Analysis of Microsoft Mathematics's Use in Mathematics Learning: A Case Study on Matrix Multiplication and Determinants

Abstract

This study aims to determine the impact of using Microsoft Mathematics application on students' concept understanding ability in multiplying two matrices and determining matrix determinant. This type of research is qualitative research with a case study approach. This research was conducted in one of the state high schools in Kolaka in class XI IPA. The number of subjects in this study were 3 students. Data collection techniques in this study were using tests and interviews to determine students' understanding of the concept of multiplication of two matrices and the concept of determinant. The results of this study are students who previously did not understand well related to the concept of multiplying two matrices, but after using the microsof mathematics application understand well related to the concept of multiplying two matrices and when the two matrices can be multiplied. In addition, students also understand well the procedures and concepts in determining the determinant of the matrix. Therefore, Microsoft Mathematics application is highly recommended to be used by teachers in introducing the concept of multiplication of two matrices and the concept in determining the determinant of the matrix.

Full text

Logaritma : Jurnal Ilmu-ilmu Pendidikan dan Sains
Vol. 12, No. 02 Desember 2024
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Analysis of Microsoft Mathematics's Use in Mathematics Learning:
A Case Study on Matrix Multiplication and Determinants
Aswin*1; Al Jupri2; Dayana Sabila Husain3; Rafika Meiliati4;
Dwi Maulida Sari5
1,3,4Pendidikan Matematika, Universitas Sembilanbelas November Kolaka,
2,5Pendidikan Matematika, Universitas Pendidikan Indonesia
aswinsalsri23@gmail.com*1, aljupri@upi.edu2, dayanasabila2@gmail.com3,
rafikameiliati@gmail.com4, Dwimaulidasari@upi.edu5
Abstract
This study aims to determine the impact of using Microsoft Mathematics
application on students' concept understanding ability in multiplying two
matrices and determining matrix determinant. This type of research is
qualitative research with a case study approach. This research was conducted in
one of the state high schools in Kolaka in class XI IPA. The number of subjects
in this study were 3 students. Data collection techniques in this study were
using tests and interviews to determine students' understanding of the concept
of multiplication of two matrices and the concept of determinant. The results of
this study are students who previously did not understand well related to the
concept of multiplying two matrices, but after using the microsof mathematics
application understand well related to the concept of multiplying two matrices
and when the two matrices can be multiplied. In addition, students also
understand well the procedures and concepts in determining the determinant of
the matrix. Therefore, Microsoft Mathematics application is highly
recommended to be used by teachers in introducing the concept of
multiplication of two matrices and the concept in determining the determinant
of the matrix.
Keywords: Matrix; Microsoft Mathematics; Concept Understanding.
Abstrak
Penelitian ini bertujuan untuk mengetahui bagaimana dampak penggunaan
aplikasi microsoft mathematics terhadap kemampuan pemahaman konsep siswa
dalam mengalikan dua buah matriks dan menentukan determinan matriks. Jenis
penelitian ini adalah penelitian kualitatif dengan pendekatan studi kasus.
Penelitian ini dilakukan disalah satu sekolah SMA Negeri di Kolaka pada kelas
XI IPA. Adapun jumlah subjek pada penelitian ini adalah 3 orang siswa. Teknik
pengumpulan data pada penelitian ini yaitu dengan menggunakan test dan
wawancara. Adapun hasil dari penelitian ini yaitu siswa yang sebelumnya belum
paham dengan baik terkait konsep perkalian dua buah matriks, namun setelah
menggunakan aplikasi microsof mathematics memahami dengan baik terkait
konsep perkalian dua buah matriks dan kapan kedua buah matriks dapat
dikalikan. Selain itu siswa juga mehamami dengan baik prosedur dan konsep
dalam menentukan determinan matriks. Oleh karena itu, aplikasi microsoft
mathematics sangat direkomendasikan untuk digunakan oleh guru dalam
memperkenalkan konsep perkalian dua buah matriks dan konsep dalam
menentukan determinan matriks.
Kata Kunci: Matriks; Microsoft Mathematics; Pemahaman Konsep.
*Correspondence:
Email: aswinsalsri23@gmail.com

