Factors Affecting Teachers’ Integration of Visualization Technology in
Geometry: PLS-SEM Analysis
FARIDAH HANIM YAHYA1, MOHD RIDHUAN MOHD JAMIL1,
MOHD SYAUBARI OTHMAN1, TAJUL ROSLI SHUIB1, WASILATUL MURTAFIAH2
Faculty of Human Development,
Universiti Pendidikan Sultan Idris,
35900 Tanjong Malim, Perak,
MALAYSIA
2Mathematics Education Department,
Faculty of Teacher Training and Education,
Universitas PGRI Madiun,
INDONESIAN
Abstract: - Visualization is identified as a crucial element that affects students’ performance in Geometry.
Technology plays an important role to assist weak students in visualizing concepts in Geometry. Teachers need
proper planning in teaching to help their students in understanding the concepts. This study used partial least
squares-structural equation modelling (PLS-SEM) to test the hypotheses to verify the effects of variables on
teachers’ intention of integrating visualization technology in teaching geometry. The model consists of four
constructs: teaching strategy, teaching activity, selection of media, tools and teaching aids, and assessment. The
research instrument consisted of 30 survey questions for four main constructs: teaching strategy, teaching
activity, selection of media, tools, and teaching aids and assessment. The questionnaires were distributed to
180 teachers who teach Mathematics in secondary schools. The study used a PLS-SEM modeling tool to
analyze data for reliability and validity. Results show that teaching strategy, teaching activity, selection of
media, tools and teaching aids, and assessment significantly influence the integration of visualization
technology in Geometry. This finding is a reference for policymakers and implementers to improve the quality
of teaching and learning in Geometry for secondary schools.
Key-Words: - visualization technology, secondary mathematic teachers, geometry, visual-spatial skill, level of
geometrical thinking, PLS-SEM
Received: August 2, 2022. Revised: June 19, 2023. Accepted: July 27, 2023. Published: September 7, 2023.
1 Introduction
Geometry is one of the fields in Mathematics that
requires students to construct knowledge based on
visualizing shapes and diagrams, [1]. Visualization
plays a vital role to help students master the
concepts to solve problems correctly. It is
acknowledged to be the reason for the student’s
poor performance in Geometry, [2]. Geometry is
important to students because it is related to their
life and future, [3]. Therefore, the Ministry of
Education (MOE) highlighted the students’
weakness in Geometry as one of the issues in
education that needs an immediate solution, [4]. In
addition, a report from Trend in Mathematics and
Science Studies (TIMSS) 1999-2019 showed that
Malaysian students’ scores in Geometry were below
the average international level, [4]. TIMSS is an
international assessment for Mathematics and
Science, which is conducted every four years for
students who are 14 years old, [5]. Hence, teachers
need to find ways to motivate students in learning
Geometry.
Previous studies had shown that technology
provided tools for students to visualize concepts,
[6], [7]. The teachers use digital and non-digital
technology in their teaching, [8]. In Malaysia’s
educational system, teachers are encouraged to
integrate digital technology such as Information,
Communication, and Technology (ICT) in teaching,
[9]. On the other hand, teachers can also use non-
digital technology such as graphic calculators and
scientific calculators, [10]. In [11], the author
suggested visualization technology (VT) as a
combination of visualization and technology which
can be in any form of technology that changes
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DOI: 10.37394/232018.2023.11.23
Faridah Hanim Yahya, Mohd Ridhuan Mohd Jamil,
Mohd Syaubari Othman,
Tajul Rosli Shuib, Wasilatul Murtafiah
E-ISSN: 2415-1521
253
Volume 11, 2023
information into images or graphics to make
decision making. However, there is a lack of a
teaching model that relates to the usage of
technology which supports visualization in learning,
[12]. For this reason, the authors were motivated to
conduct this present study to provide teachers with a
guideline on how to embed VT in teaching
geometry. Hence, an integration of the VT
pedagogical model in geometry for mathematics
teachers in secondary schools needs to be built, [13].
