Vol 16 No 5 - May 2017

International Journal
of
Learning, Teaching
And
Educational Research
p-ISSN:1694-2493
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Vol.16 No.5

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International Journal of Learning, Teaching and
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VOLUME 16 NUMBER 5 May 2017
Table of Contents
The Sustainability of Inclusionary Practices: A Case Study..............................................................................................1
Catherine Richmond-Cullen, Ed.D., Dona Bauman, Ph.D., Vanessa Ferrance, D.Ed. and Sonya Kunkel, M.S.
The Mathematical Beauty .................................................................................................................................................... 14
Van-Tha Nguyen and Ngoc-Giang Nguyen
The Implication of Distance Learning in Competence-Based Maritime Education and Training ............................ 31
Yanning JIANG and Quan LI
Education in Iran: Limitations Imposed by Theocracy....................................................................................................42
David V. Powell and Simin Cwick
Enhancing Interactivity in Online Classes: A Framework for Enhancing Instructor-Student, Student-Student, and
Student-Content Engagement............................................................................................................................................. 53
Carl Kalani Beyer, Stephen Brownson and Suzanne Evans
How a Hands-on BIONICS Lesson May Intervene with Science Motivation and Technology Interest .................. 72
Marth Michaela and Franz X. Bogner

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© 2017 The authors and IJLTER.ORG. All rights reserved.
International Journal of Learning, Teaching and Educational Research
Vol. 16, No. 5, pp. 1-13, May 2017
The Sustainability of Inclusionary Practices:
A Case Study
Catherine Richmond-Cullen, Ed.D., Dona Bauman, Ph.D.
and Vanessa Ferrance, D.Ed.
The University of Scranton
Scranton, Pennsylvania, U.S.A.
Sonya Kunkel, M.S.
Capital Region Education Council
Hartford, Connecticut, U.S.A.
Abstract. In this article the authors describe a qualitative study that
researched the sustainability of responsible inclusive practices in a public
elementary school in Connecticut. Through focus group sessions that
included teachers, administrators and support staff, five themes were
identified that demonstrate importance in the sustainability of inclusion.
The data revealed the following five consistent themes as integral to
responsible inclusive practices: (1) Public Service with a Moral Purpose,
(2) Culture and Commitment, (3) Data-Driven Decision Making. (4)
Leadership Qualities and (5) Co-Teaching and Community Involvement.
Keywords: responsible inclusion; sustainability of inclusion; leadership
qualities
Introduction
The purpose of this study was to answer the question “what are the key
factors that have sustained responsible inclusion?”. The Silver Lane Elementary
School, located in the East Hartford Public Schools in East Hartford,
Connecticut, was the site at which the study was conducted. Focus groups that
were comprised of teachers, administrators and support staff were selected and
represented a mix of veteran and non-tenured educators. Some of the educators
at Silver Lane Elementary School were committed to inclusion initiatives for a
longer period of time than other educators who became involved during the
phase in which more inclusive practices were required and implemented at the
school.
The data was analyzed by the researchers to determine definable and
consistent themes. The following five themes were independently identified by
each of the researchers through the transcript analysis: (1) Public Service with a

2
Moral Purpose, (2) Culture and Commitment, (3) Data-Driven Decision Making.
(4) Leadership Qualities and (5) Co-Teaching and Community Involvement.
Public Service with a Moral Purpose
The issue of moral purpose of a leader is particularly interesting as it
includes the implementation by the school leader of aspects of its context: 1)
raising the bar for student learning; 2) treating people with respect; and 3)
altering the social environment for the better (Fullan, 2002).
Loehr and Schwartz (2003) base their leadership discussion on four
principles one of which is; “to build capacity we must push beyond our normal
limits, training in the way that elite athletes do” (p.13). School leaders need to
work consistently at developing a school climate that fosters collegiality and
cooperation. The metaphor of the athlete is important as it indicates the
importance of diligent and consistent dedication to the advancement of the
school in order to positively affect student achievement.
Fullan (2004) elucidates the importance for leaders to develop new
leaders in order for continuity of direction. In order for reform or change to alter
the context of schools, a critical mass of people who understand, accept and are
willing to continue the change must be cultivated. Random change needs to
become system change. System change ensures that programs will last beyond
their inceptor or creators. Leaders who affect the entire district ensure that
change and reform initiatives will be pervasive within the district. Continuity of
culture and vision are important to sustain new ideas and concepts.
Fullan (2004) describes the necessity for leaders to be energy creators.
The use of skillful and balanced management of energy is a key to effective
leadership. Energy creators are enthusiastic and always positive, use critical
thinking, creativity and imagination, stimulate and spark others, practice
leadership at all levels, are able and willing to scrutinize their practice and
willing to make their practice accessible to others and wish to improve on their
previous best (p. 37).
In his powerful summary statement regarding energy creators as leaders,
Fullan (2004) states, “We know the sources of energy creation: moral purpose,
emotional intelligence, quality relationship, quality knowledge, physical well-
being-all mobilized to engage the mind and heart in attempting to solve complex
adaptive challenges” (p. 38). The importance of an emotional connection to
leadership and the people with whom the leaders work is integral in her success.
Brain research indicates that when humans learn new content, the emotional
area of the brain is the first to receive new information. It is in this mid-brain
that decisions are made as to the importance of the information. Leaders who
consider the emotional intelligence of those whom they lead have a distinct
advantage over those leaders who do not. The human resource in organizations
is precious and should be cultivated. Through moral and emotional
connections, the leader can make a difference in how her team receives and
accepts new ideas and information.
Boylan (2016) states that “the increasing importance of educational
collaborations and networks that blur organizations boundaries” (p. 57). The
importance of engaging in collaborative leadership leads to an ethical approach

3
to school improvements for schools and the learners (p. 64). Altruistic and
moral purposes are innate in collaborative leadership models. Moral leaders
take on an identity that is driven by moral decision making. Boylan indicates
that, “Movement leaders influence identity formation through the development
of meaning for others” (p. 66). The new attitudes of all stakeholders begin to
transform the school and foster educating and leading with a moral purpose.
Perkins (2003) reflects on leaders with organizational intelligence and
reports that process smart and people smart are two separate and district
characteristics of great leaders. A process smart leader has an exceptional
knowledge base while a people smart leader identifies emotionally with people
and their values. Transformational leaders effect change in group as well as in
the individuals within the group (Heifetz, 2003). Perkins’ (2003) notion of
developmental leaders is concerned with leaders functioning as “exemplars,
facilitators and mentors within a group, helping to move it toward a progressive
culture” (p. 219). Developing human interactions through support and effective
communication is a key to becoming a true leader.
Referring again to types of challenges leaders face, adaptive challenges
require the deep participation of the people with the problem. In other words,
one must engage teachers and parents as representatives of the community in
school reform. Teachers may not have the knowledge or training to implement
reform tactics and can be part of the reason expected changes are not being
implemented. Additionally, parents may not know or understand how to effect
growth in their children. Effective leaders communicate with groups
throughout the system, thereby ensuring effective understanding and
acceptance of change of reform initiatives. By building communities of
constituents and leaders through effective discussion and communication, a
leader can positively affect the implementation of new ideas. People who feel
included, who feel important, who are offered chances to express their thoughts
and ideas are more likely to buy into change initiatives.
Data-Driven Decision Making
Since the passing of the No Child Left Behind Act, school improvement
initiatives have been fueled by data (Goren, 2012). This is the age of
accountability within the American school system. To respond to this call for
accountability, data-driven decision-making has emerged as one of the primary
school improvement strategies (USDOE, 2010). With the increasing amount of
data that is being collected by schools, educators are faced with the challenge of
how to best make sense of it (Anfara & Donhost, 2010). In conjunction with the
many other responsibilities that teachers hold, data analysis and its application
to teaching and learning can be a very complicated, dense process for teams of
educators. To assist educators with this complicated task, Anfara and Donhost
(2010) outline five primary phases in the data-driven decision-making process.
The five primary phases in the data-driven decision-making process are: (1)
organizing for success, (2) building assessment literacy, (3) identifying data
sources, (4) aligning data systems, and (5) altering instruction (Anfara &
Donhost, 2010). These five phases are not meant to be sequential, but rather to
highlight the important areas to be considered.

