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80 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
Utilization of Digital Module for Asynchronous Online Independent
Learning in Advanced Mathematics Education
Ryan V. Dio
National Research Council of the Philippines and Sorsogon State University, Sorsogon City,
Philippines
ryan.dio@sorsu.edu.ph
Abstract: The exponential increase in the number of cases and number of affected countries of
the novel coronavirus disease 2019 (COVID-19) brought significant change in the mode of
instruction from face-to-face to distance learning among the different levels of education around
the world. This descriptive-developmental method of study adopted the ADDIE (Analysis, Design,
Develop, Implement, Evaluate) model of instructional system design (ISD) framework in the
development and evaluation of digital learning module intended for asynchronous online
independent learning among students at the advanced mathematics education level. The adopted
instructional materials evaluation instrument and the 10 items open-ended teacher-made test were
used to describe the learning outcomes of the 13 enrolled graduate mathematics education
students (4Male, 9Female) during the COVID-19 pandemic period in Sorsogon, Philippines.
Findings of the study revealed that the designed digital learning modules covering the required
content topics of modern algebra arranged in increasing complexity and ensuring the presence of
the basic elements of discussions, definition, examples, and practice drills (worksheets) provide a
significant learning experience among the students in times of pandemic as exhibited by their very
satisfactory level of evaluation (Mean=4.42±2.58) on its characteristics. The utilization of the
digital module available for asynchronous online independent learning maximizes learning
outcomes which showed an increase in the mean score of 8.10 equivalent to 53.97 percentage
score indicating a highly significant improvement (t=5.034, p<0.05) in the level of students’
understanding of the content topics. Investment in strong internet connectivity is necessary to
strengthen the asynchronous learning experiences of the students with the use of digital modules
through the regular conduct of virtual conferences for monitoring and immediate feedbacking.
Keywords: Digital Module, Asynchronous Online Learning, Independent Learning, Advanced
Mathematics Education, Instructional System Design
INTRODUCTION
The pandemic phenomenon as declared by the World Health Organization (WHO) on
March 11, 2020, due to an exponential increase in the number of cases and number of affected
countries of the novel coronavirus disease 2019 (COVID-19) (Cucinotta & Vanelli, 2020;
Ducharme, 2020) showed a significant impact not only in the health sectors (Xiong et. al, 2020;
Giusti et. al., 2020; Berardi, Antonini, Genie, Cotugno, Lanteri, Melia & Paolucci, 2020) but also
in the socio-economic activities (Nicola et. al., 2020; Martin, Markhvida, Hallegatte & Walsh,
This content is covered by a Creative Commons license, Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA
4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
purposes only, and only so long as attribution is given to the creator. If you remix, adapt, or build upon the material, you must
license the modified material under identical terms.
81 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
2020; Iacus, Natale, Santamaria, Spyratos & Vespe, 2020; Sharifi & Khavarian-Garmsir, 2020)
including the education sectors (Chandasiri, 2020; Marinoni, Van’t Land & Jensen, 2020) around
the world. Similarly, in the Philippines, the Proclamation No. 929 declaring the state of calamity
throughout the country due to the COVID-19 outbreak (Gita-Carlos, 2020; Merez, 2020; Kabiling,
2020; Vallejo & Ong, 2020) brought drastic changes in the mode of instruction at a different level
of education (Tria, 2020; Toquero & Talidong,2020; Reimers & Schleicher, 2020).
The restriction of face-to-face interaction paved the way towards the adoption of online
learning among the basic, higher, and advanced levels of education in the Philippines. One of the
most salient features of the educational delivery during the pandemic period was the
implementation of synchronous and asynchronous online learning which requires stronger internet
connectivity among the teachers and learners. Each educational leader including classroom
teachers was engaged in the creation of the best instructional mode either print or non-print for
learners’ utilization.
The introduction of this new mode of instruction became a challenging task for most of the
teachers in bringing active participation and involvement among the students. Swan (2001) found
out that the clarity of design, interaction with instructors, and active discussion among course
participants significantly influenced students’ satisfaction from asynchronous online
learning. Moreover, the task of designing appropriate instructional material is necessary to support
the needs of the students and thus they will become more engaged in asynchronous online learning
(Alrajeh & Shindel, 2020). The students in advanced education level (or graduate students) have
different learning styles that need to be supported with suitable teaching approaches and strategies.
Graduate students who are generally independent learners desired more of a mentoring relationship
with faculty where they could seek guidance and information about their professional
development.