2 Background of the Study
VT is an important element to be considered when
restructuring the current curriculum for
mathematics, [14]. The factors that affected teachers
in using VT had been identified by a group of
experts from the field of Mathematics. They were
experienced teachers, lecturers from local
universities, and officers from MOE. The first factor
is teaching activity (TA). This term refers to
activities that are prepared by teachers based on the
learning objectives. Students’ weakness in
Geometry is due to two main reasons: low level of
geometrical thinking, [15], and low visual-spatial
skills (VSS), [16]. The first reason is a thinking
pattern that is connected to van Hiele’s geometrical
thinking (vHGT) model, [17]. The lowest level in
this model is visualization, where the students could
only recognize the shapes of the objects. The second
level is analysis, where the students can describe the
properties of the objects. The third level is informal
deduction, where the students will be able to prove
the relationship between the properties of the
objects. The next level is formal deductive, where
the students will be able to form hypotheses based
on their observations. The highest level is rigor,
which relates to a higher thinking level that is not
recommended for secondary school students, [18].
Students’ thinking level will move to a higher level
during their engagement in learning Geometry.
This thinking model is embedded in teaching by
using van Hiele’s learning phases, [17]. The first
phase is information, where the students will be
informed about the objectives of the lesson. The
second phase is guided orientation, where teachers
will give instructions and steps to students to learn
the new concept. The third phase is explicitation,
where the students express their opinion about the
new knowledge that they learn. The fourth phase is
free orientation, where the students will solve more
challenging problems. The last phase is integration,
where the students will make a summary of what
they have learned. Meanwhile, VSS is the ability to
rotate, view, transform and cut mentally, [16].
Therefore, teachers should create activities that
integrate three components of vGHT, VSS, and van
Hiele’s learning phases, [19]. Besides that, in [20],
the authors suggested hands-on activities to be
conducted using technology tools to improve
visualization. Moreover, in [21], the authors
proposed drawing activities in learning Geometry.
The second factor is a selection of media, tools,
and teaching aids (SMTTA). In [18], the author
suggested that teachers should create materials that
support students’ thinking patterns at each level of
the model. Hence, teachers should apply
visualization techniques in teaching such as using
concrete manipulative objects like 3D blocks and
models, [22]. Another technique is using paper
folding for activities such as origami, [23]. In [24],
the authors suggested using computer applications
in teaching. Dynamic geometrical software (DGS)
such as 3D software is a good example of a
computer application, [7]. The hands-on activities
using tools in DGS, help students to visualize the
objects, [20], [21]. However, students are facing
problems in using DGS in which they cannot
remember the steps of using the tools in the
software, [25]. Therefore, a screencast video is used
to overcome the problem. This video records all the
movements of the pointer by using special software,
[19].
The third factor is assessment (AST). It can be
done using two types of assessment: formative and
summative. Teachers must conduct tests for vGHT
and VSS before and after teaching the concepts to
the students. Based on the result, the teacher can
determine whether the students can move to the next
level of geometrical thinking, [17]. The fourth factor
is teaching strategy (TS) which refers to the method
or technique in delivering using digital and non-
digital technology to help students in visualizing the
concepts of Geometry, [26]. Teachers should
evaluate their selection of teaching methods as these
will affect the student’s understanding, [27]. If
teachers only depend on textbooks in teaching, this
may cause students to recognize the shapes or
diagrams but fail to solve the problems given to
them, [28]. Thus, teachers should select a teaching
strategy that embeds VT. This is in line with MOE
that proposed technology as a teaching strategy in
Mathematics to teach students to construct
knowledge effectively, [10].
Hence, this study analyzes the influence factors
of the integration of VT in Geometry among
mathematics teachers. Thus, the following
hypotheses have been framed for the study:
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DOI: 10.37394/232018.2023.11.23
Faridah Hanim Yahya, Mohd Ridhuan Mohd Jamil,
Mohd Syaubari Othman,
Tajul Rosli Shuib, Wasilatul Murtafiah
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1. H01, the TA has a significant relationship
with the integration of VT in Geometry.
2. H02, the SMTTA has a significant
relationship with the integration of VT in
Geometry.
3. H03, the AST has a significant relationship
with the integration of VT in Geometry.
4. H04, the TS has a significant relationship with
the integration of VT in Geometry.