4
Anfara and Donhost (2010) assert that educators must organize for
success by ensuring that they have time, teams and trust when engaging in any
data-driven decision-making process. Assessment literacy is a crucial
component in the process, as raw data by itself provides little information to
educators. Educators must be proficient in the act of interpreting the data
(Anfara & Donhost, 2010). This brings more meaning and purpose to the data-
driven decision-making process (Schildkamp & Kuiper, 2010). Educators must
also be cautious when identifying data sources, as there are many shortcomings
associated with state accountability tests (Peterson, 2007). Anfara and Donhost
(2010) promote the use of periodic assessments to increase student achievement
and enhance data-driven decision-making practices. To ease the data-based
decision-making processes, data systems within the building level must be
aligned. Otherwise, educators find themselves in a very complicated process of
trying to make sense of disparate, unaligned data systems, since there are so
many sources of data available to them (Anfara & Donhost, 2010). The final
component outlined by Anfara and Donhost (2010) in the data-based decision-
making process is the use of data to inform instruction. Collecting and
analyzing data is not enough to ensure improvement of student learning or
teaching practices. The data must be used to alter instruction. This component
may be the most complex piece of the process, as the connection between data
and instructional practice changes is the most absent in the literature (Anfara &
Donhost, 2010). Goren (2012) highlights this aspect in his research when he
asserts that our understanding of how data lead to improvement in education is
vastly immature.
Goren (2012) asserts that educators must have a deeper and better
understanding of data, its use, how practitioners make sense of the data, and
conditions that are most conducive for using data well. To do so, it is necessary
to understand the context in which data is used within the school system as well
as the meaning that teachers make of data (Timperley, 2008). Goren (2012) also
argues that educators must take a closer look at what data are actually
measuring and why. Once performance measures are introduced to the public,
they take on a life of their own, and their intended purposes get merged with
public interest.
Today’s principal is expected to be able to gather, examine, translate and
use data in order to improve instruction (Fox, 2013). In addition to these
responsibilities, the principal must also support data-driven decision-making
among his or her staff. Principals play a fundamental role in promoting the
valuable and resourceful use of data for school improvement (Skalski & Romero,
2011). The leadership practices that principals embrace set the tone for how data
will be used by the school staff. They can establish a culture that embraces data-
based decision-making practices by all employees.
Due to the tremendous amount of data that educators must sift through
and the use of data to evaluate the performance of students, teachers and
administrators, it is all too often the case that educators have learned to become
defensive and shut down when it comes to data usage. Principals can help
educators to overcome this protective stance by modeling the advantageous uses
of data to inform the educational process and also by creating a culture that
makes it secure for educators to acknowledge that some practices are

5
unsuccessful (Skalski & Romero, 2011). Skalski and Romero (2011) also support
the role of the principal in providing teachers with the structured times to meet
for discussions of the data.
Most educators are faced, not with a lack of data, but rather decisions
regarding which data make the most sense for them. The principal must assist
the data-based decision-making processes in his/her school by helping the staff
to identify which data are most informative. He or she can do this by asking
about the needs of his or her staff members and students while also asking how
the data can be used to address those needs (Skalski & Romero, 2011).
A principal can also support data sharing among their teachers by
creating opportunities for teachers to share data between grade levels and
providing professional development as well as support for his or her teachers
(Skalski & Romero, 2011). Additionally, the principal must keep data reports
understandable to parents and staff so that the reports can be used in a
meaningful way for program improvement and enhancement of student
learning. By maintaining objective and just teacher accountability, the principal
can ensure that data are not used to penalize teachers for things that are outside
of his or her control (Skalski & Romero, 2011). All of these efforts can contribute
to a school culture that uses and values data.
Fox (2013) identifies the following nine attributes of an appropriate
mind-set for data-driven decision making in a principal: (1) The principal
believes data is vital for sound decision-making and effective problem-solving.
(2) The principal understands the classroom is the critical point of impact for
student learning. (3) The principal believes one of his or her primary
responsibilities is to establish a culture of continuous improvement. (4) The
principal focuses on variables over which the school has control. (5) The
principal understands that data is a means to an end, rather than an end in itself.
(6) The principal distinguishes between change and improvement. (7) The
principal establishes a “but-free zone” for problem solving. (8) The principal
understands the difference between a situation and a problem. (9) The principal
realizes “hope” is not a strategy.
Leadership Qualities that Promote a Positive School Culture
Successful school leaders evidence certain personal and professional
qualities that enable them to guide the work of those to whom are under the
authority of administration. Research about inspired leadership and those
qualities that effective leaders possess is abundant. The Council of Chief School
Officers (2002) named strategies for school improvement as manifested through
successful principal leadership. They are setting high expectations for all
students, sharing leadership and staying engaged, encouraging collaboration
among staffing, using assessment data to support student success, keeping the
focus on students, addressing barriers to learning, reinforcing classroom
learning at home, employing systems for identifying interventions and defining
special education as the path to success in the general education program
(Fullan, p. 3).
Significant change in school culture, student achievement, professional
practice and community and parental involvement is contained in the research
on effective leadership in school settings. According to Ouchi (2003) the keys to

6
developing and sustaining effective school leaders are that every principal is an
entrepreneur, every school controls its own budget, everyone is accountable for
student performance and for budgets, everyone delegates authority to those
below, there is a burning focus on student achievement, every school is a
community of learners and families have real choices among a variety of unique
schools (Fullan, p. 10). Matthews (2015) states that best practices in inclusion
involves the general aspects of school reform and requires a distribution of
leadership actions, delegated work and expertise across a school (p. 1001).
Day, Gu and Sammons (2016) discuss transformational leadership. They
state, “Transformational leadership has traditionally emphasized vision and
inspiration, focusing on establishing structures and cultures that enhance the
quality of teaching and learning, setting directions, developing people and
(re)designing the organization” (p. 224). Their research cites studies that have
determined that it is essential to engage teachers in dialogue that enables them
to participate in decisions about learning and the craft of teaching. Effective
leadership includes practice that focuses on the internal states of organizational
members as well as addressing instructional leadership (p. 225). The need for
transformational leaders in a culture of outcomes based learning is still
pervasive. The school administrator’s attention to school culture is important
for the promotion of school improvement (p. 231). School ethos and high
expectation for faculty are considered integral to effective transformational and
instructional leadership strategies (p.246). Shared leadership and the
distribution of leadership responsibilities extended trust and fosters a more
highly personalized and enriched curriculum (p. 249). Day, Gu and Sammons
state, “The work of successful principals is intuitive, knowledge informed and
strategic. Successful principals build cultures that promote both staff and
student engagement in learning” (p. 253).
Fullan (2004) reports that solutions to developing and sustaining
effective school leaders require a systems approach to school reform and a
practical strategy to engage new concepts with an action plan. Fullan (2004)
illuminates the “new theoreticians” as people working on real problems and
solutions at the school level. His discussions include the concept of the different
challenges faced by school leaders. Adaptive challenges are those issues that
have solutions outside of the normal and tried methods of operation while
technical problems can be solved within the context of that which is currently
happening in schools. He lists eight elements of leadership which may influence
sustainability of new ideas and solutions. They are completing public service
with a moral purpose, creating a commitment to changing context at all levels,
developing the lateral capacity and building solidarity through networks,
incepting intelligent accountability and vertical relationships, crafting a culture
for deep learning to take place, having a dual commitment to short-term and
long-term results, ensuring cyclical energizing for all and the applying long
lever of leadership (Fullan, 2005).

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Method
Using a case study design, the purpose of this study was to answer
“what are the key factors that have sustained responsible inclusion for the
school?”.
Study Group
In order to avoid the possibility of teachers perceiving coercion by
administrators, a statement was included in the consent form that outlined the
voluntary nature of participation in the focus groups. The groups were
comprised of educators who had more extensive experience with inclusionary
practices and those who did not. The representative sample included six general
educators, two special educators, one executive coach, one education specialist,
two special education paraprofessionals, one speech-language pathologist, and
one administrator.
Instruments and Process
Each of the focus group sessions were approximately one hour in
duration. Each group was asked the same questions which promoted dialogue
and reflection and maintained reliability and validity. The research literature on
sustainability of school reform guided the researchers on the development of
questions asked in the focus interviews. The questions were given to practicing
school leaders for their review and suggestions from administrators were used
to edit the questions. The focus group questions are included in table 1.
Table 1
Focus Group Questions
What is the history of inclusionary practices in the school?
How did the school decide to become inclusive?
Who were the original planners and “change agents” and are they still part of
the school today?
How were decisions made about inclusion?
How were parents part of the planning process?
What kind of training and consultation were provided to teachers and staff and
is that professional development still ongoing?
What types of problem solving mechanisms are available to staff?
Do you have co-teaching and how is it maintained in the school?
How do you as a leader sustain your school’s inclusion initiative?
How do you maintain energy and renewal for yourself to sustain your focus on
all learners?
How do you incorporate the need to improve reading and math scores with
inclusive practices?
All of the focus group sessions were audio recorded and transcripts were
typed by a research assistant from the University of Scranton. Following each of
the focus group sessions, a summary form was completed by each of the
researchers who managed the focus group. The summary form included details

8
about the locations and time schedules of the interviews, information on the
educators who participated in the sessions, and descriptions of the content and
emerging themes. The summary form was completed in a timely manner after
the sessions were concluded and were then attached to the transcripts.
Themes
Data gathered from the focus group interviews was analyzed by each of
the researchers through an independent coding and theme identification
process. Through robust discussions among the researchers, the following
themes were revealed: public service with a moral purpose, culture and
commitment, data-driven decision making, leadership qualities, and best
practices. Please see Tables 2 through 6 for reference to themes, categories, and
subcategories.
Public Service with a Moral Purpose
The first theme was identified as public service with a moral purpose.
This theme includes the establishment of a caring learning community involving
all constituents (educators, school personnel, parents, students, community
members) within the public school setting. The vision of this theme involves the
guiding principle of teaching all children from the heart. Educators and staff
have a moral obligation to provide the necessary tools for all students to be
successful in school. All constituents have an equal responsibility for student
success. Special and general education students are the shared responsibility of
all service providers.
Table 2
Theme: Public Service with a Moral Purpose
Theme Categories Subcategories
Public Service
with a Moral
Purpose
Student Centered
Focus
That which happens has a great
effect on students
Heart Centered Vision Teachers instruct children from the
heart
Inclusive Philosophy Educators need to provide the
necessary tools for all students to be
successful in school
Moral Obligation Educators have an obligation to all
students that supersedes legality.
All students receive excellent and
appropriate services regardless of
whether or not they have an IEP.
Student Responsibility
and Reflective Practice
Students take ownership of their
learning. They learn to make life
choices and to self-advocate.
Professional
Development
All service providers, including
paraprofessionals receive
substantive and ongoing
professional development