Holzweiss, Joyner, Fuller, Henderson & Young (2014) reveals in their investigation that
the best learning experiences of graduate students in an online class are the activities that allowed
for the creation and/or sharing of knowledge such as problem-solving assignments, research,
writing, journal reflection, discussion forums, video lesson creation and virtual conferencing. In
addition, students enrolled in online education demonstrate strong preferences for asynchronous
mode of learning because of convenience and favored individual assignments (Butler & Pinto-
Zipp, 2005). Swan, Shen, and Hiltz (2006) explored collaborative activities such as discussion,
small group sessions, and collaborative exams as a form of assessing students’ learning in an online
class which can be possibly made by an explicit learning goal with an explicit evaluation criterion
available at the beginning of the course.
The digital learning module has been recognized as one of the common instructional
deliveries being utilized in the implementation of asynchronous online independent learning at the
advanced education level during the pandemic period. The development of the digital module
requires time to plan out the learning activities appropriate to the learners covering the course
objectives aligned to the program goal and performance indicators as reflected in the course
syllabus. The digital module shall be designed to capture advanced education students’
independence in learning mathematics concepts (Setiyani, Ferdianto & Fauji, 2020).
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
purposes only, and only so long as attribution is given to the creator. If you remix, adapt, or build upon the material, you must
license the modified material under identical terms.
82 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
OBJECTIVES
This study evaluated the utilization of the designed digital module in an asynchronous
online independent learning at the advanced mathematics education level amid the COVID-19
pandemic period. The following were the specific objectives: (1) design a digital module for
asynchronous online learning, (2) describe the learning experiences of the students in the
utilization of the digital module, and (3) test the effectiveness of the developed digital module in
student’s understanding of the subject content topics.
METHODOLOGY
The study utilized a descriptive-developmental method of research combined with a
qualitative approach to analysis. The developmental nature of this study adopted the ADDIE model
of instructional system design (ISD) framework which is composed of the five phases: Analysis,
Design, Develop, Implement, and Evaluate.
Analysis. This phase involved the review of the set program standards including the
instructional objectives for the Master of Arts in Education (MAEd) major in Mathematics. The
analysis of the approved course syllabus for the semester focusing on the content and coverage,
course objectives, and the performance standards was executed to define and meet the needs of the
advanced education mathematics students in the course during the COVID-19 pandemic period.
Design. This phase involved the logical arrangements of content topics of the course with
due consideration to the prior knowledge and needs of the enrolled graduate education students.
The listed topics were based on the previous coverage of the course subjects as reflected in the
approved course syllabus. The learning module for each of the identified topics contains the
following elements: discussions, definition, example, and practice drills to check their
understanding. The learning modules were designed in a manner that will be available in digital
format to be utilized by the students in an asynchronous online independent learning.
Development. This phase involved the creation of the learning modules for each of the
identified topics to be covered in the course. The content and discussions of each topic came from
different sources both print and non-print materials. Each learning module contains the worksheet
as drill exercises to check the student’s understanding of the topic using the developed learning
materials. The developed worksheets ensure their alignment to the content and examples provided
in the learning modules. There was a total of 22 learning modules developed with the
corresponding worksheets to be accomplished by the students before the semester ends.
Implement. This phase involved the utilization of the developed learning modules. Before
its utilization, general directions were provided to the whole class which includes the manner of
weekly distribution of each learning module virtually as well as the submission of the worksheets.
The accomplishment of the worksheets was designed on weekly basis. The synchronous learning
feature of the course was made through virtual discussion of the learning modules once a week to
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
purposes only, and only so long as attribution is given to the creator. If you remix, adapt, or build upon the material, you must
license the modified material under identical terms.
83 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
follow up students’ understanding of the content. Students are free to ask any questions regarding
the topic coverage specific for the week as reflected in the digital learning module during the
virtual discussion. The weekly format of implementation in the course follows: Digital module
distribution, utilization (asynchronous independent learning), accomplishments of worksheets,
submission of worksheets, and virtual discussions for feedbacking and deepening of skills.
Evaluate. This phase was an integral component of each stage of development from the
Analysis phase involving the two faculty members of mathematics education of the institution to
ensure alignment of the module content with the set program standards. This phase guarantees the
accuracy and reliability of the developed digital learning module appropriate for graduate
education mathematics students. The evaluation in terms of the content and coverage, theoretical
considerations, appearance/visual appeal, and language of the materials by the students who
utilized the digital module in an asynchronous online independent learning were also executed.
