of all groups. Column Volume shows the percentage of attendances of students sat in each row with respect to the
total amount of attendances. We only considered representative those rows with a percentage higher than 5%. We can
Normalized mark by row (mean is black dot)
95% family-wise confidence level
Plot of normalized mark by row
1.2
2.0
r2-r1
1.16
1.1
r4-r1
1.05
1.0
normalized mark
1.0
normalized mark
1.5
r3-r1
0.99
0.9
0.5
r3-r2
0.88
0.8
0.0
r4-r2
r1
r2
r3
r4
n=127
n=163
n=218
n=135
r1
r2
r3
r4
row
r4-r3
row
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
Figure 3: Statistical analysis of the relation position-mark in lectures
95% family-wise confidence level
Plot of normalized mark by row
1.20
Normalized mark by row (mean is black dot)
1.15
1.4
r2-r1
r3-r1
1.14
r5-r1
1.06
1.05
normalized mark
1.0
r3-r2
r4-r2
1.00
0.8
normalized mark
1.10
1.2
r4-r1
0.6
0.99
0.4
0.95
0.97
r1
r2
r3
r4
r5
r5-r2
0.96
r4-r3
n=108
n=226
n=230
n=106
n=51
r1
r2
r3
r4
r5
row
r5-r3
r5-r4
row
-0.2
-0.1
0.0
0.1
Figure 4: Statistical analysis of the relation position-mark in practicals
see that the students in the first row obtain, as an average,
a 16% higher mark than the mean. Similarly, in the laboratory, the students in the first row obtain, as an average, a
14% higher mark than the mean. Clearly, marks are more
uniform in the laboratory, which means that the position is
not so influential.
With the collected data shown in these tables, we can perform an analysis with a huge sample (more than 1300 attendances) obtained from different groups, courses, students,
professors, exams, classrooms, academic years, terms, and
degrees (all of them from engineering schools). This sample
is big and heterogeneous enough to obtain conclusions (or
at least indicators) free from being affected by local factors
of a given subsample.
We processed all the data to extract statistically supported conclusions. Firstly, we considered lecture groups.
We can observe a standard boxplot showing the distribution
of data in Figure 3 (left). It shows the Q1, Q2 (median),
and Q3 quartiles for each row. The white point in row 1 is
an outlier. We performed the Mantel test based on Pearson
product-moment correlation coefficient with 999 replicates,
and we got a p-value of 0,069. This value indicates that the
null hypothesis may be rejected. Therefore, we performed
an analysis of variance (ANOVA) using R, and got the following result:
row
Df
Sum Sq
M ean Sq
F value
P r(> F )
3
6.78
2.2611
8.348
1.89e − 05
With this result, and assuming a significance level of 0.05,
we can reject the null hypothesis because the significance
probability value associated with the F Value, P r(> F ) =
1.89e − 05, is three orders of magnitude bellow the significance level. Hence, the first important conclusion is that
the position in a classroom actually influences the students’
marks. Figure 3 (centre) shows the plot with the relation
row-mark.
To complement the ANOVA and study the differences
between each row, we used the TukeyHSD post-hoc test.
It produced the plot in Figure 3 (right), where significant
differences are the ones which do not cross the zero value.
Hence, this plot provides evidences that rows (r4-r1), (r3-r1),
(r3-r2) have different influence on the mark. The influence
is the expected one: the closer to the professor (and to the
blackboard) the better mark is obtained.
We repeated the analysis for practical groups. The standard boxplot with the distribution of data is shown in Figure 4 (left). We also performed the Mantel test based on
Pearson product-moment correlation coefficient with 999
replicates, and we got a p-value of 0,013. Again, this value
indicates that the null hypothesis may be rejected. Therefore, we performed an analysis of variance (ANOVA) using
R, and got the following result:
row
Df
Sum Sq
M ean Sq
F value
P r(> F )
4
2.90
0.7243
12.57
6.9e − 10
A value of 6.9e − 10 for the probability P r(> F ) clearly
indicates that the position in the lab does influence the students’ marks. Figure 4 (centre) shows the plot with the
row-mark relation. The TukeyHSD post-hoc test produced
the plot in Figure 4 (right), which provides evidence that
row r1 has a positive influence on marks w.r.t. rows r2, r3,
and r5; and row r4 also has a positive influence on marks
w.r.t. rows r2 and r3.
After having analyzed the data, our (subjective) interpretation of this phenomenon is that central rows in the lab
concentrated the largest number of students, leading them
to share computer and to have classmates by their sides,
front and back, which certainly influenced negatively their
academic achievement.
3.
CONCLUSIONS
We believe that this experiment is an excellent starting
point for a debate about how to handle the students’ location in a classroom. An advanced knowledge would allow the
professor to know where the students who need more help
should be placed, or it could allow a software tool to recommend laboratory partners in order to form pairs of students
who help each other in their learning.
This experiment provides a lot of useful information for
professors, but it has generated new questions that must be
further investigated. In particular, we would like to analyze
the influence of the student’s gender in the results, and the
behavior of repeaters (students). Another interesting study
would be to repeat the experiment in another area not related to engineering to compare the results. All this information may be useful in the future to define recommendations
or methodologies for student distributions inside classrooms
as it is studied in [2, 8].
4.
ACKNOWLEDGEMENTS
This work has been partially supported by the European
Union (FEDER) and the Spanish Ministerio de Economı́a
y Competitividad under grant TIN2013-44742-C4-1-R and
by the Generalitat Valenciana under grant PROMETEOII/2015/013 (SmartLogic). Salvador Tamarit was partially
supported by Madrid regional projects N-GREENS SoftwareCM (S2013/ICE-2731), and by the European Union project
POLCA (STREP FP7-ICT-2013.3.4 610686). The authors
acknowledge a partial support of COST Action IC1405 on
Reversible Computation. The authors thank the colleagues
who helped them to carry out the experiment and all the
students who participated in it.
5.
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