9
Culture and Commitment
A collaborative culture where professionals share strategies and
communicate in a natural, positive manner about the progress and successes of
all students is pivotal in the theme of culture and commitment. Helping
students to understand their strengths and needs while becoming thinkers,
problem solvers and self-sufficient learners is a strategic aspect of a collaborative
culture. In this culture, educators empower children to become all that they are
created to be. Through courageous conversations, educators facilitate a positive
community for all stakeholders. A collaborative culture is driven by a
philosophy that includes sharing strategies to promote student success.
Through shared responsibility, strong leadership, and the development of equal
partnerships, all teachers are responsible for the success of all students. There is
a pervasive culture of collaborative communication among school staff in which
teachers are ambassadors and a voice for the program. Faculty and staff
dedication helps to keep the program vital, although educators know that there
will be both successes and failures. Teachers focus on student progress and
empower students to become thinkers, problem solvers and self-sufficient
learners by assisting students to better understand their strengths and learning
needs.
Table 3
Theme: Culture and Commitment
Culture and
Commitment
Collaborative There is a collaborative culture
Teachers and stakeholders practice sharing
strategies.
Ambassadors Teachers are ambassadors and a voice for
the program.
Communication There is a pervasive culture of natural
communication among school staff.
Dedication and
Intensity
All faculty and staff are dedicated to the
success of the program.
Leadership Strong and effective leadership is key to the
success of the program.
Focus on Student
Progress
There is a need for all students to be more
successful.
Shared
Responsibility/Equal
Partnership
Stakeholders take equal responsibility for
special education students.
Empowering
Thinking Children
All stakeholders are assisting students to
understand their challenges and become
thinkers/problem solvers/self-sufficient.
Staff Keep it Alive The staff realize full inclusion is a process
and will have successes and failures.
Proactive Pre-
Teaching
There is movement away from re-teaching
to pre-teaching; resetting the student so
that he/she can learn successfully.

10
Data Driven Decision Making
The theme data-driven decision-making is defined as the practice of
collecting and reporting out on data. Data drives teaching practices, including
co-teaching. An ongoing process of assessment enables teachers to reflect on
grouping strategies and make adjustments. In the collection and reporting
process, the principal makes presentations to the teachers and data is analyzed
by a team. The teachers present at the board of education meeting to appeal for
financial resources to support effective practices. Data team meetings provide
staff with an opportunity to participate in the decision-making process whereby
individual student achievement is analyzed. In a collaborative co-teaching
environment, data-driven decision-making involves everyone on the team,
including administrators, teachers, the school board, parents, paraprofessionals,
and the student making adjustments to the curriculum and instruction based on
the data that has been collected. Teachers and principals collect and analyze
data through data-team meetings where all school staff has a choice and a voice
in the process. After an initial presentation from the principal and a completed
analysis by the data team, the teachers present at school board meetings to
appeal for additional money in support of resources needed to drive student
progress. The data drives the co-teaching practices, as teachers reflect on and
make changes in an ongoing process in the classroom. Teachers make formative
assessments and create instructional adjustments based on individual needs.
Table 4
Theme: Data-Driven Decision Making
Data-Driven
Decision
Making
Collect Data and
Report Out
Teachers collect data
The principal makes a presentation to
teachers – the team analyzes the data.
The teachers present at the board of
education and appeal for financial
support to what has been effective.
Data Team Meetings The meetings provide school staff with
choice and voice.
Individualized
Decision Making
Process
Each child’s data results are analyzed.
Data Drives Practice The data drives the co-teaching
practices.
Educators reflect on and change
grouping strategies.
The process is ongoing.
Leadership Qualities
Effective leadership that empowers teachers and staff is another theme
that emerged in the transcripts. Professional development communities are
established to encourage buy-in from school personnel. The school

11
administrators provide resources to all educators and staff in order to promote
equal education for all children. The school leader values her staff and
acknowledges their ideas as well as their strengths. Resources such as co-
planning time and financial support are provided in order for the educational
program to be successful.
Table 5
Theme: Leadership Qualities
Leadership
Qualities
Empowering Teachers The process uses teachers in a
collaborative way so that the principal
can get input and make decisions.
The process energizes the school staff.
The process makes school staff feel
valued.
Empowerment acknowledges the
knowledge and abilities of staff.
The process is a give and take process
between collaborators.
Empowerment encourages leadership
through professional development
opportunities.
Decision Making The principal must occasionally make
the hard decisions – i.e., “this is how
it’s going to be”
Promotes “Buy-In” The principal encourages school staff
willingness – i.e., “a reason or
relationship”.
Providing Resources All teachers receive resources
including general and special
education teachers.
Professional development for general
education teachers on special needs
services and strategies.
Scheduling Time to
Collaborate/Co-Plan
Many models are reviewed.
Time for co-planning is deliberate and
built into the schedule.
The schedule becomes more fluid.
Promotes Range of
Options
There are many delivery options.
Co-Teaching and Community Involvement
The best practices identified in the research study were co-teaching and
strong and effective parent-school relationships. Co-teaching is based on co-
ownership of the classroom between the educators responsible for instruction
and assessment. Collaboratively developing an IEP based on the academic and
common-core standards is a salient element of best practices. Administrative

12
input into developing a schedule which allows teachers to have co-planning
time is essential. Through mutual respect and collegial participation, co-teachers
learn to work well together to foster a passionate attitude toward their students.
Part of the school culture is the development of strong parent-school
relationships which enable the constituents to share strategies that foster student
success. Parents talking to teachers and teachers talking to parents create a
child-first philosophy where the “students’ faces drive the process”. The focus is
on continuous development of student strengths and the efficient delivery of
related services, which helps every child to reach his or her highest potential.
Table 6
Theme: Co-Teaching and Community Involvement
Co-Teaching
and
Community
Involvement
Co-Teaching Co-teachers work well together.
The teachers are passionate.
Building a reasonable schedule allows
for co-planning time.
Embedding IEP goals into the general
education curriculum is a key
component.
The teachers have co-ownership of the
classroom.
Standards-Based/Common Core
Parent-School
Relationships
This collaboration makes a difference
for a school.
Sharing strategies, talking, and
decision making is part of the process.
Child First The students’ faces drive the process.
Related Services All stakeholders are not focusing only
on student challenges but become
familiar with the aligned curriculum.
Conclusion
The data that was analyzed from the focus groups revealed the five
identified themes which enhance the sustainability of inclusionary practices in
an elementary school setting: (1) Public Service with a Moral Purpose, (2)
Culture and Commitment, (3) Data-Driven Decision Making. (4) Leadership
Qualities and (5) Co-Teaching and Community Involvement. The stakeholders
in this culture that is designed to promote inclusion have successfully
implemented the concepts and practices identified in the themes. This case
study provides an exemplary model for school leaders to implement and sustain
responsible inclusionary practices.

13
References
Anfara, V. A., & Donhost, M. J. (2010). Data-driven decision making. Middle School
Journal, November 2010, 56-63.
Boylan, M. (2016). Deepening system leadership: Teachers leading from below.
Educational Management Administration & Leadership, 44 (1), 57-72.
Council of Chief School Officers (2002). Expecting success: A study of five high performing,
high poverty schools. Washington, DC: Author.
Day, C., Gu, Q., & Sammons, S. (2016). The impact of leadership on student outcomes.
Educational Administration Quarterly, 52 (2), 221-258.
Fox. D. (2013). The principal’s mind-set for data. Leadership, January/February 2013, 12-
36.
Fullan, M. (2005). Leadership and sustainability. Thousand Oaks, CA: Corwin Press.
Fullan, M. (2004). Leading in a culture of change. San Francisco, CA: Jossey-Bass.
Fullan, M. (2002). Principals as leaders in a culture of change. Educational Leadership,
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Journal of Education, 118, 233-237.
Heifetz, R. (2003). Adaptive work. In T. Bentley & J. Wilsdon (Eds.), The adaptive state
(pp. 68-78). London: Demos.
Loehr, J., & Schwartz, T. (2003). The power of full engagement. New York: Free Press.
Matthews, D. E. (2015). Clearing a path for inclusion: Distributing leadership in a high
performing elementary school. Journal of School Leadership, 25, 1000-1038.
Ouchi. W. (2003). Making schools work. New York: Wiley.
Perkins, D. (2003). King Arthur’s roundtable. New York: Wiley.
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what purposes, and promoting and hindering factors. Teaching and Teacher
Education: An International Journal of Research and Studies, 26, 482-496.
Skalski, A., & Romero, M. (2011). Data-based decision making. Principal Leadership, 11
(5), 12-16.
Timperley, H. (2008). Evidence-Informed conversations making a difference to student
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(2010). Use of Education Data at the Local Level: From Accountability to Instructional
Improvement (Contract No. ED-01-CO-0040). Retrieved from
http://www2.ed.gov/rachstat/eval/tech/use-of-education-data/index.html

14
Vol. 16, No. 5, pp. 14-30, May 2017
The Mathematical Beauty
Van-Tha Nguyen
Phung Hung High School
14A, Street 1, Ward 16, Go Vap District,
Ho Chi Minh city, Vietnam
Ngoc-Giang Nguyen
Dr of Banking University Ho Chi Minh,
36 Ton That Dam, Nguyen Thai Binh Ward, District 1,
Ho Chi Minh city, Vietnam
Abstract. Mathematics is a science. However, Mathematics has
exceptional features that other sciences can hardly attain; for instance
the beauty in cognitive development, in Mathematics applied in other
fields such as Physics, Computer Science, Music, Fine Art, Literature,
etc… Mathematical beauty manifests itself in many forms and is divided
into many different categories. Mathematical beauty can be divided into
inner and outer beauty, or it can be categorized by fields or divided into the
beauty in method, in problem development, and in mathematical formulas.
The charactersitics of mathematical are repetition, harmony and Non-
monotonicity. Beauty is a vague concept. It is not easy to define, measure,
or estimate.
Keywords. Mathematical beauty, outer beauty, inner beauty,
mathematical formula.
1. Introduction
Mathematical beauty is the notion that some mathematicians generally use to
describe mathematical results, methods,… which are interesting, unique, and
elegant. Mathematicians often regard these results and methods as elegant and
creative. They are often likened to a good poem or a passionate song.
Mathematical beauty manifests itself in a variety of ways. It might be cognitive,
or it might be in the form of symmetrical shapes. It might be visible or hidden
away. This is a broad notion that involves a large number of aspects of life, in
science and in art.
2. Main results
2.1. The concept of beauty
It is quite difficult to define beauty. It is an aesthetic category. It affects the
human senses and brings about feelings of joy and excitement, and creates
perfection and meaningfulness.
Mohammed said: “If I had only two loaves of bread, I would barter one to
nourish my soul.” (Huntley, 1970)
Richard Jefferies wrote: “The hours when we absorbed by beauty are the only
hours when we really live … These are the only hours that absorb the soul and

