The Effects of Learning Integrals and Its Application Using Ti-Nspire Cx Graphing Calculator's Towards Mathematics Pre-Service Teachers' ...
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REVIEW OF INTERNATIONAL GEOGRAPHICAL EDUCATION
ISSN: 2146-0353 ● © RIGEO ● 11(4), WINTER, 2021
www.rigeo.org Research Article
The Effects of Learning Integrals and Its
Application Using Ti-Nspire Cx Graphing
Calculator’s Towards Mathematics Pre-Service
Teachers’ Mathematical Reasoning
Amila Saliza Abd Wahab1 Nor’ain Mohd Tajudin2
Malaysian Vocational Certificate Unit, Malaysian Examinations Department of Mathematics, Sultan Idris Education University
Syndicate, Ministry of Education, Malaysia
Endah Retnowati4
Mohan Chinnappan3 Department of Mathematics Education, University of
School of Education, University of South Australia, Adelaide, Yogyakarta, Indonesia
Australia
Yerizon5
Mathematics Education Program, Postgraduate of Universitas
Negeri Padang, Indonesia
2Corresponding Author: E-mail: norain@fsmt.upsi.edu.my
Abstract
Reasoning is critical in learning of mathematics for the reason that it is a basis of mathematical ability and
their absence causes students to be unsuccessful and unable to engage in mathematics teaching.
Recent technological advancements have opened the way for mathematics educators to use the
capabilities of these technology tools in providing teaching and learning to reinforce reasoning skills. This
quasi-experimental non-equivalent pre-post-test design study investigated the effectiveness of using TI-
Nspire CX graphing calculator’s activities in learning Integrals and Application of Integration topic
towards mathematics pre-service teachers’ mathematical reasoning. A sample of 44 students was
randomly chosen to take part in the study such that there are 22 pre-service mathematics teachers in the
experimental group and there are 22 pre-service mathematics teachers in the control group. The
instrument used for the pre and post- test was the Mathematical Reasoning test (MRT) to measure the
pre-service teachers’ level of reasoning. The data test were analysed quantitatively using the inferential
statistics, namely the independent sample t-test and the paired sample t-test. The findings revealed that
the experimental group that learned the topic of Integrals and Application of Integration using the TI-
Nspire CX graphing calculator activity module performed better in the MRT as compared to the control
group that underwent learning using conventional method. In conclusion, this study is very meaningful
and relevant nowadays because it displays a different method of teaching and learning at the level of
higher education institutions that is by integrating graphing calculator technology in developing the
capability of pre-service mathematics teachers with reasoning skills.
Keywords
Reasoning skill, TI-Nspire CX graphing calculator, pre-service mathematics teachers, Integrals and Application of
Integration, quasi-experimental design
To cite this article: Wahab, A, S, A; Tajudin, N, M.; Chinnappan, M; Retnowati, E,; Yerizon. (2021) The Effects
of Learning Integrals and Its Application Using Ti-Nspire Cx Graphing Calculator’s Towards Mathematics Pre-Service
Teachers’ Mathematical Reasoning. Review of International Geographical Education (RIGEO), 11(4), 881-890. doi:
10.48047/rigeo.11.04.81
Submitted: 06-05-2021 ● Revised: 18-05-2021 ● Accepted: 26-05-2021© RIGEO ● Review of International Geographical Education 11(4), WINTER, 2021
Introduction
Mathematics teachers are those who are responsible for delivering mathematics’ contents to
students and fostering mathematical reasoning among them. However, in order to produce
teachers that have these skills, they should be trained during the teacher training program. These
future teachers should not just be experts in mathematics content and pedagogical skills, but they
also should be prepared with the needs of an ever-changing technological world and they as
well need to be updated with the innovations and inventions of the latest technology [1].
