Abstract. In recent years, the concepts of Problem Solving Ability, Creative
Learning, Experiential activities, Real World Problem, Modeling have been no more
strange to managers and teachers in high schools. With the aim of improving the
quality of education and the progress of students, this study clarified the capacity of
teachers of mathematics teachers in teaching problem-solving skill through creative
experiential activities, real-world linkage, and mathematical modeling. From the
results of theoretical and practical studies, we would like to offer suggestions for
improving the quality of mathematics instruction in high schools.

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HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1075.2018-0167
Educational Sciences, 2018, Volume 63, Issue 9, pp. 42-52
This paper is available online at
DEVELOPING A PROBLEM-SOLVING TEACHING PROCESS THROUGH
THE EXPERIENTIAL ACTIVITIESS OF HIGH SCHOOL STUDENTS
Tran Viet Cuong1 and Le Hong Quang2
1Department of Training, Thai Nguyen University of Education,
2Xuan Giang High School
Abstract. In recent years, the concepts of Problem Solving Ability, Creative
Learning, Experiential activities, Real World Problem, Modeling have been no more
strange to managers and teachers in high schools. With the aim of improving the
quality of education and the progress of students, this study clarified the capacity of
teachers of mathematics teachers in teaching problem-solving skill through creative
experiential activities, real-world linkage, and mathematical modeling. From the
results of theoretical and practical studies, we would like to offer suggestions for
improving the quality of mathematics instruction in high schools.
Keywords: Creative learning, activities, real world problem.
1. Introduction
The problem-solving experiences that students encounter in schools have no longer fit
into today's world. Solving mathematical problems concerns a lot about how to go from a
particular situation where the goals and solutions are clearly defined to mathematical
knowledge. Moreover, the challenging of the problems encountered in many professions
now involve mathematical thinking, model relationships and rules. In view of Lesh, Doerr
(2003) [1] and Farzad Bahmaei (2011) [2], the importance of mathematics has increased
in global market change to meet the the demand for mathematically talented workforce.
Nowadays we always use problem-solving skills. In addition, most of us have to plan
daily, make business decisions and manage our budgets. All these events require logical
thinking and problem solving skills (Weidemann, 1995. ) [3]. Problem solving is recognized
as an important living skill that involves a range of processes including analysis,
interpretation, reasoning, forecasting, evaluation, and reflection (Anderson, 2009) [4]. For
these reasons, one of the goals of teaching mathematics is to educate students become
problem solvers. Therefore, problem solving is considered as a key objective for
mathematical education in the school.
Received September 8, 2018. Revised November 24, 2018. Accepted November 30, 2018.
Contact Tran Viet Cuong, e-mail address: tinhquang80@gmail.com
Developing a problem-solving teaching process through the experiential activitiess of high school students
43
In the US, it was highlighted in the reform texts of the Mathematics Teachers Council
(NCTM, 2000) [5] as a major requirement for changing the form of mathematical
education. NCTM (2000) [5] states that students should have the opportunity to apply a
variety of appropriate strategies to solve problems, to monitor and reflect on the problem
solving process in mathematics programs. Similarly, Kilpatrick, Swafford and Findell
(2001) [6] argue that problem solving provides an important context for students to learn
numbers and other mathematical terms. Problem solving ability will be enhanced when
students have the opportunity to solve problems themselves and see problems resolved.
So solving the problem is very important as a way to do, study and teach mathematics.
Therefore, preparing the mathematics curriculum with the main objective of problem
solving seems very important.
In addition, we find that almost problems arises from real world contexts, through
experiential activities, exploring, experimenting hypotheses, researching the relationship
between theory and practice. From there, they gain knowledge, promote creativity, self-
learning, self-discovery. Thus, creative experiential activity should be considered in the
teaching of mathematics in high school.
2. Content
- Objectives of the study: This research aims to develop a process for problem-solving
teaching through students’ experiences in order to help high school math teachers
improve their teaching capacity.