15
fill it with beauty. This is real life, and all else is illusion, or mere endurance.”
(Huntley, 1970)
The Shorter Oxford English Dictionary states that, beauty is “That quality or
combination of qualities which affords keen pleasure to the senses, especially
that of sight, or which charms the intellectual or moral faculties.” (William, 2002)
Aquinas said “Beauty is that which pleases in mere contemplation” (Viktor,
2012)
According to an English proverb, “Beauty is in the eyes of the beholder.”
Whether something is beautiful or not is dependent on a person’s perception.
One might regard a painting as pretty and meaningful, while another regards
the same painting as ugly and meaningless. A beautiful painting or statue is not
likely to be loved by all. On the other hand, when it has earned the love of all
people, whether the painting is beautiful or not is of little importance. Beauty is
a vague concept. It is not easy to define, measure, or estimate.
2.2. The concept of mathematical beauty
There are many different views on mathematical beauty. It appears in a variety
of fields, from natural sciences to social sciences, and in everyday life. According
to Bertrand Russell, mathematical beauty is defined as follows: “Mathematics,
rightly viewed, possesses not only truth, but supreme beauty – a beauty cold
and austere, like that of sculpture, without appeal to any part of our weaker
nature, without the gorgeous trappings of painting or music, yet sublimely pure,
and capable of a stern perfection such as only the greatest art can show. The true
spirit of delight, the exaltation, the sense of being more than Man, which is the
touchstone of the highest excellence, is to be found in mathematics as surely as
poetry.” (Russell, 1919)
Edna St. Vincent Millay said “Euclid alone has looked on beauty bare …” (Huntley,
1970)
Rota wrote: “We think to instances of mathematics beauty as if they had been
perceived by an instantaneous realization, in moment of truth, like a light-bulb
suddenly being it. All the effort that went in understanding the proof of a beautiful
theorem, all the background material that is needed if the statement is to make any
sense, all the difficulties we met in following an intricate sequence of logical
inferences, all these features disappear once we become aware of the beauty of a
mathematical theorem and what will remain in our memory of our process of
learning is the image of an instant flash of insight, of a sudden light in the darkness”
(Viktor, 2012)
From our point of view, the aesthetic element of mathematical beauty depends on our
outlook on the perfection of methods, problems, as well as on the perspective of the
mathematical subject. Mathematical beauty is the result of discovering both the inner
and outer link between mathematical objects and phenomena.
2.3. The characteristics of mathematical beauty
2.3.1. Repetition
As stated above, “Beauty is in the eyes of the beholder”, but the creator of a problem,
a formula or a drawing can only be considered successful when his creations are
acknowledged as being beautiful.
The first characteristic of mathematical beauty is repetition.

16
Picture 1. Pythagorean Tree
A piece of music has repetitive beats in addition to choruses. A poem has repetitive
rhymes.
The most common and obvious feature of repetition is symmetry, which is when an
object has similar parts that can rotate or swap places without changing the overall
shape of the object itself.
There might be no other field in Mathematics that has as beautiful symmetrical
shapes as Fractals. The Pythagorean Tree above, as well as the following Mandelbrot
set, expresses the captivating beauty of repetition.
Picture 2. Mandelbrot set
2.3.2. Harmony
Harmony is an abstract concept. There is a combination of elements that gives off the
impression of being beautiful. Any two things are considered harmonious when they
are in tune with each other.
For example, if the movements of a swimmer (hands, legs, breathing, etc.)
correspond, his posture will look graceful and elegant; on the other hand, if his
movements are messy and out of tune, which indicates a lack of harmony, it is
difficult to stay afloat. In a painting, if the most important visuals are shoved into one
corner while the rest of the painting is blank, it is inharmonious, since the size of the
piece is not proportionate to the content. In a piece of music, it is common that there
are multiple notes sounding together at one time, rather than only one single note. If
all those notes resonate (in a physical sense), they sound pleasant and harmonious,
while separate notes not resonating make lousy sounds. A harmonious mathematical
problem must have a graceful way of wording, creating a number of meaningful
results. Take Fermat’s Last Theorem as an example: Prove that the Diophantine equation
n n n
x y z  has no integer solutions for  2n and , , 0.x y z A problem is
inharmonious when it has excessively complicated wording, and the solution uses too
many unnecessary tricks.

17
2.3.3. Non-monotonicity
Amateur “artists” can imitate famous works of art; for example, the Mona Lisa by
Leonardo de Vinci has been recreated numerous times by various artists. However,
no matter how similar they are, the copies are always inferior to the original in some
way. A great piece of art ought to have something new, different from its
predecessors.
Even in the same piece of art, if a single motif, however interesting it might be, is
repeated time and again, it can become monotonous. Therefore, it is necessary to
change, to create an element of surprise, in order to generate interest among the
audience. In Mathematics, applying a single method to a multitude of problems
would be far more monotonous than using different methods for different problems.
2.3.4. Human-relatedness
It is easier for people to grasp things that can be linked to information already existing
in their heads. Meanwhile, strange and random things that have no connection to
anything cannot stir up emotions within a person. That is the reason why many
paintings and sculptures have the human body as their main theme, since it is the
most familiar thing to people. A painting or a sculpture of a “Martian”, no matter
how beautiful, could hardly garner interest, as a “Martian” is a foreign concept to
humans.
Mathematical problems as well as topics have to be suitable for the person solving it.
If he has the ability to understand the results, his interest will be piqued, and he will
want to put more effort into his study. On the other hand, if he is unfamiliar with the
knowledge, it is easier for him to give up. According to Vygotsky, a person who
solves mathematical problems is only interested in the knowledge that is in his Zone
of Proximal Development. Problems that are too familiar are simple and
uninteresting, while ones that are too unfamiliar are too complex, and therefore also
uninteresting.
2.4. Categorizing mathematical beauty
There are many ways to categorize mathematical beauty. It can be divided into inner
and outer beauty, or it can be categorized by fields, such as mathematical beauty in
Art, Computer Science, Physics or Music, etc. Or it can be divided into the beauty in
method, in problem development, and in mathematical formulas.
2.4.1. Categorizing mathematical beauty according to method, problem
development, and mathematical formulas
Mathematical beauty in method has the following characteristics:
- A proof that uses the additional assumptions or previous results.
- A proof that is quite simple.
- A new proof.
- A proof based on original insights.
- A proof can easily generalize to solve similar problems.
- A proof that might be long, but results in new, interesting and insightful results.
The following example illustrates the beauty in method. Our new proof for the
Bouniakowsky inequality is as follows (published on Romanian Mathematical
Magazine):

18
Problem 1 (The CBS – inequality)
Given 1 2 1 2, , .., ; , , ..., .n nx x x y y y Prove that
    
22 2 2 2 2 2
1 2 1 2 1 1 2 2... ... ... .n n n nx x x y y y x y x y x y         
The new solution is as follows
Case 1
If 2 2 2
1 2 ... 0nx x x    or 2 2 2
1 2 ... 0ny y y    we have Q. E. D.
Case 2
If 2 2 2
1 2 ... 0nx x x    or 2 2 2
1 2 ... 0ny y y    then we let
2 2 2 2 2 2 2 2
1 2 1 2... ; ... (1)x n y nR x x x R y y y       
We have
1 1 2 2 1
2 1 2 2 1
3 1 2 2
1
sin sin ...sin sin
sin sin ...sin cos
sin sin ...cos
...
cos
x n n
x n n
x n
n x
x R
x R
x R
x R
   
   
  

 
 


 




and
1 1 2 2 1
2 1 2 2 1
3 1 2 2
1
sin sin ...sin sin
sin sin ...sin cos
sin sin ...cos .
...
cos
y n n
y n n
y n
n y
y R
y R
y R
y R
   
   
  

 
 








 
We have
2 2
1 1 1 1 2 2 1 1
1 1
sin sin sin sin ; sin sin cos cos .
n n
x y k k n n x y k k n n
k k
x y R R x y R R       
 
   
 
  
Thus,
2
1 1 2 2 1 1 2 2 1 1
1
2
1
| | sin sin . cos( )
. sin sin .
n
x y k k n n
k
n
x y k k
k
x y x y x y x y R R
R R
   
 

 



    



From this relation, we have:
1 1 2 2 3 3 1 1 2 2| ... | | |(2).n n x yx y x y x y x y x y x y R R      
From (1) and (2), we have
    
22 2 2 2 2 2
1 2 1 2 1 1 2 2... ... ... . ( . . )n n n nx x x y y y x y x y x y Q E D         
The equality happens if and only if 1 2
1 2
... .n
n
xx x
y y y
  
The beauty in problem development is the beauty of creativity in Mathematics.
Assimilating, specializing, and generalizing mathematical problems bring about a
deep understanding about a subject and help a person to discover the hidden link
between things. Through the results, the person will be able to realize the good and
exciting things that are normally hard to see.