The evaluation phase includes the qualitative approach to the analysis of students’ experiences
with the use of a digital learning module in an asynchronous online independent learning.
Moreover, the evaluation phase of the current study also involved the test for the
effectiveness of the digital learning module in understanding the learning content of the course
through a one-group pre-test post-test design. The study involved 13 officially enrolled students
of the regular class (4 Males, 9 Females) under the Master of Arts in Education (MAEd) major in
Mathematics during the First Semester (August – December) of AY 2020-2021 in Sorsogon,
Philippines.
Instrument
The Board of Trustees (BOT) approved Instructional Materials Evaluation instrument of the
institution was used in the assessment of the developed digital learning module. The study made
use of the interview guide focusing on their learning experiences in the asynchronous online
independent learning with the use of a digital module. The questions include: How is your
experience with this subject? How does the digital module help you in meeting your learning needs
with this subject course?
Moreover, the teacher-made test for the pre-test and post-test was used in the assessment
of students’ understanding of the content topics in the subject offered during the semester. The test
is an open-ended test question that requires a graduate student who is pursuing the MAEd degree
major in mathematics to show solutions and/or explanations to justify their answer in a particular
item. The 10-item teacher-made open-ended test item requires a substantial response expected
from a graduate mathematics education student to get a maximum score of 15 points. This type of
test item will ensure assessment of student attainment of the performance standards and program
outcomes required for a graduate education student.
Data Collection Procedures
The data were collected through virtual/online surveys and interviews. The teacher-made
test was conducted before (pretest) and after (posttest) utilization of the digital module to test
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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84 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
students’ conceptual understanding. The test was conducted virtually with a specific time allotment
of submission within the day. The students were explicitly provided with the learning goals,
targets, and performance indicators that they need to accomplish in the course which is made
available through the distribution of the course syllabus at the beginning of the semester. This was
made to ensure clarity of the students’ tasks and deliverables before the study implementation.
Data Analysis Procedures
Descriptive statistical measures such as frequency count, mean, and standard deviation
were used in the evaluation of the digital learning module. Cronbach’s alpha (𝛼) was also used in
the assessment of the consistency of students’ evaluation of the digital module. This was supported
with a qualitative approach to the analysis of the textual responses and information from the
respondent’s learning experiences in the utilization of the digital module. Coding of responses was
used to evolve the themes or categories of the experiences in the asynchronous online independent
learning.
The t-test was used to test the effectiveness of the digital learning module in students’
understanding of the required mathematics content topics after its utilization in asynchronous
online independent learning. Test of normality of scores in the pretest (D = 0.265, p=0.541) and
posttest (D= 0.217, p = 0.506) were confirmed through the Kolmogorov-Smirnov (K-S) test
statistic (D). Both the pre-test and post-test scores of the students were translated into percentage
scores (PS) to show the difference in students’ level of understanding of the required content before
and after utilization of the digital module. The responses of the students in the pretest and posttest
were analyzed to further show evidence of learning of the identified content topics.
RESULTS AND DISCUSSIONS
The Designed Digital Module in Learning Mathematics Course for Graduate Students
The Modern Algebra course, also known as Abstract Algebra, has been identified by the
mathematics education major students as one of the most challenging subjects because of its
symbolic features and structures which made its concept foreign to study (Ko & Knuth, 2013;
Mowahed, Song, Xinrong, & Changgen, 2019). The course intends to enhance logical and
analytical reasoning and symbolic thinking of the students in the appreciation of basic algebraic
structures: groups, semigroups, and rings. The New Normal phenomenon made the teaching and
learning of the subject more challenging because of the absence of the usual face-to-face classroom
interaction among the higher education institutions (HEIs) worldwide. The digital learning module
on selected 22 primer topics in modern algebra has been conceived as one of the self-learning
materials intended for the mathematics major students of the Teacher Education Institutions (TEIs)
in response to the New Normal teaching and learning approach brought by the pandemic due to
the Corona Virus Disease (COVID -19).
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
purposes only, and only so long as attribution is given to the creator. If you remix, adapt, or build upon the material, you must
license the modified material under identical terms.
85 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
The primary reason for designing the digital module is to make possible the attainment of
the set of educational objectives for a one-semester modern algebra (abstract algebra) course.
Students were assumed that they have learned the most essential foundational topics and concepts
of the set theory, linear algebra, number theory, and probability theory to better understand the
content of this course materials. They are expected to exert time and effort to learn every topic
which were arranged in a manner that prerequisites are considered first. The material hopes to help
students learn the salient and essential topics of the subject, both in synchronous and asynchronous
blended teaching-learning approach.
