Abstract. Creativity is human copious activity. It is one of the goals of teaching
mathematics at secondary school. At the age of secondary students, the way of thinking
has changed into an intellectual, logical and formal one. Mathematics is a subject which
seeks the understanding of all patterns permeating both the world around us and the mind
within us. Experiential Learning Approach (ELA) on Mathematical Creativity at secondary
school offers students a lot of opportunities to experience creativity. This article goes
further into the effects and the positive impacts on Mathematical Creativity of ELA among
Secondary School Students.

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HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1075.2017-0124
Educational Sci., 2017, Vol. 62, Iss. 6, pp. 19-27
This paper is available online at
EFFECTS OF EXPERIENTIAL LEARNING APPROACH
ONMATHEMATICAL CREATIVITY
AMONG SECONDARY SCHOOL STUDENTS
Nguyen Huu Tuyen
Bac Ninh Pedagogical College
Abstract. Creativity is human copious activity. It is one of the goals of teaching
mathematics at secondary school. At the age of secondary students, the way of thinking
has changed into an intellectual, logical and formal one. Mathematics is a subject which
seeks the understanding of all patterns permeating both the world around us and the mind
within us. Experiential LearningApproach (ELA) onMathematical Creativity at secondary
school offers students a lot of opportunities to experience creativity. This article goes
further into the effects and the positive impacts on Mathematical Creativity of ELA among
Secondary School Students.
Keywords: Experiential Learning Approach, Mathematical Creativity, Experiential
transformation, Experiential learning model, Teaching Mathematics at secondary school
1. Introduction
Experiential Learning Approach (ELA) originated from ancient times with the typical
example: the Confucius educational phylosophy (551-479 BC) with the conception "What I
do, I will understand", Xocrat (470-399) paid a special attention to learning by doing specific
work. When Vygotsky (1896-1934) - a Russian psychologist - presented the idea of "the nearest
developmental area" where it contained personal experience, and served as a basis for learners
thanks to previous learning and experience. In the 19th century, spychologists and educators in the
world such as John Dewey, Kurt Lewin, Jean Piaget, lev Vygotsky, David Kolb, William James,
Carl Jung, Paulo Freire, Carl Rogers. . . [7] deeply and systematically carried out the researches
on ELA in some aspects. Experiential learning theory, officially made public for the first time
by David Kolb in 1971, was quite comprehensive as a learning approach based on experience,
accumulation of experience and experiential transformation. It has been applied in more than
thirty fields and disciplines since then. Its principles, definition and process have been widely
used to develop and popularize the curriculum of secondary schools, university education and
professional training [8]. Nowadays, experiential education is one of the tendencies of advanced
educations. According to the draft curriculum for secondary education, experiential activity is
not only a subject - one of three main elements of the new secondary curriculum- but also an
approach to innovate teaching methods in all of the subjects to achieve educational objectives.
Mathematics at secondary schools has a lot of opportunities to apply Kolb’s theory of Experiential
learning approach. Hence it brings about creative thinking to students - the core activity of teaching
Received date: 25/3/2017. Published date: 10/6/2017.
Contact: Nguyen Huu Tuyen, e-mail: nguyenhuutuyen.bacninh@moet.edu.vn
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Nguyen Huu Tuyen
mathematics at secondary school. Experiential learning is similar to "learning through doing",
but the conception of this theory states that learning is a process creating new knowledge based
on real experience (an interactive environment, real life models, knowledge, skills, approaches,
done mathematical tasks, surrounding people’s experience) (Concrete experience). Basing on
the evaluation and analysis of the available knowledge and experience, students first observe,
analyse and reflect (Reflective observation). Then students feel their ways, predict, choose the
suitable solutions to given tasks and find out new knowledge (Conceptualization). Finally, students
actively apply in new situations (Active Experimentation). Experiential learning is considered to be
contrary to academic learning - a process to get knowledge through studying a matter without direct
experience. Up to present, the application of experiential learning approach in some countries from
all over the world as well as the announcement of the domestic and overseas researches on this field
have only focused on extra -lesson activities in the society and out of the mathematical content in
curriculum.