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INTRODUCTION
One of the important skills in mathematics learning is understanding the
concepts being taught. This involves the ability to demonstrate understanding of the
mathematical concepts being studied, explain the relationships between those
concepts, and apply concepts or algorithms flexibly, accurately, efficiently, and
appropriately when solving problems. According to (NCTM, 2000), for students
to achieve a deep mathematical understanding, mathematics education must aim
to develop their ability to connect various mathematical ideas, understand the
relationships between mathematical concepts to form a comprehensive
understanding, and apply mathematics in contexts outside the field of mathematics.
One of the mathematical topics that students need to understand well is the concept
of matrices.
Matrices is one of the subjects taught at the high school level, specifically
in the 11th grade. Students often make mistakes when solving problems related to
matrices. The common errors made by students in matrix operations are during
the multiplication of two matrices and determining the determinant of a matrix.
This is in line with the research conducted by (Bahar et al., 2022; Wahyuningsi,
2020) which states that many students still make mistakes in solving matrix
problems, especially in matrix operations. Furthermore, this is also in line with the
research conducted by (Prasetyo et al., 2023) which states that many students
often make mistakes in determining the operation of two matrices and mistakes in
determining the determinant of a matrix.
The causes of students' errors in solving matrix problems are the students'
lack of understanding in operating numbers, the lack of understanding of the
concept of multiplying two matrices, and the many students who only memorize
the determinant formula without a deep understanding. This is in line with the
research revealed by (Gustianingum & Kartini, 2021; Nuritasari et al., 2017) that
students often make mistakes because they do not have a deep understanding of the
concept of matrix multiplication and the concept of determining the determinant,
so students only memorize the formulas and are at risk of forgetting them.

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Therefore, a solution needs to be considered to address this issue so that students'
mistakes can be minimized.
One of the efforts to reduce student errors in solving matrix problems is
through the use of the Microsoft Mathematics application. This is in line with the
research conducted by (Suryacitra & Oktavia, 2018) which states that the use of
Microsoft Mathematics can train students' precision, thereby reducing their
mistakes. Additionally, the use of this application also aims to enhance students'
interest in learning (Gunawan & Rojali, 2018) and make them more active in
participating in lessons, so that every learning process undertaken by students will
gain experience and become meaningful learning because students engage with it
directly. This is in line with the research conducted by (Yuliandari et al., 2024)
which states that when students take an active role in learning, they will better
understand the concepts or material being taught, thereby reducing the mistakes
that may occur.
In addition, the use of technology in learning can also be utilized by
teachers as a tool to help students understand the concepts of the material being
taught. The use of the application can serve as scaffolding, which will later be
controlled so that students do not become dependent on using the application but
instead gain a good understanding from its use. The provision of scaffolding in
learning is very important because it can also minimize the mistakes made by
students, as the scaffolding is based on the difficulties faced by students in solving
the given problems. This is in line with the research conducted by (Hanifah, 2017;
Purwasih & Rahmadhani, 2022; Susilowati & Ratu, 2018) which states that
providing scaffolding to students in learning can reduce the mistakes made by
students.
Therefore, this research aims to determine the impact of using Microsoft
Mathematics in mathematics learning. Where the ability measured is the ability to
understand the concept of students in multiplying two matrices and determining
the determinant of the matrix.

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RESEARCH METHODS
This research is qualitative, with a case study approach. This research
begins with a literature review related to the theories underlying the use of
technology in learning, the structure of the Microsoft Mathematics application,
and its use in matrix material. This research aims to examine the use of the
Microsoft Mathematics application in mathematics learning on the topic of
multiplying two matrices and determining the determinant of a matrix. The
subjects of this research are a group of students from one of the public high
schools in SMAN 1 Kolaka. The number of subjects in this study is 3 students.
This study involved three subjects chosen based on their previous mathematics
test scores, reflecting their varying levels of understanding of matrix concepts.
The selection criteria ensured diversity in their initial comprehension, allowing
the study to examine how the Microsoft Mathematics application affects their
grasp of specific topics such as matrix multiplication and determinants. By
including students with differing levels of prior knowledge, the research aims to
track changes in understanding among both those with limited initial
comprehension and those with a foundational grasp. This approach provides a
comprehensive perspective on the role of technology in improving students'
mathematical understanding. The data collection technique in this study uses tests
to determine the extent of students' understanding before and after using the
application, and interviews to confirm the understanding gained by students after
using the Microsoft Mathematics application. The interview guide used in this
study was designed to explore the extent of students' understanding of the
mathematical concepts taught, particularly after using the Microsoft Mathematics
application. The guide includes a series of questions focusing on two main areas:
first, students' understanding of the procedures for multiplying two matrices and
the conditions under which the matrices can be multiplied; and second, students'
comprehension of the steps involved in determining the determinant of a matrix.
After the researcher selected the subjects for the study, the researcher
administered an initial test to determine the extent of the students' conceptual
understanding related to matrix multiplication and determinants. After that, the