Therefore, mathematics classroom instruction that integrates technology should focus on the use
of specific technologies in helping pre-service mathematics teachers to create awareness and
confidence to implement innovative teaching approaches, thus improving achievement [2]. One
of the mathematical technology tools that can help pre-service teachers to develop their
mathematical reasoning is the graphing calculator that can be used in subjects related such as
algebra, geometry and statistics. TI-Nspire CX graphing calculator, which will be used in this study,
is one of the latest graphing calculators with functionality that can help educators and students
in teaching and learning mathematics. In line with current developments in wireless technology,
TI-Nspire CX Navigator System is wireless classroom learning systems that can engage students,
encourage participation and increase achievement. Through a wireless network of TI-Nspire CX
handhelds, these systems enable interactive learning. Students can also present their work from
anywhere in the class.
To achieve optimal teaching and learning, teachers themselves require knowledge about the
graphing calculators, before they take the full advantage of the new opportunities offered by
graphing calculators. Another issue of mathematical teaching is that teachers still embrace an
inactive traditional lecture teaching style with textbooks as the main source in their teaching
practices [3, 4]. This is further supported by [5] who explains that mathematics is a complex subject
that usually results in decreased interest and motivation to learn mathematics. The traditional
approach needs to be changed to a new approach that uses the latest technology such as the
graphing calculators. Furthermore, professional development among teachers should be
implemented so that they are exposed to basic operations of graphing calculator and
collaborate in providing worksheets and resources that are available to be used for classroom
teaching [6]. The strategy of using graphing calculator is able to help solve the problem posed by
[7] which he stated that although the graphing calculator was distributed to selected schools
almost 20 years ago, but the success of the practice of using this tool in mathematics classroom
does not show something encouraging due to lack of knowledge on how to use it in mathematics
teaching and learning.
The graphing calculator tool plays an important role in mathematics learning because it allows
students to explore, investigate, model mathematical problems as well as be able to make various
representations of mathematical problems. As stated by [8], technology tools such as graphing
calculators are able to support various representations as well as improve student visualization in
problem solving and can also strengthen students' understanding. In this era, problem solving skills
are necessary to continue to succeed in life. Basic mathematical knowledge is the key to being
a good problem solver and [9] states that it is important for a person to develop his or her basic
mathematical knowledge first where reasoning skills are one of them. According to [10], there are
some areas of mathematics which encompasses reasoning, and these areas are algebra,
geometry and statistics. Since this field is the basis of the concept of calculus, reasoning skills are
very important in calculus learning. To date, very few studies can be obtained and can prove
whether graphic calculators affect students' thinking ability in problem solving especially in the
field of calculus. In addition, [11] also stated that the use of technology can affect students'
reasoning skills. However, according to [12], there is no empirical evidence related to it in previous
research. As is well known, reasoning is an important process in the conceptual understanding of
the field of calculus. Thus, reasoning skills are very useful and need to be improved in the process
of mastering the content of calculus [13].
In the perspective of mathematics curriculum implementation in Malaysia, the use of technology
in teaching and learning of mathematics has long begun. According to [9], the technology that
has been used by teachers of mathematics is the calculator, educational software, web sites,
computer, and also learning packages. All these technologies helped to drive the new and fresh
pedagogical approach from the teachers and at the same time this approach is successful to
encourage students' understanding of mathematical concepts in depth, appropriately and
882Aprizal, ; Ali sjahbana, S,W,; Nurhasanah, A. (2021) The Development of the Flood Inundation Area …
meaningfully. Hence teachers nowadays should be equipped with the skills and knowledge in
using technology such as TI-Nspire in order to deliver mathematics teaching effectively. The
effective use of technological tools in mathematics classes can be achieved if teachers can be
given adequate and appropriate training as well as continuous instruction assistance. They should
also have an in-depth understanding of technological capabilities and how the tools can be used
to facilitate student learning in mastering mathematical concepts [2]. Therefore, it is a necessity
for us to try our best to prepare mathematics teachers to diversify teaching methods and
strategies that integrate the latest technology such as calculator graphing tools for present and
future needs. Appropriate guidance should be given to teachers so that they can continue to
develop this relevant knowledge to teach mathematics [7].
Based on previous researches done on the use of graphic calculators and related issues, there is
a need to carry out an effectiveness studies on the use TI-Nspire CX graphing calculator in
developing mathematical reasoning among teachers. Pre-service teachers today are teachers
who need to have 21st century learning practices such as having the skills to use the latest
technology because it is these teachers who will fill the career needs as teachers in schools in this
century. Thus, this study should start from pre-service mathematic teachers, since technology is
one of the needs towards quality teaching and learning in the 21st century.