This research states the conception of ELA in teaching mathematics at secondary school. It
also analyses and makes mathematical creativity and the effects of ELA on mathematical creativity
clear. Moreover, this reasearch analyses the mentioned content above by an illustruting example,
which is the most difficult and desired problem now because it has not been clearly mentioned and
there has not been any document published. On the basis of the example, teachers can examine to
design a lot of lessons in the mathematics’ curriculum of secondary education.
2. Content
2.1. Mathematical creativity
According to Mann, creativity has been proposed as one of the major components to
be included in the 21st century education [3]. There are various ways to define mathematical
creativity. Among them, there is a commonly agreed definition that mathematical creativity is
a novel way of thinking characterised by fluency, flexibility, originality and elaboration [4-7].
According to this, fluency is the number of responses in which a learner can give to a mathematical
question, the number of related ideas. It shows the ability to give several different responses to
a mathematical task that relates to the coherence of the ideas, flow of association and use of
basic and universal knowledge [3, 5]. Flexibility is the shift in the caterories in the responses to a
given mathematical task; it is the number of catergories or classes in a learner’s pool of ideas and
responses. In other word, it may be defined as the ability to generate a wide range of ideas and a
variety of solutions [4, 5]. Originality is defined as statistical infrequency. It is characterised by
a unique way of thinking and unique products of mental activity [5]. This is when responses are
novel compared to others to the same mathematical task. Elaboration is the ability of a learner to
produce detailed steps [8]. It is building on other ideas. It refers to the number of details in solving
a problem [3].
Mathematical creativity is an essential aspect in the formation and the development of
mathematical talent [3] as well as constructing mathematical knowledge. Mathematical creativity
is a construct involving divergent and convergent thinking, problem finding and problem solving,
self expression, intrinsic motivation, a questioning attitude and self confidence [9]. Therefore, the
main goal of mathematics education is the "mathematisation" of the children’s thinking. Clarity of
thought and pursuing assumptions to logical conclusions is the central to mathematical enterprise
introduced a criterion for measuring mathematical creative ability [9, 10]. He addressed both
convergent thinking characterised by determining patterns and breaking from established mind
set and divergent thinking defined as formulating mathematical hypotheses, evaluating unusal
mathematical ideas, sensing what is missing from a problem and splitting general problems into
specific sub problems.
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Effects of experiential learning approach on mathematical creativity among...
2.2. Experiential learning in teaching mathematics
"Experiential education" has been introduced to the modern educations in a lot of countries
in the world since the early 20th century. In 1977, with the foundation of Association for
Experiential Education (AEE), Experiential education was officially recognised and publicly
stated. At the summit conference of the United Nations about "2002 stable development" UNESCO
approved the program named "Teaching for a stable future". In that, an important part of
"Experiential education" was introduced, popularised and widely developed. Nowadays, UNESCO
acknowledges "Experiential education" as a bright prospect in coming decades. The opinion of
learning through experiencing has become an education mainstream way of thinking associated
with the psychologists and educators such as John Dewey, Kurt Lewin, Jean Piaget, lev Vygotsky,
David Kolb, William James, Carl Jung, Paulo Freire, Carl Rogers. . . These days the idea "Learning
through doing, learning through experiencing" was still an American typical education philosophy.
According to International Association for Experiential Education "Experiential education is a
catergory consisting of a variety of approaches. There, teachers encourage learners to experience,
then reflect, summarize to reinforce their knowledge, develop skills, form living values and
develop their own potential, contribute to community and society actively". Educators here can
be teachers, volunteers, guiders, trainers or psychological doctors etc. This shows the simplicity,
the diversity, the popularization and the application of "Experiential education”. In my opinion,
Experiential learning in teaching mathematics at secondary school is a process that students
themselves directly feel their ways, predict and find out new mathematical knowledge basing
on their own experience. Students gradually transform their learning experience to widen their
knowledge, to broaden the value system and to change their lifestyle.