Conditioning
(Prerequisite)
Assessment
(Worksheet)
Discussion Definition Example
LESSON PROPER
Figure 1. Manner of Utilization of the Digital Module in Asynchronous Learning
The learning modules were designed in a manner that will be available in digital format to
be utilized by the students in an asynchronous online independent learning. With the intent of
ensuring that the material would cater to independent learning, topics were arranged from simple
to increasing complexity so as prerequisites are discussed first and deepened through an integrative
approach between and among content topics as shown in Figure 1. The user of the module is
encouraged to have some review of the topics on properties of real numbers, properties involving
equations, and inequalities to have a better understanding of the course. These topics can be found
in the appendices (Appendices A to C) of the compiled format of the module for easy reference
which was distributed at the beginning of the semester. Each module corresponds to a specific
identified topic of Modern Algebra provided to students every week with a corresponding assigned
task to be accomplished and to be returned in the succeeding week. The topics included are divided
into two main parts; part I deals with the preliminary topics intended for those students who have
a little background, if none, in Abstract Algebra, Number Theory, and Probability Theory. On
other hand, part II deals with the basics of algebraic structures which will lead students to deepen
their understanding of group theory and ring theory as illustrated in Figure 2.
The learning module for each of the identified topics contains the following basic elements:
discussions, definition, example, and practice drills (worksheets) to check their understanding. The
discussion component of the module contains the basic concepts and ideas about the topic being
introduced in the module. This serves as the backgrounder leading towards the understanding of
the content topic and how it is related to their prior and acquired knowledge and skills in the
previous lessons to connect with the new lesson. The definition component of the module will
strengthen student understanding of the new mathematics concepts introduced in the lesson.
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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86 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
Essential mathematics concepts which bear significance in students’ understanding of the new
concepts are defined in the lesson.
Figure 2. Screenshots of Some parts of the Digital Module
The example component of the module further elaborates the defined mathematics concepts
through illustrations. This element of the module may contain computations, techniques,
algorithms, approaches, among others which will expound the mathematics concepts and
procedures to fully demonstrate understanding by the students. The students will see the pattern
and the techniques in applying the definition on how certain mathematics expressions are
converted in another form. The definition and example components are integral parts of the
discussion component of the module which further explains and provides a concrete representation
of the content topic being introduced.
Moreover, the practice drills component of the module will provide a venue for the student
to further explore and test their understanding of the content topics being discussed. Each of the
lessons (content topic) has a corresponding worksheet which serves as the practice drill. It contains
several forms of assessment depending on the nature of the topic and the objectives of the lesson
which may vary from multiple-choice, True or False, Short Answer test, Essay, and problem-
solving. Answer key for each of the worksheets is provided to check their understanding of the
lesson following the principle of independent learning. Further discussions and follow-up are held
during the conduct of the virtual meeting via google meet, queries and questions from the students
were entertained for clarification of the module content, see Figure 4.
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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87 MATHEMATICS TEACHING RESEARCH JOURNAL
SPRING 2022
Vol 14 no 1
Characteristics
Content and Coverage
Theoretical Consideration
Appearance/Visual Appeal
Language
Over-all
Cronbach’s
Mean (Sd) Description
Alpha (
𝛼
)
Reliability
4.56 (1.66) Outstanding 0.95 High
4.26 (1.27) VS 0.81 High
4.27 (1.48) VS 0.96 High
4.51(1.13) Outstanding 0.87 High
4.42 (2.58) VS 0.95 High
Table 1. Users (n=13) Evaluation on the Characteristics of the Digital Module
Table 1 shows the results of the students’ evaluation after a semester of the utilization of
the digital module which illustrates the characteristics of the digital module along with content and
coverage, theoretical consideration, appearance/visual appeal, and language used which represents
the content validity and construct validity of the materials. The data reveals that the digital learning
module has obtained an overall very satisfactory rating (Mean = 4.42 ± 2.58) from the students
with a corresponding Cronbach’s alpha (𝛼) value of 0.95 which signifies a high internal
consistency rating from among the student evaluators. An enrolled male graduate mathematics
education student teaching in a private school at the basic education level expresses his
appreciation in the utilization of the digital module, he stated that “The provided instructional
materials helped me greatly for the acquisition of learning even during the pandemic where we
can learn anytime and anywhere”. This expression is supported by the statement from a female
mathematics teacher of a public school who enrolled in the same course expounded that “the
provision of the digital module is an effective tool for continuous learning despite the pandemic
since face-to-face is not possible at the moment”. This only means that the students are generally
and consistently satisfied with the utilization of the digital learning module along with its
characteristics.