Objectives and Hypotheses of the Study
The objective of this research is:
i. To examine the effectiveness of using TI-Nspire CX graphing calculator’s activities in
learning Integrals and Application of Integration topic towards mathematics pre-service teachers’
mathematical reasoning.
The research hypotheses are as follows:
i.H01: There is no significant difference in the mean scores of pre-achievement test and pre-
mathematical reasoning test between the control group and the experiment group.
ii. H02: There is no significant difference between the mean scores of pre-test and post-test
for the achievement and mathematical reasoning test for the experiment group.
iii.H03: There is no significant difference between the mean scores of pre-test and post-test for the
achievement and mathematical reasoning test for the control group.
iv. H04: There is no significant difference in the mean scores of post-achievement test andpost-
mathematical reasoning test between the control group and the experiment group.
Methodology
Research Design
This study employed the quasi-experimental method with non-equivalent control group pre-
test/post-test design. This quasi-experimental design study is most appropriate in studying the
effectiveness of the intervention with the presence of existing groups in the school without
changing the available classes and used whenever the actual experimental design is not feasible
[14]. This design allows the researcher to find the cause and effect of the results of the treatment
conducted to make an interpretation of the variables studied [15]. In addition, another
advantage of quasi-experimental design is that readily selected classes without individual random
selection of students to specific classes can have a minimal impact on reactive arrangement [16].
Population and Sampling
The assessable population for this study is pre-service teachers in Bachelor of Education
(Mathematics) Program, who enrolled Beginning Calculus course during the first semester in year
2017/2018 in a Malaysian public university. For this study, the class sample was selected using
random sampling technique, whereby two groups of semester 1 students from Bachelor of
Education (Mathematics) program intake February 2016/2017 were being chosen. Similarly, by
using the random sampling technique, one class was assigned as an experimental group and
another class was assigned as the control group. The selection of two groups of pre-service
mathematics teachers, which to be used as the experimental group and the control group was
883© RIGEO ● Review of International Geographical Education 11(4), WINTER, 2021
coincide as suggested by [12], which states that selection the entire sample in one classroom is
very suitable for carrying quasi experimental because it can prevent interference during the
learning process in the class. For this purpose, both classes have a number of students with the
same features, criteria, characteristics and multiple abilities. Forty four students took part in the
research such that there are 22 pre-service mathematics teachers in the experimental group and
there are 22 pre-service mathematics teachers in the control group. Based on [17], the suitable
sample size for an experiment research is around 15 to 30 respondents. Both of this group sample
size is 30 participants which are suitable for this study. Participants in this study are male and female
pre-service mathematics teachers, where their ages are between 18 and 19, vary in race,
nonetheless most of the pre-service teachers are Malays.
Research Instrument
For this research, the instruments used for the pre-test and post-test is the Mathematical Reasoning
Test (MRT). It is designed to measure the pre-service teachers’ level of reasoning. This test was
adapted with minor changes from the instrument that was developed by [11]. The MRT was then
validated by the two experts in mathematics teaching and learning. The instruments developed
by [11] was based on five main elements of reasoning vi-a-vis problem analysis, solution initiation
strategies, self-improvement monitoring, finding and applying relationships, and reflecting
problem-solving processes. Assessment of mathematical reasoning is carried out based on these
elements and measurements are made using scores from the answers given by the pre-service
teacher.The MRT has four questions; all questions are from the topic of Integrals and Application
of Integration in Beginning Calculus course. Each question in the test is divided into eight sub-
questions that are built to test the ability of students in five main area of reasoning. The traditional
method of using pencil and paper or a graphing calculator tool can be used to solve all the
questions. The questions for pre-test and post-test for the Mathematical Reasoning Test are the
same. Table 1 below elucidates the mathematical reasoning element in each question of the MRT
test.
Table 1:
Mathematical Reasoning Element in each Question of the MRT Test.
Five elements of Description Sub-questions
reasoning
Problem analysis Involves the first two sub-questions for each a,b
question. Respondents need to know the
mathematical concepts and relationships
used in the problem. Respondents need to
give some conclusions about the solution of
the problem.
