Mathematics Future Classroom Lab to Measure the Affective Domain
of Pre-Service Teachers
ANA ISABEL MONTERO-IZQUIERDO, JIN SU JEONG*, DAVID GONZÁLEZ-GÓMEZ
Departamento de Didáctica de las Ciencias Experimentales y Matemáticas,
Facultad de Formación del Profesorado, Universidad de Extremadura,
Avenida de la Universidad s/n, 10004 Cáceres,
SPAIN
*Corresponding Author
Abstract: - The affective domain has a great influence on mathematics learning and academic performance.
Therefore, it is important to analyze different variables to propose mathematics interventions that stimulate
positive emotion, self-efficacy, and attitude in students. Pre-service teachers (PST) benefit from a novel
pedagogical intervention in which they experience a positive classroom environment. The scope of this study is
to understand the effects of PSTs by performing an innovative didactic intervention in the future classroom lab
(FCL) in a mathematics course.
Key-Words: - Mathematic education, FCL, Learning spaces, Affective domain, Active methodology,
Technology, Emotion, Attitude, Self-efficacy.
Received: July 29, 2023. Revised: November 2, 2023. Accepted: February 5, 2024. Published: March 26, 2024.
1 Introduction
It is known that various affective factors, such as
emotion, self-efficacy, and attitude, influence
learning mathematics, [1]. Learning is facilitated by
positive emotional states, [2]. Emotion is important
for mathematics performance and influences the
way students approach mathematical problem-
solving, [3]. According to research, positive
emotions in mathematics are associated with high
academic achievement, [4] and promoting positive
emotional experiences helps students to reduce the
anxiety associated with mathematics, [5]. Self-
efficacy is another factor from the affective domain
and is one's belief about the own ability to
successfully perform the actions necessary to
achieve a goal, [6], [7], [8] and is considered an
essential element in predicting students'
performance in mathematics as well as other
cognitive and affective aspects, [9]. Research
indicates that learners’ success in mathematics is
significantly positively correlated with their level of
mathematics self-efficacy, [10], [11], [12], [13]. The
objective grade alone is not as important as the
students’ interpretation of their performance when it
comes to mathematics self-efficacy, [14]. Students
who succeed in a mathematical activity and interpret
their achievement favorably, raise their opinion of
their mathematical competency, [15]. Attitude is
another factor that may affect mathematics learning.
Attitude toward mathematics is defined as one's
emotional disposition, positive or negative, about
mathematics, [16]. The effect of students’ attitudes
toward mathematics on their learning and
achievement is a multifaceted and intricate
phenomenon, [17]. Favorable attitudes toward
mathematics have a positive impact on learning
outcomes, [18], [19]. On the contrary, pre-service
teachers (PSTs) negative attitudes toward
mathematics have an unfavorable effect on learners'
motivation and engagement, [20]. Thus, the
importance of the affective domain in mathematics
education is evident.
An external aspect that seems to affect learners’
affective domain and academic performance is the
learning environment. According to some authors,
there is a correlation between enhanced students’
attitudes in innovative learning settings and higher
academic achievement in mathematics, [21]. Also,
the classroom environment has an impact on
students' self-efficacy, [22]. The physical space of
the classroom and the pedagogical style of the
teachers are two malleable elements of the learning
environment that might influence students' ability
beliefs, [6]. Moreover, academic achievement has
also been demonstrated to be predicted by students'
self-efficacy to self-regulate, or their beliefs about
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DOI: 10.37394/232010.2024.21.1
Ana Isabel Montero-Izquierdo,
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E-ISSN: 2224-3410
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Volume 21, 2024
their capacity to manage their work well, [23].