Moreover, the students have an outstanding rating of the content and coverage (Mean =
4.56 ± 1.66) as well as the language (Mean = 4.51 ± 1.13) used in the digital module exceeding
their learning needs and requirements on their asynchronous learning utilization. One of the newly
enrolled graduate mathematics education male students in Sorsogon City mentioned that “the
content and approach of the module arranged from very simple ideas to increasing complexity
together with the worksheets for practice assisted me in learning the subject”. Another
manifestation of a female student from Masbate Province commented that “Though it was a
difficult subject, I am satisfied with the content of the module because I learned new topics”. The
result of evaluation signifies that the material can provoke and sustain students’ understanding of
the content through the language used appropriately to their level of thinking.
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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88 MATHEMATICS TEACHING RESEARCH JOURNAL
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Figure 3. Screenshots of the Sample Lecture Videos Created by the Graduate Students
The very satisfactory rating along with the theoretical considerations (Mean = 4.26 ± 1.27)
and appearance (Mean = 4.27 ± 1.48) also indicates that the digital module can sustain their
interests in learning the content of the lesson with corresponding high internal consistency
Cronbach’s alpha (𝛼) values exceeding the acceptable value of 0.70 (George and Mallery, 2003;
Hair, Black, Babin & Anderson, 2010). The qualitative and quantitative data revealed that the
presentation of the important concept suitable to the level of student understanding by building on
their previous knowledge is necessary to capture student interest in the subject. The newly enrolled
male student in Sorsogon City also expounded his appreciation of the particular topic by saying “I
enjoyed learning the mathematical concepts behind the modulo art … we were asked to do modulo
art design since in our elementary years without even knowing the reasons behind the patterns”.
The graduate students’ appreciation of the mentioned topic can be further expounded by their
output on the creation of lecture video as one of the proofs and outcome of their learning as
demonstrated in Figure 3.
Learning Experiences of the Students on the Use of the Digital Module
The sudden change of the mode of instruction in any level of education brought a
significant effect on the teaching-learning situation. There were some challenges encountered by
both the students and teachers during the pandemic in the flexible learning environment (Laguador,
2021) limiting face-to-face interactions and promoting online distance learning through
synchronous and asynchronous learning approaches. The utilization of the developed digital
module for the asynchronous mode of learning boosted the learning experiences of graduate
education students.
Table 2 summarizes graduate mathematics education students learning experiences based
on their feedbacks and written responses in the utilization of the digital module for asynchronous
independent learning showing their identified challenges encountered. The corresponding features
of the digital module were designed together with their learning strategies as an adaptive
mechanism to minimize, if not eliminate, the challenges encountered. The feedbacks of the
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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students show that their challenges can be grouped into three broad categories: (1) the nature of
the subject itself, (2) online learning facilities, and (3) the learning modalities.
Challenges
Encountered
Complex nature of the
subject with a new set of
topic/lessons encountered
by the
students
Some new encountered
content topics/lessons need
further elaborations.
Unstable internet facilities
Modular Distance Learning
(MDL) is time-consuming
on the part of graduate
students who are working
at the same time.
Teachers hardly provide
and/or get immediate
feedback on students’
difficulties.
Limited interaction among
teachers and classmates.
Features of the Digital Module Students’ Adaptive
Utilization Mechanism
The module is comprehensive and
informative with a complete
discussion of the topics.
Topics are arranged in increasing
complexity bridging students’ prior
knowledge with supplemental
learning materials.
Availability of digital module for
asynchronous learning modality.
The digital module is available at their
most convenient time for independent
learning.
Worksheets are attached in each
lesson to check student
understanding of the lesson.
Constant communication and
monitoring of student progress
through the conduct of weekly
synchronous online teaching for
feedbacking.
Each module was designed in an
interactive manner featuring the
lesson discussions, definition,
example, and practice drills
(worksheets) to check their
understanding.
Eagerness to learn and upgrade
their content knowledge in their
area of specialization.
Students explored available online
resources such as e-books and
video lectures on YouTube as
supplemental materials/lessons on
challenging topics.
Students look for a place with a
strong internet connection and/or
available Wi-Fi.
Students find time in reading the
module and answering the
worksheets to beat the agreed
schedule of submission (Time
management skills).