- Research questions: This study aims to answer the following questions: What is
problem-solving teaching through students’ learning experiences in mathematics instruction? How
to develop a problem-solving teaching process through student activities?
- Research Methods: Study theory and practice; Make survey teaching mathematics in some
high schools; Interview experts, educational researchers and students.
In details: Making survey with 120 students, 50 administrators and teachers of mathematics
in 5 high schools (Xuan Giang High School, Soc Son Hanoi; Nguyen Hoang High School, Thanh
Hoa; Le Quy Don High School, Ha Noi; Le Hong Phong High School, Dong Nai; High School for
Gifted Students, Hanoi National University of Education).
- Data analysis: Survey results were statistically and proportionally evaluated, from which
the research team analyzed and made conclusions.
2.1. Exchange and discussion
2.1.1. Literature reviews
Since the 1960s, teachers have become accustomed to the term "problem-solving
teaching," but so far they has not mastered in using it. It is thought that the term
"problem" can be misleading as the problems which teacher raises for the student to solve,
so some people proposed to use "suggest” instead of "problem". In fact, firstly it’s
necessary to practice for students the ability to detect problems from a learning situation
or in practice. This is a very important possibility for each individual and not easy to
obtain. On the other hand, success in life depends not only on the ability to detect in a
timely manner the problems that arise in practice but also on the ability to properly solve
the problems posed.
Tran Viet Cương and Le Hong Quang
44
The authors (Kilpatric, et al., 2001) [6] said that problem solving ability is enhanced
when students have the opportunity to solve problems themselves and see problems being
solved. Problem solving also provides opportunities for teachers to assess students’
achievement; George Polya (1945) [7] showed the idea that problem-solving can be
taught as a practical art, such as playing the piano or swimming. Polya finds solving the
problem as an exploration and discovery exercise to describe the possibilities needed to
successfully investigate new problems. He encouraged mathematical presentation not as a
complete set of facts and rules, but as an empirical and inductive science. The purpose of
problem-solving teaching as art is to develop the student's ability to become skillful and
enthusiastic problem solvers, independent thinkers who are capable of dealing with open,
unclear issues.
According to NCTM (2000) [5], problem solving is an integral part of studying
mathematics. Students should work frequently with tasks in which solutions are unclear
and problem solving requires more flexibility than algorithms are available. Solving
problems is not only a math learning goal but also a major means of doing so. Students
need regular opportunities to build, cope and solve complex problems that require great
effort and encourage them to think. When students think about new issues, they not only
learn to solve similar problems, they can also develop new skills and ideas.
Polya (1945) [7] argued that problem solving consists of four stages: problem
understanding, planning, plan implementation, and review. Lajoie (1992) defines
mathematical problem solving such as problem modeling, hypothesis-building and
verification by data collection and interpretation using sample analysis, graphing, or
calculating. and computer. This definition focuses on the processes of construction,
investigation and verification, but it does not include the key elements inherent in the
review phase of Polya, including methods of assessment, result interpretation. The
revision phase includes activities such as:
- Verify results
- Test alternative methods
- Determine the validity of an argument
- Apply results or methods to solve other problems
- Explain the results
- Generalize the solution
- Create new problems to solve
Reviewing may be the most important aspect of problem-solving teaching because it
provides students with the opportunity to learn about problem-solving and other related
problems.
Many studies indicate that mathematical learning that is embedded in practical
contexts helps learners acquire knowledge effectively. Modeling is a way for students to
access knowledge, apply knowledge gently and excitedly. They learn through practical
issues or models close to real life. Maaß (2006) [8] argues that the model is one of a
number of fact-based learning activities that involve simplifying a complex real-world
situation, creating a model, working mathematically with it, and explaining the results in
the actual situation. Mathematical models are used to explain real-world situations or non-
mathematical situations in mathematical formats (Fox, Watters, 2005) [9]. For example,
Developing a problem-solving teaching process through the experiential activitiess of high school students
45
charts, tables and equations are used to model and interpret understandably complex
relationships between different phenomena.