Experiential learning approach asserts that acquisition of skills and constructions of
knowledge by the learners is direct result of experience. The learner is said to have the ability to
select and participate in experiences that will further their growth [11]. Experiential learning can
exist without a teacher and relates solely to the meaning making progress of the individuals’ direct
experience. This is in agreement with Roger’s opinion (1969) [12], he asserts that experiential
learning is equipvalent to personal growth and change. According to Newsome, Wardlow and
Johnson (2005) experiential learning approach elevates students’ recognition levels, increases use
of critical thinking skills and therefore enhances students’ ability to obtain, retain and retrieve
knowledge hence increased achievement. Learning is a cycle that begins with experience continues
with reflection and later leads to action which itself becomes a concrete experience for reflections.
David Kolb (1984) developed a learning model based on experiential learning which is often
known as the Kolb’s learning model [2]. It is the inheritance and the suppliment of Lewin’s
model of action research and laboratory training, of Deway’s learning model and Piaget’s learning
and concious development model. Kolb’s opinion is consistent with the models above. It closely
connects with the intellectual initiation in Deway, Lewin and Piaget’s works. Moreover it puts the
emphasis on the central role of experience in learning process. It aims at "processing learning" with
clearly defined stages and actions. Through this process of learning, both teachers and learners
can continuously improve the learning levels. This is one of the models that are widely used in
envisaging curriculums, planning lessons, in training and instructing for tertiary education courses.
In this process, Kolb recommended that the order of experiential learning model is followed,
but it is not necessary to start at the certain stage of the process. However, Kolb based on an
important assumption of learning - knowledge originates from experience. Knowledge needs
creating (or re-creating) by learners not remembering what has existed. Therefore, Kolb’s process
should be used correctly to gain the greatest effect.
Kolb and other researchers further realized that the choice of the point to start and the bias
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Nguyen Huu Tuyen
The Kolb’s experiential learning model
in favor a certain stage reflect the learning method of each learner (or each subject). The basic
point of view of this learning model based on experience is that learners need to reflect their own
experience then generalize and formularize the ideas so that they can apply these ideas in real
world to see whether they are right or wrong, useful or useless etc... After that, the learners have
got new experiences to get started for the next learning process. The processes are repeated until
the planned objectives can be achieved. This process requires learners have discipline in learning
by planning, doing, reflecting and applying theory.
Detail description of the stages of Kolb’s process.
Concrete Experience: Learners can have some experience by reading material, attending
lectures, watching videos relating to the topic that they are learning or trying following the
instructions of some introductory lessons, or self - performing with the teachers’ assistance. All of
those factors help students have a certain experience that then becomes an important input material
of the learning process. This stage provides the basis for the learning process in which the lessons
engage the individual personally; learning relies on open mindedness and adaptability rather than
a systematic approach to stituation and problem. There is involvement in personal experiences
and an emphasis on feeling over thinking. Creative work involves a certain amount of pre-existing
domain knowledge and its transformation into new knowledge [13]. The role of the teachers is
describing the activity and learners do it. However, the most important experience is the one that
learners can feel on their own.
Reflective observation: Learners need to analyse and evaluate the existing facts and
experience. There must be reflection in this stage that is learners self- consider the experience
carefully to see how they feel, whether they can understand the ideas or not, whether it is
logical or not, whether they choose the right way or not etc... In learning process, reflection
deeply implies that learners always ask themselves and give answers to a question: "Is this way
going on well?" and purely use their intuition to answer the question. In the reflection process,
learners take down the consideration in a natural way on their own. Hence, learners not only draw
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Effects of experiential learning approach on mathematical creativity among...