3 Methodology
3.1 Research Design
The questionnaire used to measure the four latent
variables (TA, SMTTA, AST, and TS) was
developed from the literature. Data were collected
from an online questionnaire distributed to
secondary mathematics teachers, with 30 questions
considered indicator variables. The questionnaire
was divided into Part I and Part II. Part I contains
items related to the respondents’ demographic
backgrounds while the items in Part II focus on four
constructs: TA (7 items), SMTTA (7 items), AST (4
items), and TS (12 items).
3.1 Analyzing Data
For this purpose, a VT pedagogical model was
suggested and verified using partial least squares
structural equation modeling (PLS-SEM), to
examine factors contributing to the integration of
VT in Geometry. The PLS-SEM is chosen as a
method to explore the relationship between the
research variables, [29], [30]. It consists of two
phases: testing the measurement model and the
structural model. The first phase is a procedure to
test internal consistency and convergence validity.
The aspect of convergence validity can be seen at
the values of outer loading, composite reliability
(CR), and average variance extracted (AVE), while
discriminant validity can be seen in Fornell Larcker,
cross-loading, and Heterotrait- Monotrait Ratio
(HTMT).
The aspects of convergence and discriminant
validity are important in assessing the quality of
results obtained from a research study that uses
structural equation modeling (SEM) techniques.
Convergence validity refers to the extent to which
different measures of the same construct are related
to one another. This can be assessed by examining
the values of outer loading, composite reliability
(CR), and average variance extracted (AVE). If
these values are high, it means that the measures are
converging on the same underlying construct, which
increases the overall validity of the research study.
Discriminant validity, on the other hand, refers to
the extent to which different constructs are not
related to one another. This can be assessed by
examining Fornell Larcker, cross-loading, and
Heterotrait-Monotrait Ratio (HTMT). If these values
are low, it means that the different constructs are not
overlapping and are distinct from one another,
which also increases the overall validity of the
research study. In conclusion, the results of the
research study will be more reliable and valid if
both convergence and discriminant validity are
adequately assessed and satisfied.
The second phase is concerning the evaluation of
the structural model. The structural model’s
assessment includes the level and significance of the
path coefficients by performing a bootstrapping
procedure with 5,000 resamples, [31]. The
procedure in this phase is to identify five items:
internal VIF or Multicollinearity (Inner VIF),
structural model coefficient (T), coefficient (R
square, R2), size effect (f2), and predictive relevance
(Q2), [30].
4 Problem Solution
A total of 180 mathematics teachers from secondary
schools in Malaysia participated in this study as
shown in Table 1. The number of participants to
perform the structural equation model (SEM) is
between 100 to 200, [32], [33].
Table 1. Respondents’ Demographic Information
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Faridah Hanim Yahya, Mohd Ridhuan Mohd Jamil,
Mohd Syaubari Othman,
Tajul Rosli Shuib, Wasilatul Murtafiah
E-ISSN: 2415-1521
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4.1 Measurement Model
The first element in the convergence validity is the
outer load value. Table 2 shows that the results of
CR ranged between 0.904 to 0.926 which were
above the recommended value of 0.7, [34].
Meanwhile, the AVE values should be above the
threshold of 0.5, [35], [36]. From Table 2, the AVE
value for the TS constructs was <0.50. Therefore, to
increase the AVE value to >0.50, items for outer
loading which is <0.50 in each construct need to be
eliminated, [30].
Table 2. Results For the Test of Measurement
Model – Stage 1
Construct
Item
Outer
loading
>0.50
AVE
>0.50
TS
S1
0.782
0.45
S2
0.788
S3
0.735
S4
0.654
S5
0.67
S6
0.545
S7
0.707
S8
0.745
S9
0.717
S10
0.642
S11
0.578
S12
0.371
SMTTA
M1
0.832
0.577
M2
0.831
M3
0.857
M4
0.597
M5
0.822
M6
0.599
M7
0.729
TA
A1
0.813
0.603
A2
0.664
A3
0.832
A4
0.771
A5
0.659
A6
0.844
A7
0.829
AST
P1
0.801
0.757
P2
0.885
P3
0.877
P4
0.914
After removing the items (S12 and S6), all
values of AVE reached corresponding thresholds as
shown in Table 3. Even though some values for
outer loading were less than 0.70, they were
accepted since all AVE values were above 0.50,
[30], [37]. Therefore, convergent validity was
adequately indicated.