In our opinion, solving a problem is a process, a continuous activity in which we use
what we have known to discover what we haven’t known yet. It involves overcoming
obstacles by creating hypotheses, checking predictions, and providing satisfactory
solutions.
Problem solving includes three basic functions: finding information; create new
knowledge; make decision.
Thus, problem solving is an important part of the math curriculum. It assumes that
students may be responsible for their studies and may act alone to solve problems, resolve
conflicts, think alternatives. It provides students the opportunity to use new knowledge
acquired in real-life experiences and to help them work at a higher level.
2.1.2. Teaching problem-solving through experiential learning
The experiential activity was actually introduced into modern education from the
early 20th century. In the United States, in 1902, the first "Corn Growers Club" for
children was established. The goal is to teach students how to plant corn, to apply science
and technology to agriculture through practical work of farmers. More than 100 years
later, this club system became the core of the largest youth development organization in
the United States, pioneering the application of learning through working, experience.
In England, in 1907, a British general in the British Army organized a first Scout
camp. This activity later developed into Scouting around the globe. Scouting is a type of
experiential activity, paying particular attention to outdoor practice activities, including:
camping, life skills in the forest, survival skills, campfire, collective games and sports.
Until 1977 with the founding of the Association for Experiential Education (AEE),
Experiential Education was officially recognized in writing and widely publicized. It was
a stepping-stone in 2002 when "Teaching and Learning for a Sustainable Future" was
accepted at the United Nations Conference on Sustainable Development, of which
important components of experience were introduced, popularized and developed
extensively.
Today, Experimental Education is continuing to evolve and form a vast network of
individuals, educational institutions and schools around the world to apply. UNESCO also
sees Experimental activities as a bright future for global education in the coming decades.
In Vietnam, the concept of experiential activity in schools is practical education
activities which are carried out in parallel with teaching activities in schools. Through
experiential activities real-world issues will be addressed. These activities are
intended, organized, conducted on or off campus to develop and enhance personal
qualities and potentials, nurture the sense of self-reliant, at the same time care, share
with the people around. When participating in experiential activities students are
exposed to the role of subject, self-motivation, self-awareness and creativity, and
participate in solving problems in order to set up and develop living values and the
necessary capacities for students.
Tran Viet Cương and Le Hong Quang
46
(Jenna Stadsvold, 2017) [10] state that, Experiential learning is the process of
learning through experience and is both an active and reflective process. Experiential
learning focuses on gaining knowledge firsthand instead of simply hearing or reading
about a topic, but just because an activity is hands-on does not mean it is experiential
learning. A key element of experiential learning is reflecting on the experience and
applying the concepts. Often the actual learning happens after the activity is complete and
participants are reflecting and discussing what they experienced. Participants should be
prompted to reflect on what they are doing and why the activity is relevant or important.
We state that, experiential learning is a process through which students develop
knowledge, skills, and values from direct experiences outside a traditional academic
setting. Thus, it can be said that experiential activity is part of the teaching process and it
has an organic relationship with problem solving in which the instructor encourages the
learner to engage in practical activity, then summarize to enhance understanding, develop
skills, shape living values and develop oneself potential, and proceed to contribute
positively to the community and society.
Experimental activity is also based on a theory (Edgar Dale 1946) which states: We
remember 20% of what we read; 20% of what we hear; 30% of what we look at and 90%
of what we do.
- The outstanding features of problem solving through experiential activity
+ Students have opportunities to develop comprehensively their intelligence,
emotion, physical, skills and social relationships in the process of participating in
problem solving.
+ The model is designed to require learners to be creative, self-confident, and
satisfied with the results achieved when solving problems.
+ Through experiential learning, students are actively engaged in problem solving:
questioning, exploring, experimenting, performing, taking responsibility.