According to the International Society for
Technology in Education (ISTE) Report, learning
environments need to be active, enabling students to
interact and communicate in a way that would be
expected of them in the workplace of the future. The
authors discussed the idea of active learning to show
how combining pedagogy, technology, and physical
space may help teachers transform what occurs in
the classroom. Classrooms purposefully created
with active methodologies enhanced student
engagement in comparison to standard classrooms,
[24]. Innovative learning contexts, such as the future
classroom lab (FCL), aim to provide appropriate
physical spaces and motivational technologies for
learning. Using technology not only improves
students' knowledge, and competencies, but also
increases their motivation to learn, [25] as well as
their learning process, [26]. It is important to rethink
and implement strategies to teach students in such a
way that they become interested in mathematics and
advocate for interdisciplinary projects and
innovative technology for accelerated learning that
awakens emotions in students, [27]. The FCL
comprises six learning zones: investigate, interact,
exchange, develop, create, and present, and the goal
is to reconsider pedagogy, technology, and learning
environments, [28].
Learning environments and methodology seem
to be interrelated and to have an impact on students’
affective domain. In recent years, pedagogical and
technological changes have also affected learning
spaces. There has been an increase in the use of
active learning spaces, which allows the physical
layout of the classroom to support a learner-centered
educational approach, [29]. The purpose of the
teacher in active learning is to foster interaction
rather than impart knowledge which is possible by
the architecture of these venues, [30]. Unlike a
standard lecture hall, which largely enables one-
sided discourse, the physical design of learning
spaces allows for dynamic interactions between
learners, [31]. Thus, physical space is considered
important by the students for their learning, [32] and
students' enjoyment of mathematics is greatly
influenced by the learning environment, [33]. The
learning environment must provide comfort, safety,
and flexibility in a way that facilitates a variety of
working styles, interactions, and collaboration
between students, [34]. Learners’ interest in
studying mathematics and their performance are
greatly influenced by a pleasant learning
environment, [35]. Moreover, the use of novel
teaching methodologies has proved to enhance
classroom atmosphere, attitudes, and the
development of mathematical concepts, [36].
The objective of this research is to analyze the
effect of affective domain influences by this
intervention proposal in the mathematics FCL.
Therefore, by facilitating an intervention based on
active methodologies in an innovative learning
space supported by digital technologies, the main
goal is to reveal the impact on PSTs’ affective
domain after applying this pedagogical proposal
while learning mathematics in the FCL. In the
following section, the intervention design and
methodology are described.
2 Intervention Design
The intervention has been created considering the
different learning zones, which contain the FCL.
These areas, within the learning classroom, have
been defined as investigating, creating, developing,
interacting, presenting, and interchanging and favor
collaborative work. The pedagogical proposal aims
to work on mathematics contents as well as promote
the development of competencies while working in
the diverse learning areas of the FCL. During the
whole intervention, the students are active in their
learning and can move through every learning area,
using diverse materials, digital devices, and learning
resources that offer the FCL (digital whiteboards,
glass wall, video camera, chroma, laptops, mobile
phones, etc.). The teacher has the role of facilitator
of the PSTs’ learning experience, being able to
guide them and give constantly constructive
feedback to scaffold their learning and help them to
achieve their academic goal in a supportive manner.
In the first activity, the students should select any
base of a numeral system and create a new one by
creating novel characters. The activity consisted of
designing a numeral system and performing
different arithmetic operations. Here, the PSTs may
discuss and be able to express any number of the
numeral consistently, following the grouping
principle in which a new sign represents a certain
number of units. Then, the new number system must
be represented using a new set of characters,
clarifying the relationship between the decimal and
planned numeral systems. With this new system,
different arithmetic operations must be performed
(addition, subtraction, multiplication, and division).
For example, participants should draw their number
system on the digital board and on the glass wall to
share their results inside the mathematics FCL
(Figure 1 and Figure 2).
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Fig. 1: PSTs create their numeral system in the
digital board within the mathematics FCL
Fig. 2: PSTs create their numeral system in the glass
wall within the mathematics FCL
Then, to gamify the experience an augmented
reality application must be used to create an
augmented reality flag, which contains the
characters of their numeral system design (Figure
3). Finally, a learning product must be created. It
consisted of generating a video recording in the
chroma in which students show and resume all the
findings developed throughout the session. It
permits the teacher to be the facilitator and give
formative evaluation through their process and the
development of competencies has been promoted
throughout the session.