Table 3. Results For the Test of Measurement
Model – Stage 2
Construct
Item
Outer
loading
>0.50
CR
>0.70
AVE
>0.50
TS
S1
0.798
0.909
0.577
S2
0.649
S3
0.571
S4
0.797
S5
0.743
S7
0.662
S8
0.680
S9
0.696
S10
0.745
S11
0.722
SMTTA
M1
0.832
0.904
0.577
M2
0.829
M3
0.855
M4
0.601
M5
0.820
M6
0.602
M7
0.731
TA
A1
0.813
0.913
0.639
A2
0.661
A3
0.834
A4
0.769
A5
0.656
A6
0.845
A7
0.831
AST
P1
0.802
0.926
0.757
P2
0.884
P3
0.877
P4
0.914
To confirm discriminant validity, the value of the
square root of AVE should be higher than its
correlation with other variables (based on the
Fornell-Larcker criterion). The reflective construct
TA had a value of 0.777 for the square root of its
AVE as shown in Table 4. This value was higher
than the SMTTA (0.761) and TS (0.589). However,
the value for AST was above the value of TA.
Consequently, it showed that there was no
relationship between both variables, [38]. Therefore,
the variable for teaching activity had no relationship
with the variable of assessment. Meanwhile, the
reflective construct for SMTTA had a value of 0.76
for its AVE. This value was higher than the AST
(0.674) and TS (0.701). Similarly, the reflective
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construct for AST had a value of 0.87 for its AVE.
This value was higher than TS (0.603).
Table 4. Inter-Correlations of The Latent Variables
Construct
TA
SMTTA
AST
TS
TA
0.777
SMTTA
0.761
0.76
AST
0.78*
0.674
0.87
TS
0.589
0.701
0.603
0.709
Table 5 shows the cross-loading values for each
item reflected on four different latent constructs.
Items A1, A2, A3, A4, A5, A6, and A7 loaded high
on their corresponding construct TA and much
lower on other constructs of SMTTA, AST, and TS.
Items M1, M2, M3, M4, M5, M6, and M7 loaded
high on their corresponding construct SMTTA and
also lower on other constructs of TA, TS, and AST.
Items P1, P2, P3, and P4 also appeared to load high
on their corresponding construct of AST but much
lower on other constructs of TA, TS, and SMTTA.
Furthermore, items S1, S2, S3, S4, S5, S7, S8, S9,
S10, and S11 also loaded higher on their
corresponding construct of TS and lower on other
constructs of TA, AST, and SMTTA. This shows
that the value for cross-loading is smaller than the
value for factor loading. Therefore, it indicates good
discriminant validity, [39].
Table 5. Cross Loading for Constructs TA,
SMTAA, AST, and TS
Item
TA
SMTTA
AST
TS
A1
0.813
0.623
0.67
0.507
A2
0.661
0.398
0.403
0.354
A3
0.834
0.69
0.674
0.477
A4
0.769
0.492
0.595
0.479
A5
0.656
0.368
0.392
0.361
A6
0.845
0.731
0.695
0.503
A7
0.831
0.721
0.713
0.491
M1
0.604
0.832
0.552
0.629
M2
0.654
0.829
0.562
0.509
M3
0.664
0.855
0.591
0.55
M4
0.407
0.601
0.338
0.581
M5
0.609
0.82
0.566
0.538
M6
0.49
0.602
0.392
0.436
M7
0.579
0.731
0.537
0.491
P1
0.593
0.49
0.802
0.54
P2
0.721
0.636
0.884
0.497
P3
0.67
0.585
0.877
0.552
P4
0.724
0.626
0.914
0.514
S1
0.393
0.495
0.448
0.798
S2
0.406
0.489
0.481
0.797
S3
0.416
0.445
0.433
0.743
S4
0.383
0.531
0.395
0.662
S5
0.476
0.498
0.456
0.68
S7
0.45
0.586
0.45
0.696
S8
0.401
0.51
0.442
0.745
S9
0.487
0.538
0.445
0.722
S10
0.426
0.513
0.4
0.649
S11
0.322
0.335
0.296
0.571
In Table 6, the HTMTs of this measurement
model were all less than 1, indicating that the
measurement model had good discriminant validity,
[37]. Therefore, the model and scale constructed in
this study had high reliability and validity, [40].