19
The following example demonstrates the beauty in mathematical problem
development.
Problem 2
ABCD is a rectangle. Let M be the midpoint of AB , let H be the foot of the
perpendicular from C on BD, let N be the midpoint of DH . Prove that
0
90CNM  .
The following are some solutions
Solution 1 (The synthetic method)
From N , draw //NG DC . By the midline theorem, we have:
1
// , .
2
NG DC NG DC
Thus //NG MB and NG MB or NGBM is a parallelogram. We have
MB BC , so .NG BC Thus, G is the orthocentre of the triangle NBC . Thus,
.BG NC It follows ,MN NC i.e., 0
90 .CNM 
Solution 2 (The synthetic method)
Let P the midpoint of .CD We have 1 .PNB PMB PCB v   Thus, five points
, , , ,P N M B C lie on a circle with the diameter .MC Thus, we have 0
90 .CNM 
Solution 3 (The vectorial method)

20
We have
 2 2
2 2
1 1 1
. ( ) . ( ) ( ) . ( )
2 2 4
1
. . cos . . cos . . sin
4
1 1
( . . ) ( . ) 0.
4 4
MN NC AD BH DC HC AD BH HB BC DC
AD HB AD BH BC BH BH DC
HD
CH BH DC CH BH HD
DC
  
      
     
    
Thus, 0
90 .CNM 
Solution 4 (The trigonometric method)
In order to prove 0
90 ,CNM  we need to prove that MBCN is a concyclic
quadrilateral.
Indeed, we have
1 1
. .
2 2
tan tan .
BC HC BC HC
CAB BDC
AB HD BM NH
BMC BNC BMC BNC
    
   
Thus, MNCB is a concyclic quadrilateral, which is 0
90 .CNM 
Solution 5 (The coordinate method)
Consider the system of Cartesian coordinates Dxy as the above figure. We have
11
1 1(0 ; 0), ( ; 0), (0 ; ), ( ; ), ( ; ), ; .
2 2 2
yxb
D C b A d M d H x y N
 
 
 
The equation of the line MN is
1 1
1 1 11
1 1 1 1
1 1 11
1 1
2 2 2 .
2 2 2 2
2 2
2 2
. .
2 2
x x b
x x b y x bx
x y
y y y d y d
y d
y d y y dx
y x
x b x b
   
    
 
 
 
   
 
The equation of the line NC is
1 1 1
1 1 1
2
. .
2 2
x b x b y y
y x b
y y x b x b
 
   
 

21
The necessary and sufficient condition for MN NC is
2 2 21 1
1 1 1 1
1 1
2 2 2
1 1 1 1
2
. 1 2 3 2
2
2 3 2 .
y d y
dy y x bx b
x b x b
dy x y bx b

      
 
    
Consider the equality
2 2 2 2 2 2 2
1 1 1 1 1
2 2 2
1
2
1 1
1
2 3 2 2 3 2( )
2 2 2( )
.
cos cos .
dy x y bx b dy DH DH DH HC
dy DH DH HC
dy HC dy HD HB
y HB
ADB HBC
HD BC
        
    
   
   
This is obvious. Thus, we have MN NC , which is 0
90 .CNM 
Solution 6 (The transformative method)
Considering the vectorial rotation 0
90 , we have
' .
' . .
DA DA x DC
HB HC y HC


Since .
HB DA
x y k
HC DC
   
Thus
1 1
( ) ' ( ) .
2 2
NM DA HB NM k DC HC kNC    
Hence ,MN NC which is 0
90 .CNM 
Solution 7 (The complex method)
Suppose that ( ), ( ), ( ), ( ), ( ), ( ), ( ).A a B b C c D d M m N n H h
We have 2 ; 2 .m a b n d h   
We need to prove ( )m n i c n  
Or we need to prove ( ) 2( ) (2 ).
2
d h
m n i c m n i c d h

       
We have 4( ) 2(2 2 ) 2( ).m n m n a b d h      
Thus, the thing which needs to be proved is equivalent to
2( ) 4 2 ( ).a b d h ic i d h     

22
By the hypothesis, ABCD is a rectangle and CH BD , so we have
2
( )(1 ) ( )
( )
1 2
2 ( ).
b ic i b c i b c
b h i c h b h ic ih h
i
h b c i b c
    
         

    
The thing which needs to be proved is equivalent to
 
2( ) 2 4 2 2
2( ) 4 2 2 (1 )
2( ) 4 2 ( ) (1 )
2 2 2 ( 1) 4 ( )(1 ) ( 1)( )
a b d h ic id ih
a b d ic id h i
a b d ic id b c i b c i
a b d i ic b c i i b c
b c ib ic ib ic b c
     
      
         
          
       
Or we need to prove that
( 1) 0 ( ).a d i ic a d i c d       
This is obvious. Thus, we have ( )m n i c n   , which is ,MN NC or
0
90 .CNM 
By drawing byroads, we obtain the similar problems of the problem 2. If we take
the point K on the opposite ray of the ray CD such that C is the midpoint of
CK , then CN is the midline of the triangle DHK (the figure).
Thus, //NC KH .
By the proof 1 of the problem 2, we have BG NC .
From two these things, we have .KH BG
Thus, we have just proved the similar problem of the problem 2 as follow
Problem 3
Given a triang1e BCD with 0
90 ;C  the altitude CH . Let G be the midpoint of
.CH Let K be the point symmetric to D with respect to the point .C Prove that
.KH BG
Combining the problem 2 with the problem 3, we see that .KH BG On the
other hand //BG NM . Thus, .KH MN
We obtain the following problem

23
Problem 4
ABCD is a rectangle. Let CH be the altitude of the triangle .BCD Let M be the
midpoint of ,AB N be the midpoint of .DH Let K be the point symmetric to D
with respect to the point .C Prove that .KH MN
Using the parallel lines to AM or BN , we obtain problems which are similar to
the problem 2. Connect .AH Let E be the midpoint of segment ,BC F be the
midpoint of segment AH (the figure).
We have CNFE being a parallelogram, so // .EF CN Because CN BG ,
.EF BG Thus, we have just proved the similar problem of the problem 2 as
follow
Problem 5
ABCD is a rectangle. Let H be the projection from C onto .BD Let , ,G E F be
the midpoints of segments ,CH BC and ,AH respectively. Prove that .EF BG
We now combine the problem 2 and the problem 4, then we see that //NM BG
and .BG EF
From this, we have the new following problem
Problem 6
ABCD is a rectangle. Let H be the projection from C onto .BD Let , , ,M N E F
be the midpoints of , , , ,AB DH CB AH respectively. Prove that .MN EF
From the problem 2, we generalize it to the problem in the space as follow
Problem 7
SABC is a pyramid with ABC is isosceles at A . Let D be the midpoint of
segment .BC Draw DE such that ( ).DE AB E AB  Know that ( ).SE ABC
Let M be the midpoint of .DE Prove that ( ).AM SEC
Indeed, we have ( )SE ABC , so .SE AM

24
By the problem 2, .AM CE
From two results, we have ( ).
AM SE
AM SEC
AM CE
 
 
 
A generalization of problem 2 is as follows
Problem 8
ABCD is a parallelogram. Let H be the projection from C onto .BD Take the
points M on AB , N on HD and K on HC such that .
HN HK BM
HD HC BA
  Prove
that // .MN BK
The beauty in mathematical formulas is that mathematical results in different areas
are connected, which is hard to realize at the very beginning. This connection is
described as deep.
The example for the previous statement is the following Euler’s identity: 1 0.i
e 
 
Physicist Richard Fetnman has regarded this as “our jewel” and “the most
remarkable formula in mathematics”.
2.4.2. Categorizing mathematical beauty into inner and outer beauty
Outer mathematical beauty is the visual feature that affects a person’s senses. A
drawing, a formula, or a problem interests a person and makes him pay more
attention. This is the outer mathematical beauty.
In contrast to outer beauty, there is inner mathematical beauty. It is impossible to see
this beauty at first glance. The person has to spend a large amount of time
contemplating, thinking, and studying in order to discover the inner connection
between things, as well as the outer connection. When he has discovered these results,
he feels happy and satisfied.
Both inner beauty and outer mathematical beauty are important. However, the inner
beauty is harder to see, and a person has to have adequate ability to do so. In many
cases, the discovery of the outer and inner beauty of a mathematical problem is
synonymous to mathematical creativity.
For example, Fermat’s Last Theorem: Prove that the Diophantine equation n n n
x y z 
has no integer solutions for  2n and , , 0,x y z the outer beauty is the simplicity of
the equation, and the inner beauty is that it is an interesting and surprising theorem
about the combination of integers in a formula. These integers are dancing
harmoniously in the musical piece that is the formula, and this is the true beauty of
Fermat’s Last Theorem, expressed by mathematical symbols.
2.4.3. Categorizing mathematical beauty into different fields
a) Mathematical beauty in Computer Science
There is a close connection between Mathematics and Computer science. There are
two applications of Mathematics in Computer Science. The first one is the
mathematical theories models that are the basis for the development of Computer
Science. The second one is using Mathematics to solve Computer Science problems
and applications, finding mathematical theories and tools and putting them into use.
Mathematics makes Computer Science more beautiful and profound. Most problems
in Computer Science need the use of high to very high level modern Mathematics.
An example of mathematical beauty in Computer Science is the following algorithm