Fig. 3: PSTs create their augmented reality flag in
the mathematics FCL
2.1 Sample
The sample consisted of a total of 94 PSTs, 54
participants in the academic year 2021/2022 and 45
in the academic year 2022/2023. Both groups are in
the second year of Primary Education degree in the
Teacher Training School of the University of
Extremadura, Spain. The PSTs were enrolled in the
second year of the degree and specifically in the
subject ‘Mathematics and its Didactics’.
Male Female Science
Social
Science
Technology Others
54 20.2 40 60 37 50 7 4
Male Female Science
Social
Science
Technology Others
45 20.02 40 60 22.22 68.89 6.67 2.22
N
Age
Gender (%)
Educational Background (%)
2021/22
N
Age
Gender (%)
Educational Background (%)
2022/23
Fig. 4: Demographic information of the sample
As shown in Figure 4, the sample size is roughly
the same and has a similar characteristic regarding
the gender distribution. The main difference
observed concerns studies background. In the
academic year 2022/2023, a total of 68.89% of
students has a Social Science background while in
the academic year 2021/2022, the percentage is
50%. Therefore, most of the students enrolled in
these years for Primary Education degree have a
lack of mathematical literacy base.
2.2 Instrument
The data was collected through an online-based
questionnaire in concern with emotion, attitude, and
self-efficacy towards mathematics and the
intervention in the FCL. The questionnaire has been
adapted from validated previous research. In Table
1, all the items of the survey are described. A five-
point Likert scale was applied, in which the lowest
value was “Strongly Agree” and the highest value
was “Strongly Disagreed” before and after
intervention implementation.
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Table 1. Items within the questionnaire.
Emotion items
E1. Joy
E2. Satisfaction
E3. Enthusiasm
E4. Fun
E5. Trust
E6. Hope
E7. Pride
E8. Uncertainty
E9. Nervousness
E10. Concern
E11. Frustration
E12. Boredom
E13. Fear
E14. Anxiety
Self-efficacy
S1. I understand math concepts well enough to teach
mathematics at the lower educational levels.
S2. I will usually be able to answer students'
mathematics questions.
S3. When I put my all into it, I will succeed in
teaching mathematics as well as I would in other
subjects.
S4. I believe I have the necessary skills to teach
mathematics.
S5. Mathematics is useful for solving everyday
problems.
S6. It is important to know mathematics to get a good
job.
S7. I know the steps necessary to teach mathematics
effectively.
S8. I encounter difficulties when trying to explain a
mathematical concept.
S9. The use of motivating teaching spaces is essential
to achieve good learning results.
S10. I know how to work in a Classroom of the
Future.
Attitude
A1. I prefer Classroom of the Future to a traditional
theory class to teach mathematical content.
A2. I prefer a Classroom of the Future to a traditional
lab session to teach mathematical content.
A3. Working on the contents of several subjects
simultaneously favors learning.
A4. Working in a future classroom-type environment
enhances creativity in students.
A5. Working in a future classroom-type environment
enhances collaboration among students.
3 Results
3.1 Reliability of the Instrument's Internal
Consistency
The data analysis for this research was
conducted through Jamovi software. First, the
Cronbach’s alpha coefficient () was obtained to
check the reliability of the instrument's internal
consistency. Alpha is the ratio of the variance
between the real and observed scores. Consequently,
higher dependability indicates a tighter match
between the true and observed values, [37]. To show
how effectively a set of items assesses a
unidimensional latent property, internal consistency
was utilized. Because of this, independent
coefficient studies were conducted for every
domain. For this investigation, the Cronbach’s alpha
coefficients greater than 0.70 were considered
acceptable. The results demonstrate good reliability
(Table 2).
Table 2. Statistics on scale reliability, [37].
Scale
Cronbach’s alpha ()
Positive Emotion
0.955
Negative Emotion
0.850
Self-efficacy
0.870
Attitude
0.813
Table 3. Mann-Whitney U test (p-value).