Students challenge themselves to
discover and perform higher-order
learning tasks.
Students develop independent
learning skills in critical thinking
and analyzing information.
Table 2. Learning Experiences of the Graduate Students
Nine out of 13 enrolled students in the subject have just encountered some set of topics
specified in the subject since most of them are teaching at the basic education level and have not
been teaching algebraic structures in general. “I am not familiar with most of the topics, I am just
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
purposes only, and only so long as attribution is given to the creator. If you remix, adapt, or build upon the material, you must
license the modified material under identical terms.
90 MATHEMATICS TEACHING RESEARCH JOURNAL
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Vol 14 no 1
starting to learn the concepts on my own,” said one of the newly enrolled female students in the
program. While the other four students are fresh graduates at the undergraduate level and able to
recall some of the prerequisite contents included in the course.
Though students agreed that the digital module provided them with comprehensive inputs
and information about the topics which are arranged from simple to complex, they still looked for
other available online learning resources to supplement their understanding of the topics. A female
graduate mathematics education student in the Municipality of Irosin mentioned that to further
validate and deepen her understanding of the concepts discussed in the developed digital module
she tried to search for more examples from the available materials online such as the video lecture
on the YouTube website. This is supported by the feedback of her classmate in Sorsogon City who
said that “I enjoyed the given worksheets for it has driven my curiosity to read articles and watch
videos on YouTube”.
This is an indication that the students at the graduate level are independent learners capable
of looking for additional learning resources coupled with an eagerness to learn new things and
upgrade their knowledge in their area of specialization. The module has been designed in a manner
that will provide the graduate students with the overview and ideas regarding the concepts
presented building on what they have learned already that would aggravate them to learn further
and deepen their understanding about the abstract concepts of mathematics such as group,
subgroup, and ring. The students will not able to determine whether G = {a, b, c, d} with operation
* defined by the table below, as excerpted from the problems in Worksheet number 8 (Group),
* a b
c
d
a
a
b
c
d
b
b
a
d
c
c
c
d
b
a
d
d
c
a
b
is a group without understanding the concept and definition of a group as well as the binary
operation as reflected in the digital module which they explored during the asynchronous
independent learning. The students at the advanced education level after a walk-through of the
specific topic in the digital module were given a chance to further explore the available learning
resources whether print or non-print materials with an already preconceived idea about the topic,
e.g., group, for their verification and deepening of conceptual understanding. This will make them
more confident with the completion of the task given in the worksheets and apply the mathematics
concept in solving problems in the relevant field of study. Teachers, therefore, need to design well
the learning materials and activities that would provoke students’ willingness to adopt the
principles of independence in online distance learning despite the complex nature of the subject.
The Province of Sorsogon, together with its neighboring Provinces such as Masbate, is in
the southernmost tip of Luzon Island in the Philippines experienced unstable internet connectivity
especially those in the remote area as supported by the feedbacks from most of the students (8 out
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of 13 students). The limitations during the online synchronous lessons such as video conferencing
due to poor internet connectivity are strengthened by the utilization of the provided digital module.
The provided module available on weekly basis according to the scheduled topic helped the
graduate student a lot for self-learning at their most convenient time. Students were given enough
time to study the module and answer the worksheets to check their understanding anytime they
want. This is also supported by the feedback of an enrolled graduate student from the rural area of
the Province of Masbate as follows “For me, it is more convenient to have modules/worksheets as
a mode of instruction while I am working at the same time. I can learn anytime”.
Figure 4. Captured Moments during the Video conferencing with the students
Feedback mechanism on students’ outputs and learning is provided during the conduct of
the online synchronous teaching where students find ways to look for a place with strong internet
connectivity in their respective area once a week. Feedback from another student in Masbate
Province highlighted that “… since I am aware of poor internet connectivity in our area as one of
the reasons of not participating in our video conference via google meet, I find a place where I
could stay with strong internet connection for me to attend our online meeting”. The virtual
sessions as shown in Figure 4 provided the students an opportunity to interact and share their
experiences with their classmates. The students felt the need to attend the virtual session utilizing
any available facilities, equipment, or devices such as personal computers and mobile phones with
the internet connection either through Wi-Fi or prepaid load so that areas needing improvement
along with the content of the module are discussed to unlock any difficulties encountered.