25
Problem 8
Write code that sums according to the expression       1 2 3 ... ( 1) .S n n
The algorithm for this problem is:
1. 0; 0.S i 
2. Input natural number n
3. While ( i n )
3.1. Increment i by 1
3.2. .S S i 
4. Repeat from step 2
5. End algorithm
However, for this problem, we can use Mathematics to produce a result much
faster. We have
( 1)
1 2 3 ... ( 1) .
2
n n
n n

       So the algorithm can be:
1. Input natural number n .
2. Output
( 1)
.
2
n n 
Above is only one example of mathematical beauty in Computer Science. Using
Mathematics, one can simplify a great number of programming problems. This
illustrates the close link between the two fields. Mathematics makes Computer
Science more beautiful.
b) Mathematical beauty in Physics
mathematics and Physics are closely tied to each other. Without Mathematics,
Physics wouldn’t have developed so rapidly. Many physicists have built their
theories on mathematical background. A typical example is Albert Einstein, who
built his General Theory of Relativity based on mathematical background and
non-Euclidean geometry. There is an entire subject called Equations of
Mathematical Physics for students studying Physics.
Einstein once remarked that, “beautiful theories” are often accepted more readily,
even if they have yet to be proven. An example is one of his own, most famous
equation, E = mc2. In a lecture at Oxford University in 1933, Einstein said that
mathematical beauty was what guided him as a theoretical physicist. In other
words, finding the simplest, most mathematically correct relationships, and then
applying theories about how they operate. According to Einstein, the pinnacle of
science is beauty and simplicity.
Newton’s laws can be expressed in the form of the following equation:
Beauty is eternal. So are beautiful equations. They are always true as they reflect
what is inherent in nature, although previously hidden. Everything has its own
law, which can be expressed in equation form and is comprehensible. One just

26
needs to spend time looking into it, like Einstein said “Look deep into nature,
and then you will understand everything better”. (Cesti)
c) Mathematical beauty in interior design and in everyday life
Geometric beauty can be observed in many aspects of life. An example of this is
ratios which are considered harmonious. A ratio in mathematics is a relationship
between measurements of different things or different parts in one thing. For
instance, the ratio between body measurements of someone who is 1.7m tall
with a 90cm chest, 60cm waist and 90cm hips is 170:90:60:90, which is equal to
17:9:6:9. If one wants to make a 17cm tall figurine looking exactly like that
person (or in mathematical terms, the figurine is geometrically similar to that
person), the bust-waist-hips measurements of the figurine must be 9cm, 6cm and
9cm respectively, which are the real person’s measurements divided by 10.
(Nguyen, T., D)
Homothety, as well as the Thales’ theorem is directly related to ratio and
similarity. Homothety preserves ratio and maps a straight line into a straight
line parallel to it. A cinema projector actually uses homothety to project films
onto a big screen.
While mentioning ratio, it is crucial not to leave out the golden ratio since it
appears in patterns in nature and plays an important role in human society.
Consider two segments, a is the length of the longer segment, b is the length of
the shorter segment and a + b is the sum of a and b. When these quantities satisfy


a b a
a b
, the ratio
a
b
is said to be the golden ratio. Solving a quadratic
equation gives the value of the ratio, which is 1.61803398875 (approximately
1.62). The Greek letter phi ( ) is used to represent the golden ratio.
Now, consider a golden rectangle (the ratio of the longer side to the shorter side
is  ), there’s some kind of connection to the natural essence in it. It appears that
compositions displayed in a golden rectangle can make people feel at ease. They
are also regarded as being well-organized and pleasing to the eyes.
Should the quantities a, b which satisfy the golden ratio be generally extended,
one of them is the Fibonacci sequence. The Fibonacci sequence is defined by the
recurrent relation 1 2  n n nF F F with    *
1 2 1,F F n N . This sequence is of
great importance because it represents numerous laws of nature. Arranging
rectangles based on the Fibonacci numbers in ascending order results in the
image of a spiral depicting the sequence - the golden spiral. The golden spiral
occurs a lot in nature.

27
In interior design, the use of the golden ratio mainly focusing on golden
rectangle can create spatial harmony. This ratio helps to design furnishings by
keeping their widths and lengths in proportion. Furthermore, it suggests which
part of the room should be decorated, which should be used to store the
furniture, etc... (Ahd)
d) Mathematical beauty in poetry
The four lines of this poem is very known:
A Book of Verses undernearth the Bough,
A Jug of Wine, A Loaf of Bread – and Thou
Beside me singing in the Wilderness –
Oh, Wilderness were Paradise enow!
The four-line stanza above is a poem written by Omar Khayyam in Persian in
the XI-XII centuries and was translated into English by Edward Fitzgerald (1809-
1883) in the IX century. Of the millions of people who know Khayyam’s poems,
only a few know that he was a brilliant mathematician and astronomer in his
time. In 1070, when he was only 22, Khayyam wrote a notable mathematical
book named Treatise on Demonstrations of Problems of Algebra. In this book,
“Pascal’s triangle” (a triangular array of Newton’s binomial coefficients) and a
geometric solution to cubic equations – the intersection of a hyperbola with a
circle - were found. Khayyam also contributed greatly to non-Euclidean
geometry with a book titled Explanations of the Difficulties in the Postulates of
Euclid. In the book, he proved some non-Euclidean properties of figures (though
it is unknown whether or not non-Euclidean spaces really existed).
In Persia, Omar Khayyam originally achieved fame in the role of an astronomer.
He was the one who introduced detailed astronomical tables (or ephemeris,
which gives the positions of naturally occurring astronomical objects) and

28
calculated the precise length of a solar year (365,24219858156 days). Based on
these calculations, Khayyam proposed the Jalali calendar. The Jalali calendar is
even more accurate than the present calendar.
People who’ve always seen mathematicians as impassive, unemotional people
might be surprised if they find these sayings of none other than the “dry”
mathematicians themselves:
“A mathematician who is not also something of a poet will never be a complete
mathematician.” - Karl Weierstrass.
“It is impossible to be a mathematician without being a poet in soul.” - Sofia
Kovalevskaya.
But why do mathematicians need to be “poets in soul”? It’s simply because
Mathematics is in accordance with poetry. The ultimate aim of both
Mathematics and poetry is creating high aesthetic values. Therefore, only
beautiful poems can last for a long time. The same goes for Mathematics; only
beautiful mathematical works with high value can withstand the power of time
and become classics. As Godfrey H. Hardy (1877-1947) once said: “Beauty is the
first test: there is no permanent place in the world for ugly mathematics”.
Both Mathematics and poetry are symbols of creativity. To create, one must have
inspiration. If a “muse” is a poet’s source of inspiration, a “maths’ muse” must
be the inspiration of mathematicians. Although they might serve different
subjects on different occasions, “muse” or “maths’ muse”, they are in fact the
same.
In Mathematics, not only can creativity result in new theorems, but also new
areas of mathematics growing over time. It’s no different in poetry, various
poetic styles have been created through the course of history as old styles are not
necessarily used.
Mathematics and poetry both require vivid imagination, perceptive creativity,
language coherence, a thorough grasp of grammar and rules and so on. The
language used in poetry is the normal language, while Mathematics has its own
language with special concepts and symbols. However, they both use language
to express ideas.
There’s an especially significant quality which Mathematics and poetry share,
that is succinctness. As British poet Robert Browning (1821 – 1889) once said: “All
poetry is putting the infinite within the finite”. Voltaire (1694 – 1778), a renowned
philosopher also said: “One merit of poetry few persons will deny: it says more and in
fewer words than prose”. Mathematics, too, is succinct. The mathematical concepts
and theorems can be very short, but comprehensive. It’s as if they contain a
whole universe in such few words and because of this, it’s not always easy to
understand Mathematics, or poetry. (Nguyen, T., D.)
e) Mathematical beauty in other fields
Mathematics has a tremendous impact on all life aspects nowadays, from natural
environment to social life. For instance, thanks to simulation modeling,
engineers can predict and solve many technical problems. Mathematics has
undoubtedly become extremely important in the modern world.

29
6. Conclusion
Mathematical beauty is a relatively abstract concept. There’s no one who can
quantify or measure it. It is also highly subjective. Whether or not a
mathematical problem is beautiful really depends on the perspective of the one
who solves it. Some fundamental traits that mathematical beauty possesses are:
repetition, symmetry, harmony, non-monotonicity and human-relatedness.
There are various ideas of categorizing mathematical beauty. It can be
categorized based on problem developing, problem solutions or mathematical
formulae. Beauty can be on the inside or outside. But no matter how
mathematical beauty is categorized, it’s undeniable that Mathematics is truly
beautiful and there needs to be more in-depth researches on the beauty of it.
References
Aharoni, R. (2014), Mathematics, Poetry and Beauty,
World Scientific Publishing Co.
Doan, Q., Van, N., C., Pham, K., B., Ta, M. (2017), Advanced geometry 11th, The Vietnamese
Educational Publishing House.
Doan, Q., Van, N., C., Pham, V., K., Bui, V., N. (2017), Advanced geometric exercises 10th,
The Vietnamese Educational Publishing House.
Dowson, M. (2015), Beginning C++ Through Game Programming, Cengage Learning PTR; 4
edition
Hoang, C. (1997), The arithmetic – The Queen of mathematics, The Vietnamese Educational
Publishing House.
Hoang, C. (2000), Solving elementary problems on the computer, The Vietnamese
Hoang, C. (2000), What is the fractal geometry?, The Vietnamese Educational Publishing
House.
Hoang, Q. (1997), Mathematical Romance, The Vietnamese Educational Publishing House.
Huntley, H., E. (1970), The divine proportion, A study in Mathematical Beauty, Dover
Publications, Inc., New York.
Nguyen, C., T. (2003), 74 stories on learning mathematics intelligently and creatively, Nghe
An Publishing House.
Nguyen, T., D. (2016), Maths and Arts, The Vietnamese Literature publishing.
Nguyen, X., H. (2015), The creation in Algorithms proggramming (Volume 1), The
Information and Media Publishing House.
Polster, B. (2004), Q.E.D. Beauty in mathematical proof, Bloomsbury USA.
Russell, B. (1919), The Study of Mathematics, Longman, p.60.
Sinclair, N. (2006), Mathematics and beauty, Teachers College Press.
Stewart, I. (2008), Why Beauty is Truth, First Trade Paper Edition.
Tran, V., H., Nguyen, M., H., Nguyen, V., D., Tran, D., H. (2017), Basic geometry 10th, The
Vietnam Educational Publishing House.
Tran, V., H., Nguyen, M., H., Khu, Q., A., Nguyen, H., T., Phan, V., V. (2017), Basic
geometry 11th, The Vietnamese Educational Publishing House.
Van, N., C., Pham, K., B., Ta, M. (2017), Advanced geometric exercises 11th, The Vietnamese
Viktor, B. (2012), A definition of Mathematical Beauty and Its History, Journal of Humanistic
Mathematics, Vol 2.
Vu, Q., L. (2015), The hapiness of creation, The Vietnamese Educational Publishing House.