Items
2022
2023
E1
< .001
< .001
E2
< .001
< .001
E3
< .001
0.001
E4
< .001
< .001
E5
< .001
< .001
E6
< .001
< .001
E7
< .001
< .001
E8
< .001
< .001
E9
< .001
0.002
E10
< .001
0.023
E11
< .001
0.404
E12
< .001
0.360
E13
< .001
0.270
E14
0.004
0.057
S1
< .001
0.009
S2
< .001
0.102
S3
0.006
0.691
S4
0.002
0.035
S5
0.028
0.421
S6
< .001
0.905
S7
< .001
< .001
S8
0.006
0.649
S9
< .001
0.597
S10
< .001
< .001
A1
< .001
0.106
A2
< .001
< .001
A3
< .001
0.193
A4
0.003
0.161
A5
0.008
0.429
Therefore, the instrument applied for this
research has a good internal consistency for each
construct. Second, the Kolmogorov-Smirnov test
was conducted to check if the data was normally
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Jin Su Jeong, David González-Gómez
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Volume 21, 2024
distributed. As it was not normally distributed, non-
parametric tests were conducted. Therefore, the
Mann-Whitney U Test was performed to test the
existence of significant differences between the
mean values. As shown in Table 3, within the
column of 2022 year, all the items presented p-
values lower than 0.05, which demonstrates a
significance in all the items. Whereas in 2023, half
of the items presented p-values above 0.05,
therefore the results represent non-significance in
these items. However, for both years all the items
regarding positive emotion were significant.
Therefore, applying this intervention the results
showed meaningful results regarding positive
emotion.
3.2 Analysis of Variance
The analysis of variance for non-parametric data
was tested through the Kruskal-Wallis’s test. The
significance level accepted is 0.05. The hypothesis
indicated that H0 = there are no differences between
groups and H1 = there exists difference between the
groups. Every item presented a significant p-values
in the Kruskal-Wallis’s test (p< .005). Finally, to
determine the specific differences between the
groups a post-hoc test was conducted. As shown in
Table 4, most of the items presented no significant
difference except items E11, S8, and S9 comparing
post-test 2022 and post-test 2023 the groups
presented meaningful differences in their responses,
and in item S10 in the pre-test 2022 and pre-test
2023 answers revealed significant differences.
Therefore, the items shown in Table 4 are not
reliable for reporting significant results due to the
differences in the groups.
Table 4. Dunn's Post Hoc comparisons.
Comparison
Item
p
pbonf
pholm
2-4
E11
0.010**
0.060
0.050*
2-4
S8
< .001***
0.002**
0.001**
2-4
S9
0.005**
0.032*
0.026*
1-3
S10
< .001***
< .001***
< .001***
Note: * p < .05, ** p < .01, *** p < .001.
1-3=Pre-test 2022-Pre-test 2023
2-4=Post-test 2022-Post-test 2023
3.3 Exploratory Factor Analysis
Then, the exploratory factor analysis (EFA) has
been conducted and represented in Table 5. The
factors obtained represent the different variables
mentioned before positive emotion (factor 1), self-
efficacy (factor 2), negative emotion (factor 3), and
attitude (factor 4). The extraction method of
factorization along the principal axis was used in
combination with an 'oblimin' rotation. After
applying the EFA to all the items of the
questionnaire, it can be revealed that S9 and S10
have been added and regrouped to the variable
attitude.
Factors loadings, variance percentage, and
cumulative variance for the factors are represented
in Table 5. It showed that four factors positive
emotion, self-efficacy, negative emotion, and
attitude accounted for 59.1% of the total 29
variances.
Table 5. Factors loadings, variance percentage, and
cumulative variance
Factors
Loadings
%Variance
%Cumulative
1
5.50
19.0
19.0
2
4.33
14.9
33.9
3
4.02
13.9
47.8
4
3.27
11.3
59.1
The correlation between the factors is shown in
Table 6. The correlations are between 0.247 and
0.404, which indicate medium correlations through
the factors. The highest correlation is represented
between positive emotion and attitude (0.404).
