Developing a Problem-Solving teaching process through the experiential activitiess of high school students

42 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