It is, therefore, necessary that the teachers should be vigilant on the weekly need of the
students and see to it that appropriate instructions and feedbacking is provided during the conduct
of online teaching. Professors may also provide for the extension of the submission of weekly
outputs, if necessary, especially for those students who are working at the same time and residing
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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in an area with poor internet connectivity. The unexpected change of the mode of instruction
implementing online distance learning for the first time has to make adjustments on the part of the
professors towards accomplishing the task within the semester without sacrificing the quality of
instruction.
Moreover, the independent learning modalities with the utilization of the digital module
brought some big adjustments on the part of the students such as the time management skills, need
for immediate feedback mechanism, and limited interactions with teachers and classmates. “The
distance learning limits interaction, and meaningful learning experience between the teachers and
students which led us to rely the information on the provided module/worksheets,” said a female
student who is a fresh graduate from her undergraduate education. The conditioning mechanism
on the very first day of the semester which includes orientations and leveling of expectations is
necessary to implement independent online learning modalities. This conditioning mechanism is
an important strategy to assess students’ needs and readiness to adopt the new approach to learning.
This led to the design of the digital module as a teaching-learning approach to implement
asynchronous online independent learning coupled with a weekly scheduled online synchronous
teaching for feedbacking. Consistency of submitting students’ outputs per week is necessary, with
some considerations to students’ needs, to check their progress through active participation during
the scheduled online teaching.
Generally, students’ reflections revealed that the digital module provided them a guide on
what to learn, what to do, and what to accomplish per week which developed their time
management skills, creativity, and independent learning skills which eventually improved their
critical thinking skills and problem-solving skills. The graduate students enrolled in online
education demonstrate a strong preference for an asynchronous mode of learning because of
convenience and favored individual assignments (Butler & Pinto-Zipp, 2005). One male student
mentioned that he can save a lot of money, time, and effort in traveling at a most 2-hour distance
from home every weekend.
Effectiveness of the Digital Module in Asynchronous Online Independent Learning
Table 3 displays the differences between the posttest and pretest scores and the
corresponding equivalent percentage scores (PS) of the students. It can be noted that eight out of
the 13 enrolled students were considered in the analysis of the pretest scores since these are the
only students who were able to satisfy the requirements of submitting the test within the allotted
time duration during the conduct of the test. There were three out of eight students who has no
sufficient knowledge of the content topics before the utilization of the digital module with an
overall mean score of 3.75 or 25% level of understanding.
The pretest answer sheet of student 4 referred to in Table 3 reflected the statements as “I
humbly apologized that I have not been able to answer any of the questions because I forgot
already the concepts which made me difficult to deal with the problems. I do not teach these lessons
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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since my first year of teaching but I am much eager to learn and appreciate them again.” This is
an indication that the graduate students in this particular educational institution have different
needs along with their acquired knowledge and skills of the course content of Modern Algebra
including the pre-requisites of the course. These are some of the areas of concern to address in
times of pandemic through the conduct of online distance learning.
Through the utilization of the digital module featuring the basic elements of discussion,
definition, examples, and practice drill (worksheets) during the asynchronous learning coupled
with the constant checkup and follow-up during the synchronous online learning via google meet,
the aforementioned student can obtain a score of 13 or 86.7 PS during the posttest. He was able to
properly execute the requirement in a problem on “Determine whether the product of the following
permutation in cycle notation form (1 3 5 2 4), (1 3 5) and (2 4) in S5 is odd or even” he obtained
the product which is (1 5 3 2) that gave him the idea that the product is an odd permutation. Many
of the learners of Modern Algebra find difficulty in finding a product of permutation of n especially
when it is written in cycle notation format which he was able to perform properly the operation.
After performing the given operation, the student has executed his knowledge about the number
of transpositions of the given permutation, so he has able to determine whether it is odd or even.
Difference
Student Pretest Posttest (Post – Pre)
Score PS Score PS Score PS
1
0
0.0
6
40.0
6
40.0
2
4
26.7
14
93.3
10
66.7
3
1
6.7
13
86.7
12
80.0
4
0
0.0
13
86.7
13
86.7
5
9
60.0
14
93.3
5
33.3
6
0
0.0
11
73.3
11
73.3
7
9
60.0
14
93.3
5
33.3
8
7
46.7
12
80.0
5
33.3
9
-
-
14
93.3
-
-
10
-
-
11
73.3
-
-
11
-
-
7
46.7
-
-
12
-
-
12
80.0
-
-
13
-
-
13
86.7
-
-
Mean Score 3.75 25.00 11.85 78.97 8.10 53.97
Sd 4.06 27.08 2.61 17.39 - -
Table 3. Difference between Students’ Posttest and Pretest Score
Generally, the students obtained more than thrice their pretest mean scores (MS = 3.75 ± 4.06) in
the post-test (MS= 11.85 ± 2.61) with an equivalent of 78.97 MPS. The data in Table 3 also
revealed that the group of graduate students involved in this investigation have a closer level
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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94 MATHEMATICS TEACHING RESEARCH JOURNAL
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understanding of the mathematics content topics after utilization (MPS = 78.97 ± 17.39) of the
digital module as compared to their pretest percentage scores (MPS = 25 ± 27.08). Moreover, all
eight students showed a significant improvement in their test scores in the posttest with a mean
score (MS) gain of 8.10 equivalent to 53.97 MPS.