Followed by self-efficacy and attitude and then,
positive emotion and self-efficacy.
Table 6. Correlations between factors
1
2
3
4
1
-
0.346
-0.287
0.404
2
-
-0.323
0.378
3
-
-0.247
4
-
3.4 Mean and Median Comparison
These findings represent the mean and median
comparison in the PSTs’ responses for pre- and
post-test in 2022 and 2023. These results are
represented in Figure 5, Figure 6, Figure 7 and
Figure 8 for each factor, showing similarities of the
sample and more meaningful results in the
intervention in the year 2022.
Fig. 5: Mean and median comparison of positive
emotion in pre- and post-test in 2022 and 2023
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After the intervention in 2022 and 2023, as
shown in Figure 5, PSTs perceived an enhancement
of positive emotions (joy, satisfaction, enthusiasm,
fun, trust, hope, and pride) after the application of
this educational proposal in the FCL.
Fig. 6: Mean and median comparison of negative
emotion in pre- and post-test in 2022 and 2023
In Figure 6, the results show that PSTs’ negative
emotions (uncertainty, nervousness, worry,
frustration, boredom, fear, and anxiety) have
decreased after the intervention in the FCL in both
years.
Fig. 7: Mean and median comparison of self-
efficacy in pre- and post-test in 2022 and 2023
Regarding PSTs’ self-efficacy in concern with
mathematics and the FCL, results showed an
increase after the application of the intervention in
both years (Figure 7).
Fig. 8: Mean and median comparison of attitude in
pre- and post-test in 2022 and 2023.
Finally, as seen in Figure 8, PSTs reported higher
attitudes towards working in a FCL after the
intervention.
3.5 Description of Factors and
Backgrounds
Here, a descriptive analysis was conducted to obtain
the differences regarding the factors obtained and
the different backgrounds regarding their previous
studies during high school. Number 1 refers to
sciences, number 2 to humanities and social
sciences, and number 3 to studies concerning
technology. Figure 9 represents the average scores,
median, and standard deviation for the four factors
divided by pre-university studies backgrounds.
Background PE SNE A
Mean 1 -0.00462 0.0965 -0.307 -0.118
2 0.0355 -0.130 0.159 0.0409
3 -0.0792 0.542 -0.229 0.0910
4 -0.665 0.454 -0.380 -0.0640
Median 1 0.310 0.0329 -0.706 0.142
2 0.149 -0.0234 -0.0463 0.435
3 0.0419 0.661 -0.694 0.425
4 -0.665 0.454 -0.380 -0.0640
SD 1 1.02 0.779 0.808 0.882
2 0.947 1.06 0.993 1.00
3 1.10 0.747 0.832 0.713
4 0.555 0.915 0.563 1.15
Fig. 9: Description of mean, median, and standard
deviation regarding factors and backgrounds
According to the results, based on the different
factors and the background, it was revealed some
significant data to be highlighted. The PSTs who
have a background in technology presented the
highest level of self-efficacy. The ones from social
science or humanity reported the highest level of
negative emotion and PSTs with a science
background represent the ones with the highest
positive emotion. Finally, in terms of attitude, it is
observed that students with a scientific and
humanistic background and students with a
technological background have the most positive
attitude.
3.6 Mean and Typical Error
Figure 10 shows the mean and error for each item
analyzed in the pre-test and post-test about the
interventions in 2022 and 2023. The axis 'y'
represents the degrees of the Likert scale, (1)
Strongly Disagree; (2) Disagree; (3) Neither Agree
nor Disagree; (4) Agree; (5) Strongly Agree.
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Ana Isabel Montero-Izquierdo,
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E-ISSN: 2224-3410
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Volume 21, 2024
There was an improvement in all items after the
intervention in both years. The decrease observed is
referred to as a negative emotion which after the
intervention PSTs have reduced. Item S8 was
formulated negatively. For the intervention in 2023,
there are fewer differences compared to the
intervention of the previous year, but most of the
responses in the post-test after the application of the
intervention have improved in the PSTs.