Solution initiation Involves the third sub-question for each c
strategies question. Respondents need to name
several strategies that they can use in the
problem-solving process.
Self-improvement Involves the fourth sub-question. d
monitoring Respondents will be asked to solve the
problem. They can also be asked to answer
any questions asked. Next, they are asked to
write throughout the test and do not delete
any work produced during this test as this will
be used as evidence of students' thinking
process.
Finding and applying Involves the fifth sub-question. Respondents e
relationship will be asked to identify existing knowledge
of previous ideas or concepts that had been
learned. Ideas and concepts will be used to
solve the problem.
884Aprizal, ; Ali sjahbana, S,W,; Nurhasanah, A. (2021) The Development of the Flood Inundation Area …
Reflecting problem- Involves the last two sub-questions. f,g
solving processes Respondents will be asked to determine
whether the solution was correct, justify their
answers as well as provide other information
that could help them draw conclusions from
the problem.
In order to measure pre-service teachers’ reasoning skills, the grading rubric for reasoning
developed by [11] was adopted. This rubric is used as a guide to measure students’ success and
changes in the five main areas of reasoning. This rubric has values from 0 until 3, and the values
for each sub-questions for each question is ranged from 0 to 3, where 0 shows no evidence of
reasoning skills, while 3 shows great evidence of reasoning skills. The MRT Items was piloted for pre -
test and post-test and showed the value of Cronbach’s Alpha 0.771 and 0.80, respectively. This
indicates that the items has high reliability and reliable to be used in the real study [18].
Data Collection Procedures
Firstly, the researcher obtained the written permission from the Post Graduate Study of the
university to carry-out the study. The lecturer for subject Beginning Calculus for the Experiment
Group was provided with the TI-Nspire CX graphing calculators and teaching modules for the
topics selected in the Beginning Calculus Course. The researcher briefed the lecturer on how to
use the modules and how to administer the MRT instrument. The pre-service teachers were divided
into two groups, which are control and experimental groups using the random sampling
technique. Before the treatment for the experimental group started, the lecturer administered the
MRT test to both control and experimental groups to evaluate pre-service teachers’ mathematical
reasoning performance for topic Integrals and Application of Integration in the Beginning Calculus
course. This provided the researchers with pre-test data
Interventions in teaching and learning lasted over a period of 10 weeks. For the control group,
both lecturers and pre-service teachers used the conventional method such as demonstrating
using pencil and paper to make graphs as well as prioritizes the teacher-centered method only.
However, for the experimental group, pre-service teachers used the TI-Nspire CX graphics
calculator tool to build new knowledge. In the intervention implemented, the treatment group’s
lecturer used the TI-Nspire CX graphing calculator tool along with the TI-Connect computer
software to facilitate the learning process. The lesson for experimental group is based on the
activities that provided in the developed module, while lesson for control group is in accordance
with conventional method. Both groups will learn the same topics but in different approach. The
class period for control group and experiment groups is 60 minutes, and it was executed once a
week. After undergoing treatment, the lecturer again conducted the MRT test as a post test in this
study. All the assessment will be conducted according to the predetermined time. The Pre and
Post MRT test were marked by the lecturer and the researcher, where the percentage agreement
value was 90%. Therefore, the element of reasoning skills on the script is reviewed and ensured
that both evaluators reach a consensus with the percentage agreement value was 100%.
Data Analysis
The data collected that obtained from the pre-test and post-test of the MRT test was analysed
quantitatively using the inferential statistics, namely the t-test and the paired sample t-test in order
to examine whether the developed TI-Nspire CX graphing calculator’s activities for the Integrals
and Application of Integration topic is effective in improving the pre-service mathematics
teachers’ mathematical reasoning.
Result and Discussion
Demographic Analysis
In this study, 44 pre-service teachers were involved; 22 students in each group of the control group
and experimental group. Seven of the pre-service teachers for the control group were male which
885© RIGEO ● Review of International Geographical Education 11(4), WINTER, 2021
cover 31.8% of the total sample. Another 68.2% who involved in this study were 15 female. For the
experimental group, five of the pre-service teachers were male which cover 22.7% of the total
sample and another 77.3% who involved in this study were 17 female.