Table 6. Heterotrait-Monotrait (HTMT)
Construct
TA
SMTTA
AST
TS
TA
SMTTA
0.842
AST
0.856
0.757
TS
0.657
0.8
0.677
4.2 Structural Models in PLS-SEM
The first element is to test multicollinearity (Inner
VIF) to examine whether the components of the
model (TS, TA, SMTTA, and AST) are redundant
to one another, [37]. The VIF value should be less
than the threshold of 5, [30]. From Table 7, all inner
VIF values were below the threshold of 5.
Therefore, there was no collinearity issue in this
case.
Table 7. Results of the Structural Model Test for
Inner VIF
Construct
Integration of VT in Geometry
TS
3.446
TA
3.112
SMTTA
2.792
AST
2.097
The second element is to test the path coefficients
(β) by using a bootstrapping procedure. The path
coefficient should be significant if the T-statistics is
larger than 1.945, [30]. Table 8 shows that all
constructs had a T value > 1.645 and the highest
path coefficient was TS (β = 0.358). Moreover, from
Table 8, H01, H02, H03, and H04 had reached a
significant level with a p-value less than 0.05.
Therefore, all hypotheses were accepted.
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Table 8. Structural Model Evaluation Results
Hypothe
sis
Mean/βe
ta
Standa
rd
Deviati
on
T
Statistics
(O/STDE
V)
P
Valu
es
<0.0
5
H01
0.3
0.017
17.139
0.00
H02
0.279
0.016
17.145
0.00
H03
0.207
0.012
16.571
0.00
H04
0.358
0.024
14.804
0.00
The PLS-SEM path analysis model is shown in
Figure 1. The findings showed that VT should be
embedded in TS, TA, SMTAA, and AST. Teachers
should choose teaching strategies, activities, and
teaching aids that will help the students in
visualizing the concepts in Geometry by using
digital and non-digital technology. For TS, teachers
can use DGS for teaching 3-dimensional (3D)
objects. They also can use screencast videos to help
students to know the tools in the software. For TA,
teachers should allow students to be hands-on with
the software. Meanwhile, for SMTAA, teachers can
use concrete manipulative materials such as 3D
blocks and models. Furthermore, for assessment,
teachers should test the student’s level of VSS and
vGHT before and after teaching them the concepts
of Geometry.
Fig. 1: Model of Integration of VT in Geometry
The third element is to test the coefficient of
determination (R2). The value of R2 > 0.67 is strong,
R2 > 0.33 is moderate and R2 > 0.19 is weak, [29].
Table 9 shows that the determination coefficient
(R2) for the integration of VT in Geometry was
0.999. Therefore, this value was considered highly
acceptable. The R2 value suggested that 99.8% of
variants can be explained by the independent
constructs towards the dependent construct of the
research. In addition, the adjusted R2 value was very
close to the R2 value, implying that the bias of the
non-significant independent variables was very
small, [41].
Table 9. Results of the Structural Model Test for R
Square (R2)
Variable
R Square
(R2)
R Square
Adjusted
Integration of VT in
Geometry
0.999
0.998
The fourth element is to calculate the effect size
(f2). Table 10 shows that the effect sizes (f2) of all
the dependent variables were large since the f2 value
is more than 0.35, [42].
Table 10. The Values of R2, F2
Facto
r
Endogen
ous
R2
Include
R2
Exclude
Effect
Size (f2)
TS
Integrati
on of VT
in
Geometr
y
0.999
0.96
39.00
TA
0.999
0.978
21.00
SMT
TA
0.999
0.977
22.00
AST
0.999
0.987
12.00
The final element is to find the value of Q2
through a blindfolding procedure using SmartPLS
3.0, [39]. Results for the predictive relevance are
shown in Table 11. Since the Q2 value of 0.385 was
greater than 0 with just one endogenous construct of
Integration of VT in Geometry, the model was
considered as having adequate predictive power,
[43].