30
William, R. T, (2002), Shorter Oxford English Dictionary, Oxford University Press; 5th
Edition.
The Vietnamese Childhood Mathematics magazine 2.
The Vietnamese Maths and Youth magazine.
Ahd. Retrieved from: http://www.ahd.com.vn/article/thiet-ke-noi-that/ty-le-vang-
ung-dung-trong-thiet-ke-noi-that-kien-truc-va-kieu-dang-my-thuat/
Diendantoanhoc. Retrieved from: https://diendantoanhoc.net/topic/5729-
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phuong-trinh-d-p.html
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nen-cach-mang-lich-su-am-nhac-533895.html
The address:
1. Dr student Van-Tha Nguyen, Phung Hung high school,
14A, Street 1, Ward 16, Go Vap District, Ho Chi Minh city, Vietnam
Email: thamaths@gmail.com
2. Ngoc-Giang Nguyen
Dr of Banking University Ho Chi Minh,
36 Ton That Dam, Nguyen Thai Binh Ward, District 1, Ho Chi Minh city,
Vietnam
Email: nguyenngocgiang.net@gmail.com

31
Vol. 16, No. 5, pp. 31-41, May 2017
The Implication of Distance Learning in
Competence-Based Maritime Education and
Training
Yanning JIANG
Deputy Director, Ministry of Transport,
No.11 Jiangguomennei Avenue,
Beijing, China
Quan LI
Lecturer, Dalian Maritime University,
1st Linghai road,
Dalian, China
Abstract. According to Section B-I/6 of the Seafarers‟ Training, Certification and
Watchkeeping Code (STCW Code), using distance learning and e-learning method to
train the seafarers may be approval by the contracting parties considering the standards
of training and assessment set out in section A-I/6 of the STCW Code (IMO, 2011).This
paper will focus on the implication of distance education in competence-based Maritime
Education and Training (MET).
Firstly, this paper will briefly introduce the background of competence-based MET,
which is connected to the real shipping practice and may be referred as standards or
performance based. Then this paper give the background of distance learning, which the
learners and instructors are in different places. It will also introduce the fast
development of the emerging technologies in the distance learning area.
Furthermore, this paper would discuss the implication of distance-learning in
competence-based MET. Some suggestions would be made in order to enhance MET,
including the revision of related regulations and domestic laws in order to recognize the
implication of distance learning in competence-based MET. A thorough quality
standards system that monitors the competence-based MET and the whole process of
distance-learning should be implemented.
Keywords: STCW; Competence-based; Maritime Education and Training;
Distance-learning; Quality standards system

32
1. Introduction
According to the statics of International Maritime Organization (IMO), human
errors contribute to about 80% of the maritime accidents. The poor competence
of seafarers is one of the main reasons that lead to the loss of life, large number
of injuries and extensive financial loss (Ziarati, 2006). Therefore, it is important
to have more reliable and effective MET system capable to overcome the
problem of human errors and be able to keep face with shipping industry
updates (Ahmed, 2016).
The International Convention on Standards of Training, Certification and
Watchkeeping for seafarers (STCW Convention) try to give the international
minimum standards for maritime education and training and the minimum
requirements for the competences of seafarers. In 1995, the STCW Convention
was totally amended to emphasis on the minimum competence of seafarers. In
2010, this the minimum competence of seafarers were clearly enhanced by newly
Manila Amendments of STCW Convention. The use of distance learning and e-
learning in MET is encouraged by the new amendments once again (Ruan, 2013).
Distance learning and e-learning for training of seafarers are suggested under
approval in Section B-1/6 of STCW Code.
In order to be well prepared for distance education in Maritime Training and
Education (MET), it is quite essential to understand its implication. As the
seafarers are on the first line to implement the conventions and regulations
developed by the shipping industry, therefore, to improve the competence of
seafarers by all means would help the shipping industry to enhance the safety of
navigation and marine environment pollution prevention.
This paper tries to explain the development of distance education in
competence-based MET and the future challenges that MET institutions would
face. Some advices were concluded for well preparing the distance education for
MET institutions and the Maritime Safety Administration (MSA) to improve
MET practices.
2. Competence-based MET
2.1 Competence
Competence has very border meaning and usually refer to the minimum
requirements of a worker to do the job. Competence can also be defined as the
worthy performance. That is to say, in order to fulfil or exceed the objectives for
their personal work, team, even the organization, it is the competence that
describes the basic skills, knowledge and attitudes that people have to obtain
(Gilbert, 1978). Therefore, the competences integrated with knowledge, skills
and attitudes in the learning process are the basis in education and training.
Some countries, such as England, Scotland, Wales, Australia and New Zealand
even integrated competence-based training into their national vocational
qualification system. Currently, there are two main competence-based training
model, the US model and the UK model. US model often put competences into a
training program and take the priority for how to use the competences during
the whole learning process. However, the UK model regard the competence as
the units of assessment of workplace of activity. The International Maritime

33
Organization (IMO) adapted the UK standards model of competence-based
training for STCW 95(Emad& Roth, 2008).
2.2 Competence-based MET
The STCW Code Section A-1/6 Training and assessment item 3 on Qualifications
of instructors, supervisors and assessors says:
“Each party shall ensure that instructors, supervisors and assessors are
appropriately qualified for the particular types and levels of training and
assessment of competence of seafarers either on board or ashore, as required
under the Convention…”
In the Code, the numerous tables each have four columns: competence is in
column 1, knowledge, understanding and proficiency (KUP) are in column 2,
methods for demonstrating competence are described in column 3 and column 4
shows the criteria for evaluating competence.
Competence-based MET is a kind of method to approach MET that focus on
seafarer can do, in respect to meeting specific standards rather than a seafarer‟s
achievement. In competence-based education, student progress through learning
objectives as they demonstrate mastery of content, at their own pace. It allows
them to show what they know as soon as they know it. It is focused on what
seafarers can do rather than on the course they have learnt (Deibinger &
Hellwing, 2011). The main difference between competence-based education and
traditional education are stated as following. First, for the curriculum, it can be
variable in class structure as stated in the STCW where the management level,
operate level and support level are listed. However, traditional education has
standardized structure regardless of prior knowledge. Besides, all the
competence must be mastered in competence-based education. In tradition
education, some concepts may not be mastered by the student
3. Distance education
3.1 Definition
Distance education is an educational process and system in which all or a
significant proportion of the teaching is carried out by someone or something
removed in space and time from the learner (UNESCO, 2016). Therefore,
distance education is a broad approach characterized by a high degree of
variation of space and time. There are a considerable number of researcher‟s
analyses that the concept of distance learning as additional mode of
acquiring/transferring knowledge and skills in maritime education (Ng et al.,
2009; Bauk et al., 2012; Buzadija, 2011; Flatcher and Dodds, 2003; Hanzu-Pazaraet
al., 2010; Kadioglu, 2008).
With the rapidly developing of information technology, the new electronic
teaching methods particularly through the internet, and different types of media
and platforms narrow the distinctions between generations.

34
3.2 Reasons for integrated distance education in MET
Distance education has its own advantages and disadvantages like any kind
other educational program. Before the distance education program start to enrol
students, carefully consideration should undertook by both students and
teachers in order to make sure that the distance education program meets the
minimum requirements illustrated in STCW.
(1) Distance education advantages
As the traditional classroom training program require the seafarers to fix time
and location, however, distance education program in MET can give a flexible
alternative on time and location. Distance education can also relatively reduce
the training fees and allow the students to learn without entering school. Besides,
with the highly change of maritime technology and legal requirement, many
refresher courses can also be delivered through distance education.
(2) Distance education disadvantages
However, there exist some disadvantages for the distance education in MET.
Lack of social interaction is one of the main disadvantages. Although the student
can have some interaction through email, chat rooms and other on-line platform,
however, it is quite different than traditional classroom education. Besides, not
all course can be offered online. Some courses directly with practical skills are
hard to deliver by distance education.
4. Distance education in competence-based MET
4.1 Development distance education program in competence-based MET
According to STCW Code Section B-1/6 Guidance regarding training and
assessment, each party has the responsibility to supervise the objectives and
outcomes of distance and e-learning programs meeting the minimum
requirements on the competences. Besides, unambiguous and direct instructions
should be made to the distance education program to help the trainees
understand the subject well. At last, professional and timely support through
web, email, telephone and all other possible means should be provided by the
teachers to help the seafarers systematically and effectively learning in the
program.
One of the challenges that the distance learning may pose to competence-based
MET is meeting the requirements of STCW in addition to the issue on quality
assurance (C.Swapp, 2001). Therefore, on the basis of guidance from STCW, this
paper develop the Figure 1 that shows the process of how to develop a distance
education program in competence-based MET.