The exploratory data analysis was done before using the inferential statistics. The normality of the
MRT pre-test scores was assessed by obtaining the skewness and kurtosis values, as well as using
the Shapiro-Wilk test. The result of normality test for the score of MRT pre-test for both control and
experiment group is shown in the following Table 2.
Table 2:
Normality Test for the Score of MRT Pre-Test for Control and Experiment Groups
Shapiro-Wilk Sig.
Dependent Variable Group N Skewness Kurtosis
Control 22 0.545 0.101 0.647
MRT Pre-test Experime
22 0.171 -1.352 0.094
nt
Control -0.437 0.050 .568
22
MRT Post-test
Experime
-.265 -.596 .674
nt 22
Based on Table 2, for MRT Pre-test, the Skewness and Kurtosis value of control group are 0.545 and
0.101, and for the experiment group are 0.171 and -1.352, respectively. Meanwhile, the Shapiro-
Wilk significance value for control group is p=0.647 and experiment group is p=0.094. All of the
Skewness and Kurtosis value are between the range of -3.0 and +3.0, and all of the p-value for
Shapiro-Wilk are more than 0.05, hence the score of MRT pre-test for control and experiment group
meet the criteria of normality. In addition, for MRT post-test, the Skewness and Kurtosis value of
control group and experiment group is (-0.437, 0.050) and (-0.265, -0.596), and the Shapiro-Wilk
significance value for control group is p=0.568 and experiment group is p=0.674. All of the
Skewness and Kurtosis value are between the range of -3.0 and +3.0, and all of the p-value for
Shapiro-Wilk are more than 0.05, hence the score of MRT post-test for control and experiment
group meet the criteria of normality.
Descriptive Statistics
Table 3 illustrated the mean comparison for pre-MRT for control and experiment groups and also
the mean comparison for post-MRT for control and experiment groups. In the pre-test, it was found
that the control group had slightly higher scores as compare to the experiment group. However,
in the post-test, it revealed that the experiment group had higher scores that the control group.
Surprisingly, it was found that the scores in the post-test for the control group were lower than the
scores in the pre-test.
Table 3:
Mean score for pre-test and post-test (Experiment Group)
Mean N Std. Deviation
Experiment Pre-test 21.82 22 7.938
group Post-test 71.36 22 2.128
Pre-test 21.91 22 5.528
Control group Post-test 19.64 22 3.659
Results for Hypothesis H01
Table 4 showed the results for the independent-samples t-test that was carried out to compare
the MRT pre-test scores for the control and the experiment groups. There was no significant
difference in scores for the control group (M=22.91, SD=5.53), and the experimental group
[(M=21.82, SD=7.94; t(42)=.044, p=.965]. Therefore, the H 01 is not rejected. The magnitude of the
means was small with eta squared equals to .00005 [21], which means only about 0.005% of the
886Aprizal, ; Ali sjahbana, S,W,; Nurhasanah, A. (2021) The Development of the Flood Inundation Area …
variance in mathematical reasoning is explained by the group.
Table 4:
The independent t-test for comparing the pre-mathematical reasoning test for control and
experiment group
Dependent Variable t df Mean Difference Sig.
MRT Pre-Test .044 42 .91 .956
Results for Hypothesis H02
Table 5 is the results for a paired-sample t-test which was carried out to assess the effect of the
experimental method on students’ scores in the MRT test. From Table 5 the probability ( p) value
for mathematical reasoning is 0.000, which is less than 0.05. The H02 in this study is rejected. This
means that there was a statistically significant increase in MRT post-scores form the pre-test
(M=21.82, SD=7.94) to the post-test (M=71.36. SD=2.13), t(21) = - 27.502, p.05. The eta squared
statistics (.06), indicated a moderate effect size.
Table 6:
Paired t-test for the mean score of pre-test and post-test (control group)
N Mean Std. Deviation t df Sig.