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researcher analyzed the preliminary study results and applied the use of Microsoft
Mathematics. The final stage involved administering a follow-up test to determine
the extent of the students' mathematical conceptual understanding of matrix
material. The indicators of conceptual understanding used by the researcher are: (1)
students can restate the concepts learned, (2) students can analyze the properties of
the concepts, (3) apply the concepts logically, and (4) provide examples and non-
examples.
RESULTS AND DISCUSSION
The following will present the initial findings of the researchers before
applying the use of Microsoft Mathematics in solving matrix-related problems.
Figure 1. Student's Work Results S1
Based on the image above, it is evident that students do not have a good
understanding of the concept of multiplying two matrices because they do not meet
the concept comprehension indicators used in this research. Students think that
every matrix can be multiplied without considering the size of the rows and columns
of both matrices. This needs to be closely monitored so that the mistakes made by
the students do not continue to occur. Additionally, errors in solving matrix
problems do not only happen in the concept of multiplication but also in the concept
of determining the determinant of a matrix.

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Figure 2. Student's Work Results S1
Figure 2 provides an understanding that students do not yet grasp the
concept of determining the determinant of a matrix (applying the concept logically),
because students do not pay attention to the size of the given matrix, whether the
determinant of the matrix can be determined or not.
Based on the problem, the researcher attempted to use Microsoft
Mathematics to understand the concepts and procedures in determining the
multiplication of two matrices and the determinant of a matrix. The researcher
provided students with the opportunity to explore the multiplication of two matrices
first. Then, additional time was given to further explore determining the
determinant of a matrix. After using the application, the researcher provided
questions as a form of evaluation to measure the extent of the students'
understanding post-application.
Here is the trial-and-error process of students to discover the concept of
multiplying two matrices.
Figure 3. Student's Trial-and-Error Process

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After the students conducted the experiment twice, they have discovered
the concept of multiplying two matrices. Below are the students' work results
along with an interview regarding the understanding gained after using the
application.
Figure 4. Student's Work Results S1
Based on the image above, it was found that the students have a good
understanding of matrix multiplication, which they previously did not know when
two matrices could be multiplied. Here are the results of the interview excerpts
regarding the students' understanding of the multiplication concept.
P
:
Why did you multiply the matrices in question number 2 before using
the application?
S1
:
I didn’t know when two matrices can be multiplied, so I just multiplied
them directly.
P
:
What did you understand after using the application?
S1
:
Two matrices can be multiplied if the number of columns in the first
matrix is equal to the number of rows in the second matrix.
P
:
How many trials did you perform using the application to gain that
understanding?
S1
:
Two, Sir.
Based on the interview results above, it was found that after students
experimented twice using the application, S1 students could easily understand when
two matrices can be multiplied and when two matrices cannot be multiplied. (S1
has met the indicators of conceptual understanding). Therefore, the use of
applications in learning can help students understand the concepts of a subject. This

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Analysis of Microsoft Mathematics’s Use...........Aswin et al.
is in line with (Mayasari et al., 2021) who state that using Microsoft Mathematics
applications can help students understand the material well and will affect their
achievements in learning.
Then other students also experienced a good understanding after using the
Microsoft Mathematics application. Here are the results of their work.
Figure 5. Student's work results S2 and S3
P
:
Why didn’t you multiply the matrices in question number 2 before
using the application?
S2
:
I didn’t know what to do, Sir.
S3
:
I was confused, Sir.
P
:
What did you understand after using the application? Why couldn’t
question number 2 be solved?
S2
:
Two matrices can be multiplied if the number of columns in the first
matrix is equal to the number of rows in the second matrix.
S3
:
It couldn’t be solved because the number of columns in the first matrix
is not equal to the number of rows in the second matrix.
P
:
How many trials did you perform using the application to gain that
understanding?
S2
:
Three trials, Sir.
S3
:
Five trials, Sir.
In addition to understanding students' comprehension of the
multiplication of two matrices, this experiment also aims to determine the extent
of students' understanding related to calculating the determinant. The following
presents the students' work results after using the application. Based on interviews
with S2 and S3 students after using the application, although many experiments
conducted by the students were different, both students were able to understand