Table 11. Results of Predictive Relevance
Dependent
Variable
SSO
SSE
Q² (=1-
SSE/SSO)
Integration of
VT in Geometry
5,400.00
3,322.43
0.385
5 Discussion
The main purpose of this research is to determine
the influencing factors on the integration of VT in
Geometry for secondary mathematics teachers in
Malaysia. This research attempts to explain the
relationship between TS, TA, SMTTA, and AST.
This study finds that the constructs have significant
relationships with the integration of VT in
Geometry. The outcome of this finding is consistent
with those of other studies which showed that
technology had positive effects on students in
learning Geometry, [44], [45]. However, in [46], the
authors found out that teachers need more resources
on Mathematics visualization and they also need
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Faridah Hanim Yahya, Mohd Ridhuan Mohd Jamil,
Mohd Syaubari Othman,
Tajul Rosli Shuib, Wasilatul Murtafiah
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training on how to apply visualization techniques.
They also suggested that curriculum and textbooks
should be designed to embed VT in the teaching and
learning process. Another study also showed that
VT should be integrated with initial teacher training
for pre-service teachers, [47].
Furthermore, the results indicate that TS has the
greatest impact on the integration of VT in
Geometry (0.358). Similarly, these findings are also
supported by other research which found that TS
affects the integration of VT in teaching Geometry,
[15], [19]. Moreover, the findings reveal that the TS
using screencast video assists students in learning
the tools in DGS. The findings are consistent with
other studies that showed that the screencast video
helped students in using new software, [49], [19].
These findings also show that the TS using
visualization techniques can help students to
visualize the concepts in Geometry. This result is
aligned with those reported by prior studies that use
these techniques in teaching Geometry, [46]. In
addition, TS using technology show that students’
levels of vHGT and VSS had increased, [48].
Similarly, these findings are also supported by other
research which found that TS using VT increased
students’ level of VSS and vHGT, [19], [48].
For the TA, VT elements are applied through the
use of technology tools, [11]. Meanwhile, for the
SMTTA, VT elements are applied by using
manipulative materials, [24], and video screencasts,
[19]. The last component is AST which involves
measuring the level of students’ vHGT and VSS
before and after teaching Geometry. Through this
assessment, teachers can evaluate their TS, TA, and
SMTTA that are used in teaching Geometry, [48].
These results are consistence with the previous
studies that claimed that TA, SMTTA, and AST
affect the integration of VT in Geometry, [1], [23].
6 Conclusion
One of the main goals of MOE is to encourage
teachers to integrate technology in teaching and
learning Mathematics to assist weak students in
visualizing. Teachers need a new pedagogical model
that integrates non-digital and digital technology in
teaching. Thus, this model contributes to the
literature on the integration of technology in
Mathematics for secondary mathematics teachers.
Moreover, MOE should realize that Mathematics
curricula should be reformed to embed VT for
topics in Geometry. In addition, proper programs
and training should be planned by the authorities to
help teachers integrate VT into their lessons
effectively. Further research is proposed to study the
integration of VT among teachers in other fields of
Mathematics, to produce a perfect integration of the
VT model specifically for secondary Mathematics
teachers.
Acknowledgment:
This research was funded by the Ministry of Higher
Education, Malaysia through Fundamental Research
Grant Scheme (RACER/1/2019/SSI09/UPSI//3).
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed to the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This research was funded by the Ministry of Higher
Education, Malaysia through Fundamental Research
Grant Scheme (RACER/1/2019/SSI09/UPSI//3).
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
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WSEAS TRANSACTIONS on COMPUTER RESEARCH
DOI: 10.37394/232018.2023.11.23
Faridah Hanim Yahya, Mohd Ridhuan Mohd Jamil,
Mohd Syaubari Othman,
Tajul Rosli Shuib, Wasilatul Murtafiah
E-ISSN: 2415-1521
262
Volume 11, 2023