Mathematical
Reasoning 22 2.273 6.555 1.626 21 .119
Pre-Post test
Results for Hypothesis H04
Table 7 showed an independent sample t-test to compare the MRT post-test scores for the control
and experiment groups. The results revealed that there was a significant difference in MRT post-
test scores for the experiment group (M=71.36, SD=2.13) , and the control group [M=19.64,
SD=3.66); t(33.749)= -57.325, p© RIGEO ● Review of International Geographical Education 11(4), WINTER, 2021
Table 7:
The independent t-test for comparing the post-mathematical reasoning test for control and
experiment group
Dependent Variable t df Mean Difference Sig.
MRT Post-Test -57.325 33.749 .091 .000
Several previous researchers have shown that students with access to a graph calculator tool are
able to obtain higher scores in problem solving related reasoning skills compared to their peers in
the control group who do not use a graphing calculator ([19], [20], [21], [22], [23]). These findings
are consistent with the results obtained in this study.
From the reflection of the findings of the study, it is believed that this study can empirically support
the existing studies on the potential usage of graphing calculators to improve reasoning skills
among students. Specifically, this finding is consistent and further reinforced finding from a study
by [11], that the use of graphing calculators is more beneficial if its use is appropriate. In this study,
the activity module using graphing calculators has been developed and validated by
mathematics educator experts, making its use more meaningful and enabling students to easily
carry out the reaching and learning activities and effectively apply the reasoning skills.
Another possible reason that the experimental group has better performance in MRT could be
discussed in term of cognitive load theory. It was found that the experimental group conducting
the activity using a graphing calculator tool had a positive effect because the results of its use
could increase the germane cognitive load where the amount of cognitive load remained within
the capacity of low intrinsic cognitive load or low external cognitive load ([24], [25]). Here, what
happens is that the use of a graphing calculator can reduce the mental resources that students
use due to complex calculations, complex algebra manipulation as well as graph making skills.
Thus, the impact is that this situation allows students to focus their attention from irrelevant
cognitive processes to relevant schema construction processes. Hence, they can focus on solving
problems by applying the reasoning skills.
In this study, surprisingly it was also found that the control group performed poorly after the
experiment was conducted although not statistically significant. This is because, most likely, after
dealing with the various ways of solving the problem, they were mentally burdened by the less
important things to do on that day and eventually made them more tired and difficult to
comprehend, so their performance decreased. These ideas are in line with the statement by [26]
and supported by [7] that graphing calculator technology can enhance part of the cognitive
process as a result of cognition distribution, thus enabling users to centralize cognitive resources
elsewhere. Furthermore, over time students are able to build and develop cognitive skills to
complete many of the cognitive processes shown when using a graphing calculator and will in
turn be able to demonstrate knowledge of these concepts and procedures without the need for
graphing calculator assistance. However, using conventional methods such as applying the
lecture method or “chalk and talk” teaching, the above situation did not occur and caused
difficulties in using proper reasoning skills.
Conclusion
Most researchers recommend that promoting high-level thinking skills for current and future
students is important in the education system ([5], [27], [281]). The rapid development of
technology in education has led to various technology tools invented for the purpose of
education, especially in mathematics. In this era, graphic calculator is one of the most frequently
used technologies in the mathematics classroom as well as in other fields of science because of
the great potential of this tool in helping students to master important mathematical concepts
and offer features specific to mathematical concepts for mathematics learning [29].In summary,
this study has highlights several important points that is the use of TI-Nspire CX graphing calculator
tool in mathematics especially in the topic of Integrals and Application of Integration can help
pre-service mathematics teachers improve their reasoning skills by ensuring that the activities
planned should take into account the validity of the activity content. Teachers are an integral
part of the education system, which greatly influences student outcomes [30]. Therefore,
mathematics teachers need to think mathematically, creatively and innovatively in managing
the instructional process because of its huge impact on student achievement.
888Aprizal, ; Ali sjahbana, S,W,; Nurhasanah, A. (2021) The Development of the Flood Inundation Area …
Acknowledgements
We extend our gratitude to Ministry of Education Malaysia for providing the funds under the Niche
Research Grant Scheme (Code: NRGS/2014-0001-107-82-2) for project 2: Teaching and Learning)
and Sultan Idris Education University, for providing the official approval that enable us to do the
research.
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