35
Start
Identify/obtain
competency
standards
Determine the
features of DE for
CBMET
Design your CBMET
program
Develop
management
procedures
Prepare others for
CBMET program
Develop
assessment
procedures
Develop learning
activities
Get materials and
resources
Organize the
facilities
Ensure registration
as a training
provider and
accreditation of
your course
Continually monitor your DE for CBMET planning and development
Learner(s) enter(s) your DE for CBMET system
Fig 1: Development distance education program for competence-based MET
The crafting of distance education program in competence-based MET needs
much careful planning and designing and continuous quality monitoring during
the whole development process.
The first step is to identify the competences required in STCW Convention. As
the STCW convention divided the seafarers into 3 categories, which is
management level, operational level and support level. Each level would have
their own competences required in the STCW Convention, thus it is the first step
to identify and check the competences of the distance training program.
Secondly, it is also important to illustrate the course delivery tools to the
seafarers as different training providers may have different ways to delivery
their own subjects.
Then, the learning environment through distance education must be stated and
materials and resources should be provided for the learners. The program
should also give the detail information on how to assess and the minimum
requirement for passing the assessment.
At last, the management of distance education program and all the procedures
should be covered by a quality standard system.
4.2 Learning in distance education program
In distance education program of competence-based MET, the learner has more
responsibility in the learning process, however, the teachers must be qualified to
guide the learner as well as assessment procedures. Figure 2 shows the whole
process of learning in distance education program of competence-based MET
(Harris,1995).

36
Learner(s)
enter(s)your DE for
CBMET system
Continually monitor your DE for CBMET system
Learner(s)
follow(s)
instructions and
procedures
Learner identifies a
competence(s) to
work on
Learner engages in
various learning
activities in DE
Learner attempt
the competence
preferably in the
workplace
Trainer assess
learner
performance
against criteria
Learner self-assess
performance
against criteria
In the
competence(s)
achieved
Are all required
competences
completed
Learner exists with a
recognized credential
or statement of
attainment
Fig 2: Learning in distance education program for competence-based MET
Although the distance education program provides a self-paced mode of
learning and flexible delivery of competences under STCW, however, it does not
mean that learning is totally unstructured.
Firstly, it is very essential to identify which competences the learner wants to
achieve. This includes analysis how many competences already gained and
which still need to learn.
Secondly, the learner undertakes the learning activity engages in various
competences based performance is measured according to specific criteria stated
in STCW.
At last, assessment will be conducted to confirm whether all required
competence have been achieved. If some competences are already achieved, the
learner can step back to enroll this program again unless all the competences
listed in STCW are gained and relatively statement or recognized certificate will
be issued.
4.3 Example MET programs through distance education
4.3.1 Current MET programs through distance education
Singapore Maritime Academy (SMA) is deemed as the pioneer using distance
education in MET. Around 2000, SMA developed an e-learning program based
on CD-ROM to provide a training course regarding launching lifeboat.
Nowadays, more and more MET institutions and shipping companies have
involved in developing distance education programs in MET.
For Example, California Maritime Academy offers on-line training course for
maritime security awareness from 2006(Webster, 2006). Plymouth University in

37
UK have made a lot efforts in distance education and provide some course
delivered by distance education. Some Non-government organizations,
Classification Society and maritime training centre also provide some training
courses by distance education.
4.3.2 Establish a competence based training program through distance
education
Since the International Ship and Port Facility Code (ISPS) was agreed at the
International Maritime Organization in December 2002, the issue of security
amongst shipping and port industries has become of paramount importance, not
least due to the rise of piracy in several areas of the world (for example, the
Somalia Coast, the Gulf of Aden and the west coast of Africa).
The STCW 2010 Manila Amendments came into force on 1 January 2012. Ship
security training is becoming mandatory requirements for all seafarers. We have
developed a range of courses to meet the requirements of the STCW Convention
and ISPS Code.
 Module 1: Proficiency in Security Awareness(2 days)
Under the STCW 2010 Manila Amendments, this course shall be undertaken by
all seafarers employed or engaged in any capacity on ships which are required to
comply with ISPS Code (Table A-VI/6-1, STCW Code).
1. Contribute to the enhancement of maritime security through heightened
awareness
2. Recognition of security threats
3. Understanding of the need for and methods of maintaining security
awareness and vigilance
 Module 2: Proficiency in Designated Security Duties (3 days)
Every seafarer who is designated to perform security duties, including anti-
piracy and robbery-related activities, shall be required to demonstrate
competence to undertake the tasks, duties and responsibilities listed following
(Table A-VI/6-2, STCW Code):
1. Maintain the conditions set out in a ship security plan
2. Recognition of security risks and threats
3. Undertake regular security inspections of the ship
4. Proper usage of security equipment and systems, if any
 Module 3: Proficiency as Ship Security Officer (7 days)
Every candidate for a certificate of proficiency as a ship security officer shall be
required to demonstrate competence to undertake the tasks, duties and
responsibilities listed following (Table A-VI/5, STCW Code):
1. Maintain and supervise the implementation of a ship security plan
2. Assess security risk, threat and vulnerability
3. Undertake regular inspections of the ship to ensure that appropriate
security measures are implemented and maintained
4. Ensure that security equipment and systems, if any, are properly
operated, tested and calibrated
5. Encourage security awareness and vigilance.

38
5. Challenges and suggestions
5.1 Challenges
As current practice in MET, distance learning is not applicable and popularized
for mandatory certification of seafarers due to the lack of approved training
facilities, approved examination and assessment systems and quality standards
system to control the MET activities.
(1) Technical challenges
Distance education tools and technology were agreed to be effective
supplements for the traditional learning styles (Suresh& Anne, 2014). In recent
times, advanced software programs, associated hardware and simulation tools
have enable multi-mode distance learning options (Lokuketagoda,
Ranmuthugala and Jayasinghe, 2015). However, in some countries, it might be
very difficult to access the Internet. The limitation of computer and IT
technology to some extent may hamper the using of distance education. In such
a circumstance, the above provisions in the amendment constitute important
technical support, and more and more distance learning and e-learning activities
may come up then.
(2) Assessment in distance education
Assessment in distance education is also one of the key issues. Summative and
formative assessment are the two main categories of assessment based on the
function each serves and the timing of its application (William & Black, 1996;
Harlen & James, 1997). In traditional classroom education and training,
assessment can be through assignments, exams, and tests. It is important to
design valid and reliable competence-based assessment that resemble situations
that starting professionals or trainees can confronted with in real working life.
Competency-based assessment is a collection of evidence to demonstrate that the
seafarer can perform or behave according to the minimum competences in
STCW Convention (Sharon, 2012).
(3) Quality assurance
Regulation I/8 emphasizes that all training, assessment of competence,
certification, including medical certification, endorsement and revalidation
activities are continuously monitored through a quality standards system
(STCW, 2011).
Monitoring of all the processes of distance education program to improve the
accreditation standards, guidelines and procedures for quality assurance
regarding learning, faculty, students, scale and access should be fully
implemented.
(4) Competence standards
The core feature of a competence-based MET program is the minimum
standards of the competence. Therefore, it is quite essential to identify the
training needs under STCW. However, for a cadet pursuing his/her certificate
may not have all the mandatory courses available through distance education as
it is not suitable for all competences. For example, some practical skills cannot
learn and perform through distance education.

39
5.2 Suggestions
(1) Improve the legal framework
It is suggested that related administration to amend or improve the current law
and regulations under the requirements of STCW Convention to promote the
distance education as a recognized method for MET. Distance education for
seafarers has to be recognised as an authorised form of education (Jerzy & Pawel,
2014). IMO and the administration are responsible to arrange a proper transition
process to distance education(Gholamreza & Wolff, 2008).For example, it is very
important to develop a legal framework that allows certification and
examination system under distance education in MET.
(2) Promote international cooperation between MET institutions
Nowadays, the number of maritime institutions providing distance education
program is small after all. For the most of MET institutions, challenges will be
encountered during the implementation of distance education program in
respect of maintaining qualified maritime expertise, installation of training
simulators and equipment, etc. The theme of 17th Annual General Assembly of
International Association of Maritime Universities was working together: the
key way to enhance the quality of maritime education, training and research.
Therefore, co-operations and networking between MET institutions, thus, is
recommended in such a case. Likewise, the recognition of credits between two
different MET institutions may also be an issue to consider.
(3) Establish lifelong distance education platform
With the rapid development of maritime conventions and application of modern
maritime technologies, sustainable refresher learning would occur among the
whole shipping industry. Distance education may be the most flexible method to
provide this kind training. Therefore, it is suggested to establish lifelong distance
education platform with various and quality courses.
6. Conclusion
The STCW 78/10 Convention requires levels of knowledge, understanding and
skill for all seafarers on each level, and distance education is one of the methods
recommended to achieve this outcome. This paper firstly give the definitions of
competence-based MET as well as distance education. Some advantages and
disadvantages for integrating competence-based MET through distance
education were illustrated. Secondly, this paper also provides the developing
process and learning process in distance education of competence-based MET.
At last, some challenges in technical, assessment, quality assurance and
competences standards are detailed analyses and some related suggestions are
given for improving.
While distance education is growing, it may be „not as good‟ as the traditional
training programmes to some extent. This paper would welcome all maritime
academy to collaborate in coming up with solutions for seafarers training by
distance education in competence-based MET.

Vol 16 No 5 - May 2017

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