+ The results of experiential activity are not as important as the implementation
process and the lessons learned from solving the problem in that context.
+ The results belong to each person and provide the basis for learning, experiencing,
knowing how to solve problems in the future.
+ Relationships are formed and perfected: relationship between each student himself,
students with others, and students with the world around him.
- The process of teaching problem-solving through experiential learning
Based on the study of the problem-solving learning process, through experiential
activities on mathematical models in the real world of authors such as Mette Sofie
Olufsen (2003), Hermann Schichl (2017), Cheng (2001), LH Quang (2016) [11, 12], we
have proposed a process (see Figure 1) for problem-solving teaching through
experiential learning.
Developing a problem-solving teaching process through the experiential activitiess of high school students
47
Table 1. Describe process steps
Step Description
Find out the
problem
It is important for students to understand the nature of the
problem and its related goals. Encourage students to solve
problems themselves.
Describe the
difficulty
Students should be aware of any difficulties that may prevent
them from successfully completing their duties. What is the
immediate problem? Encourage students to report, analyze
difficulties, this is an important step
Propose and
implement
After understanding the nature and parameters of a problem,
students will need to choose one or more appropriate strategies
to solve the problem. Students need to understand that they have
many strategies available and there is no strategy to solve the
whole problem. Here are some possibilities to solve the problem:
- Visual description of the problem.
- Provide students with an opportunity to participate in a number
of test methods and the results may be completed or not
completed. However, it should be understood that this is not a
single approach to solve the problem but rather an attempt to
gather some preliminary data.
- Create a table of contents of the job and describe the requirements.
This table is an orderly arrangement of the data. When students have
the opportunity to design and create information boards, they begin to
Real-world problem Describe the difficulty
Group solutions
Figure 1. Modeling cycle (by T.V. Cuong, L.H. Quang)
Find out the problem
Other real-
world
problems in
life
Propose solutions
Result evaluation
Test a solution
Look for a good solution
and complete the task
Result
Tran Viet Cương and Le Hong Quang
48
understand that they can organize most of the data related to the
problem.
- By using manipulations students can develop models in which
the components of a problem are more recognizable and
intuitive.
- Search model: Finding suitable models is an important
problem-solving strategy because many similar problems exist in
predictive models.
- Define a model: Considering the model is an important strategy
for solving the problem, since so many models propose a
problem.
- Create a systematic list; Record information in a list is a
process used quite frequently to plan implementation, to identify and
solve problems. Encourage students to record their ideas in the list to
determine the accuracy, pattern, or similarity between the elements in
the problem.
Test a solution - Try a solution. It will be very important for students try a
solution when working through a strategy or a combination of
strategies
- Take note accurately and up-to-date thoughts and activities of
group. Recording data collected, predictions, and strategies used
are an important part of the problem solving process.
- Try to work through a chosen strategy or combination of strategies
until it becomes clear that it does not work, it needs to be modified, or
it brings unwanted data. As students become more competent problem
solvers, they will feel comfortable to refuse strategies they think are
not appropriate in the search for solutions.
- Carefully follow-up of steps as part of a solution. Encourage
them to carefully evaluate and monitor their progress, be careful
when giving results
- Taking the time to think about the problem, scientists rarely
come up with a solution when they firstly approach the problem.
Result evaluation It is extremely important that students have many opportunities
to evaluate their problem-solving skills and the solutions they
generate when using their skills. Normally, students are too
dependent on teachers to evaluate their performance in the
classroom. However, the process of self-assessment is not easy.
It includes risk tolerance, self-assurance, and a degree of
independence. The results also depend heavily on environmental
factors, so experiential activities help students have a good
connection between theory and practice.
Extend the real
world problem
Practical examples also encourage students to be aware of the
choices they make and how they fit into a larger social context.
Developing a problem-solving teaching process through the experiential activitiess