Figure 5 reveals the way student 7 (who obtained a Pretest Score of 9 or 60.0 PS, Posttest
score of 14 or 93.3 PS) answers a problem on subgroups content topic where they were asked to
show the subgroup diagram of the cyclic group (Z9, +). It can be seen in the figure the big
difference of how the student responded to the problem with some maturity of response during the
posttest. During the pretest, the student was able to show the set generators of the cyclic group (Z9,
+) including the set generated by each of the elements, however, student 7 did not able to show the
subgroup diagram. On the other hand, the student 7 posttest response showed all the subgroups of
the given cyclic group together with the description as trivial, set generator, or proper subgroup
and was able to show the subgroup diagram. The illustration indicates that the use of the digital
module with its basic elements of discussions, definition, and examples helped any student,
whether has prior knowledge or not about the content topic, to further expand their learning and
understanding of the mathematics concepts including its principles and processes.
Pretest Response
Posttest Response
Given: Z9 = {0,1,2,3,4,5,6,7,8} Given: (Z9, +)
<0> = {0}
<1> = {0,1,2,3,4,5,6,7,8} The subgroups of (Z9, +)
<2> = {0,1,2,3,4,5,6,7,8} <0> generates {0}, trivial subgroup
<3> = {0,3,6} <1>, <2>, <4>, <5>, <7>, and <8>
<4> = {0,1,2,3,4,5,6,7,8} generate (Z9, +) itself, set generators
<5> = {0,1,2,3,4,5,6,7,8} <3> and <6> generate {0,3,6}, proper
<6> = {0,3,6} subgroup
<7> = {0,1,2,3,4,5,6,7,8}
<8> = {0,1,2,3,4,5,6,7,8} The subgroup diagram:
<1>
Note: I cannot create a subgroup diagram.
I have no past knowledge about it. <3>
<0>
Figure 5. Comparison of the Sample of a Student Pretest-Posttest Response
The presented illustrations above can be supported by the gain in mean score after exposure
to the digital module indicating a highly significant improvement (t=5.034, p<0.05) in the level of
students’ understanding of the content topics. The statistical result signifies that the utilization of
the digital module in the asynchronous online independent learning of the graduate students
provides them with a better understanding of the content topics in Modern Algebra. The graduate
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4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial
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students’ experiences also support that the features and basic elements of the designed digital
module for asynchronous online learning are more effective when combined with a regular
schedule of virtual conferencing for monitoring and evaluation of their gained knowledge and
skills. The findings of the current investigation affirmed that any instructional materials designed
for students’ online learning will be more effective and engaging when there is constant
communication with the instructor (Swan, 2011; Alrajeh & Shindel, 2020) and provide them with
activities for the creation and sharing of knowledge (Holzweiss, Joyner, Fuller, Henderson &
Young, 2014) and experiences via video conference.
CONCLUSIONS
The designed digital learning modules cover major topics arranged in increasing
complexity for the utilization of the graduate mathematics students in an asynchronous online
independent learning. The basic elements and features of the module ensuring the presence of
discussions, the definition of important terms, examples, and practice drills (worksheets) to check
their understanding made students satisfied with the utilization of the digital learning module. The
learning experiences of the graduate students are boosted and learning outcomes are maximized
when the provision of the digital module for asynchronous online independent learning is
supported with the regular conduct of virtual conferences as an opportunity for feedbacking,
evaluation, and discussions. The regular conduct of virtual conferences allows the students to share
their ideas and thoughts responding to their needs and identified challenges along with the nature
of the subject, online learning facilities, and the learning modalities during the COVID-19
pandemic. Moreover, the utilization of the developed digital module in online learning of graduate
education level is an effective modality to better understand the mathematics content topics and
better provide them with an independent learning experience.
Teachers and instructional practitioners at a different level of education are therefore
recommended to involve