themselves some lessons but also have new orientations to make the next stage more interesting and
effective. For teaching, teachers use the same technique for both teaching and learning so as to gain
effective sollutions and activity. There are some kinds of reflection that apply more deeply than
consultation, analysis or generalization from different sources and bring forward the evaluation
of the experience. When reflecting, learners actively take part in the learning process, therefore
learning is helped. If reflection is good enough, it will help learners improve, enhance and regulate
the learning growth. Learners develop logical thoughts, verbalize those thoughts relate to others in
the group and compare experiences and opinions. The applications of classroom knowledge in the
context of real life situations are the focus of learning [3]. The role of the teacher is to promote the
atmosphere of acceptance of individual participants and diverse thinking, to design activities that
help learners to construct meaning and take the initiative becoming more creative in mathematical
learning.
Conceptualization: After experiencing detail observation and deep consideration, learners
conceptualize their gained experience. New ideas are derived from experiences. This stage is very
important for the experience to transform into knowledge and a set of ideas kept in the brains. In
this stage, learners assimilate and distil the observation and refections into a theory. The students
come to understand the general concept of which their concrete experience was one example by
assembling their experience into a general model. Abstract conceptualization requires student
to use logic and a systematic approach to problem solving. There is an emphasis on thinking
manipualiton of abstract symbols and tendency to neat and precise conceptual systems. The
students share their reactions and observations about their experiences. The learners at this stage
provide answers to the question arising from the experiences by providing solutions and making
generalizations. According to National Council of Mathematics Teachers (2000), the abilities to
solve a problem with several strategies or the abilities to reach different answers in a specific
task are valuable evidences of the development of mathematical reasoning. Without this stage,
the experiences can not be improved and developed into a more helpful new level, but it is only
concrete experience gained during the learning and practicing process. Abstract conceptualization
ends with our making plan for the next activity in the coming time. This stage usually proceeds the
last stage naturally (reflective observation) by answering the important questions arising during
reflective observation stage. It can be considered as the conclusion of the previous stage and the
next one will be the stage to verify its accuracy.
Active Experimentation: In the last stage, the learners came to a conclusion based on
reality with closely associated basis and thoughts. This conclusion can be regarded as a theory
and we have to apply it in the real world to test. This is very vital for the constitution of real
knowledge. According to Kolb and some constructivists, universal truth needs comprehensing or
verifying. This is the last stage for us to confirm or disclaim the concepts of the previous stages.
In this stage, students use the theories they developed during the abstract conceptualization stage
to make predictions about the real world situations. They connect subject matter and life skills
discussion to the larger world. Students’ action and wishes are new concrete experiences. The
learners are expected to use or test the conclusion, generalizations and solutions in new situations
(Kolb&Kolb, 2008). The learner involvement facilitates personal growth and skill development,
giving a measure of empowerment to the learners [2].
2.3. Effects of experiential learning approach on mathematical creativity
among secondary students
The use of Experiential learning approach on teaching mathematics among secondary
students gives learners an opportunity to become more creative in mathematics by constructing
meaning and having a critical mathematical thinking. Experiential learning approach also helps
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Nguyen Huu Tuyen
students to develop abilities to solve problems with several strategies or the ability to reach different
answers in a specific task which are valuable evidences of the development of mathematical
reasoning. Mathematical Creativity at classroom setting is the process that results in novel and
insightful solutions to a given problem and the formulation of new questions and possibilities that
allow an old problem to be regarded from a new point of view [3, 14]. There is a need to come up
with the teaching methods that will enhance Mathematical Creativity. It is experiential learning.
Experiential learning offers a critical link between the classroom and the real world. The findings
of this study are in agreement with those of Casanovas, Miralles, Gomez and Garcia [3, 15] who
noted that science learning based on the experiential learning model promotes students’ instruction
of scientific knowledge and increase the fluency and flexibility of ideas generated. Mathematical
Creativity is the ability to solve problems or to develop thinking structures, taking into account the
peculiar logical deductive nature of the discipline and of the fitness of the generated concepts to
integrate into the core of what is important in Mathematics. According to Stoyanova and Ellerton
creative thinking ability and exp