4 Conclusion
The effect on PSTs’ affective domain regarding the
proposed intervention in the mathematics FCL has
been analyzed in different aspects. In this research,
the instrument internal consistency was reliable for
each factor. The results presented significance
regarding positive emotion in the two compared
years. The factors have been identified and defined
more accurately manner and the correlation between
them represents the highest correlation between
positive emotion and attitude. The findings revealed
a global enhancement in PSTs’ emotions, attitudes,
and self-efficacy for both years of the intervention.
Moreover, the differences regarding the factors and
the different backgrounds revealed that PSTs with a
background in technology reported the highest level
of self-efficacy. Factors related to the pre-service
elementary school teachers' backgrounds in
mathematics influence how confident they feel in
their mathematical abilities, [38]. Thus, according to
the findings, PSTs who have a technology
background are the ones with the highest level of
self-efficacy and may feel more confident in
teaching mathematics subjects.
Fig. 10: Mean and tipical error pre- and post-test in 2022 and 2023
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According to the various authors, an important
factor in increasing teachers' self-efficacy as
mathematics educators is their view of the subject
and their university experience [39],[40]. Therefore,
this study aims to propose learning experiences in
the FCL to offer the opportunity to work in different
settings and innovative learning environments. In
addition, with the use of active methodologies and
technological devices. Having this experience in the
university may be more likely to enhance PSTs’
self-efficacy as mathematics educators in the future.
Mathematics occupies a central place in
engineering education and is a fundamental tool in
the processes of analysis and calculation that an
engineer must carry out. Learning environments and
methodology seem to be interrelated and to have an
impact on students’ affective domain. For this
reason, the FCL has been chosen as the scenario for
this teaching and learning intervention. To apply a
similar proposal in the engineering field, science,
technology, engineering, arts, and mathematics
(STEAM) methodologies can be applied to propose
interdisciplinary projects. This method is
advantageous over others that already exist in
literature because the FCL promotes the application
of and 21st competencies such as problem-solving,
critical thinking, collaboration, and digital
competence. This permits a more innovative method
based on related contents and competencies in
teaching/learning practices versus traditional content
lessons. Another benefit is that for entering the
workforce, the development of engineering students'
competencies is a key factor. Also, few works
regarding active methodologies and innovative
learning spaces have been found. Moreover, this
paper can serve as guidance for engineering to do a
similar educational proposal applying active
methodology and innovative learning environments
to foster not only traditional content acquisition but
competences acquisition in the FCL in several areas
(investigate, interact, exchange, develop, create, and
present). In addition, fostering and improving PSTs’
affective domain may support them to perform
better in the classroom, with the expectation of
improved academic performance.
The limitation of this research could be the
sample size for each year, to obtain broader results
the study will be conducted for more years. Also,
this proposal has focused on mathematics. For
future research, it can be proposed a STEAM
methodology involving these subjects as an
interdisciplinary intervention. It can promote
research in the engineering field as not many
pedagogical interventions are done focusing on
learning environments and active teaching-learning
methodologies. Then, interdisciplinary intervention
can be conducted for future research and can help
engineering professors implement new educational
strategies in the classrooms.
Acknowledgement:
The authors appreciate the invitation to publish an
article for WSEAS Transactions on Mathematics.
A.I.M.I. thanks to Ministerio de Universidades of
the Spanish Government for her scholarship (Grant
number FPU22/04217).
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Ana Isabel Montero-Izquierdo,
Jin Su Jeong, David González-Gómez
E-ISSN: 2224-3410
8
Volume 21, 2024
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Jin Su Jeong, David González-Gómez
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Contribution of Individual Authors to the
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The authors equally contributed to the present
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The authors have no conflicts of interest to declare.
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WSEAS TRANSACTIONS on ADVANCES in ENGINEERING EDUCATION
DOI: 10.37394/232010.2024.21.1
Ana Isabel Montero-Izquierdo,
Jin Su Jeong, David González-Gómez
E-ISSN: 2224-3410
10
Volume 21, 2024