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the concept of multiplying two matrices well. Thus, using the application can help
students understand a concept from the material being studied. This is in line
with the research conducted by (Mendezabal & Tindowen, 2018)which states that
learning using Microsoft Mathematics can help students understand the conceptu
al and procedural aspects of the material being studied. Furthermore, this is also
consistent with the research conducted by (Ekawati, 2016) which states that the
use of ICT- based applications greatly aids students in understanding the material
being studied, specifically the Microsoft Mathematics application.
In addition to understanding students' comprehension of the
multiplication of two matrices, this experiment also aims to determine the extent
of students' understanding related to calculating determinants. The following
presents the students' work results after using the Microsoft Mathematics
application.
Figure 6. Student's Work Results S2
Based on the results of the S2 student's work, it was found that the student
has a good understanding of when a matrix can have its determinant determined.
Here are the excerpts from the interview with the master's student.
P
:
Why didn’t you calculate the determinant before using the application?
S2
:
I forgot the formula for the determinant of a matrix, Sir.
P
:
What did you understand after using the application?
S2
:
A matrix can have its determinant calculated if it is a square matrix.
P
:
How many trials did you perform using the application to gain that
understanding?
S2
:
Three trials, Sir.

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Based on the interview results above, it was found that the S2 student has
a good understanding of the concept of matrices that can have their determinants
determined. The S2 student refers to matrices that can have their determinants
determined as cube-shaped matrices. In other words, matrices that are nxn in shape.
Furthermore, S1 and S3 students also successfully understood the concept of
matrices that can have their determinants determined. Here are the responses from
students S1 and S3.
Figure 7. Student's work results S1 and S3
Based on the two images of the work done by the S1 and S3 students, it
was found that the students already understand when a matrix can have its
determinant determined. To confirm the answer, the following interview was
conducted.
P
:
Why were you able to determine the 3 x 2 matrix before using the
application?
S1
:
I tried using what I already knew, Sir.
S3
:
I didn’t work on it, Sir.
P
:
What did you understand after using the application?
S1
:
A matrix can have its determinant calculated if its order is the same.
S3
:
A matrix can have its determinant calculated if it is a square matrix.
P
:
How many trials did you perform using the application to gain that
understanding?
S1
:
One trial, Sir.
S3
:
Four trials, Sir.

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The interview excerpt above shows that both students understand well
when a matrix can have its determinant determined. Thus, in the given problem,
both students did not make repeated mistakes.
Based on the students' work related to solving the multiplication of two
matrices and determining the determinant of a matrix, it was found that when
students use the Microsoft Mathematics application, they can understand concepts
and procedures well. Thus, the use of applications or ICT in learning greatly assists
teachers in teaching the material to be taught. The use of applications in learning is
very beneficial, in line with the research conducted (Rusmana, 2015; Suratman et
al., 2019; Zayyadi et al., 2017) which states that the use of ICT in mathematics
learning can help students understand the concepts of the material being taught.
Then, the use of applications in mathematics learning can also help
eliminate the stigma among students that learning mathematics is very difficult and
stressful. This is in line with the statement expressed by (Wangge, 2020) that the
use of ICT in learning can make students enjoy learning mathematics, thereby
dispelling the notion that mathematics is difficult. Additionally, to address the
dependency on application usage in learning, teachers should closely supervise its
use. Then, another method that can be employed is for the teacher to ask questions
that stimulate students' critical thinking skills to determine the extent of their
understanding of the concepts obtained from using the application.
Based on the results of the discussion above, it was found that S1
students were able to understand well related to multiplying two matrices and
determining the determinant with the help of Microsoft Mathematics after 2 times
of trial, while S2 and S3 students were also able after using the help of Microsoft
Mathematics 3-4 times of trial.
CONCLUSION
Microsoft Mathematics is one of the applications that can help students
find solutions to mathematical problems, especially in the topic of matrices. In
addition to finding the final solution, this application also provides students with
an understanding of the concept of matrix multiplication and determining the

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determinant of a matrix, along with its procedures. Based on the results of the
experiments conducted, it was found that students who previously did not
understand the general concept of when two matrices can be multiplied were able
to understand it well after using the application. Additionally, students who
previously worked on determinant problems that were not of size nxn, after using
the application, gained an understanding that the determinant can only be
determined for nxn matrices. Therefore, the Microsoft Mathematics application is
highly recommended for teachers to use in teaching matrix material, especially
during the multiplication of two matrices and determining the determinant of a
matrix. However, proper supervision is needed in its use so that students do not
become dependent on it.
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