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International Journal of Scientific Research and Management (IJSRM) ||Volume||5||Issue||12||Pages||7673-7680||2017|| Website: www.ijsrm.in ISSN (e): 2321-3418 Index Copernicus value (2015): 57.47, (2016):93.67, DOI: 10.18535/ijsrm/v5i12.14 Linda Kusumawardani, IJSRM Volume 05 Issue 12 December 2017 [www.ijsrm.in]
Page 7673
Student Thinking Process In Solving Open-Ended Problem Of The PISA Model Of Space And Shape Contents Based On Adversity Quotient (AQ)
Linda Kusumawardani
1
, Susanto
2
, Nanik Yuliati
2
1
Department of Mathematics Education, University of Jember Kalimantan Street 37, Jember 68121, Indonesia
2
Department of Mathematics Education, University of Jember Kalimantan Street 37, Jember 68121, Indonesia
3
Department of Elementary School Teacher Education, University of Jember Kalimantan Street 37, Jember 68121, Indonesia
Abstract:
The purpose of this research is to describe the thinking process of students with high AQ (Climber), medium AQ (Camper), and low AQ (Quitter) from grade VIII-C students of Junior High School 2 Jember in solving open-ended problem of PISA model of Space and Shape based on Polya's problem- solving. This research is a descriptive research with the qualitative approach. Data collection methods which are used are tests, interviews, and questionnaires. In this research, data analysis is done using descriptive analysis. The data analyzed in this research is the answer sheet for the student about the problem of mathematical problem-solving test and interview result. The results of the analysis show that each subject is different based on the thinking process. A Student with high AQ (Climber) shows a lot of equilibrium in it through the stage of assimilation and accommodation. Students with medium AQ (Camper) show a lot of assimilation and accommodation conditions are also slightly disequilibrium. Students with low AQ (Quitter) show a lot of disequilibrium, assimilation, accommodation and a little equilibrium
.
Keywords:
Adversity Quotient (AQ), Thinking Process, Problem Solving, PISA Model Tests of Space and ShapeContents.
1.
Introduction
The position view and role of mathematics according to Wijaya (2012:5), it is mathematics as a way to think. This view begins with how the logical and systematic character of mathematics play a role in the process of organizing ideas, analyzing information and drawing conclusions among data. In learning and studying mathematics and solving math problems, students do the thinking process until finally, students get answers. However, in fact, in learning mathematics, this thinking process receives less attention from teachers. Whereas, one of the goals in learning mathematics is to help the students to reveal how the process goes in his mind when the students solve problems, just as the teachers ask the students to tell the steps that are in their mind. It is necessary to know the errors that occur and tidy up the network knowledge of students. This is necessary because if the students have good thinking skills then the students will be better at understanding and mastering the mathematical concepts that have been studied. Santrock (2011:7) says that thinking involves the activity of manipulating and transforming information in memory. Thinking to form concepts, reasoning, thinking critically, making decisions, thinking creatively, and solving problems. While Hudojo (in Siswono, 2002: 45) states that in the process of learning mathematics, there occurs a process of thinking. In the process of thinking, people will establish relationships between parts of the information recorded as the meanings, then the concepts are inferred. 2.
According to Piaget (in Solso, 1995) says that the thought process is very important because knowledge can only be built into one's mind. Piaget (in Solso, 1995) explains that one's cognitive development has three elements, namely: cognitive content, cognitive function, and cognitive structure. Cognitive content is what a person knows. Cognitive function indicates the nature of the intellectual, such as assimilation and accommodation that is constant and continuous throughout cognitive development,
Linda Kusumawardani, IJSRM Volume 05 Issue 12 December 2017 [www.ijsrm.in]
Page 7674 while the cognitive structure is the organization of schemata. The development of cognitive structures can only work if the student assimilates and accommodates stimuli from his environment. Furthermore, the thought process is examined based on the assimilation and accommodation framework of Piaget (in Solso, 1995). He says that when someone interacts with the environment (including math problems), there will be a process of adaptation. At the time of adaptation, a person experiences two cognitive processes, namely assimilation or accommodation. 3.
In the process of thinking, there is a process between incoming information and the schema (cognitive structure) in a person's brain (Subanji and Supratman, 2015: 62). The experience or new information which is received will be adjusted through the process of assimilation or accommodation (Simatwa, 2010: 366). The cognitive process that occurs when one integrates a new perception, concept or experience into a scheme already in his mind is called assimilation (Subanji and Supratman, 2015: 64). Whereas, accommodation is the process of integrating new stimuli through the creation of new schemes or changing old schemes to adjust to problems encountered (Subanji and Supratman, 2015: 64). Mathematics is closely related to the problem. When a person is faced with a problem, one's cognition experiences a disequilibrium (unequal) condition that is usually characterized by questioning what is the problem, how to solve a problem, or why it may be so. In the presence of disequilibrium will lead to the process of assimilation and accommodation. Both of these processes take place continuously until equilibrium occurs (equilibrium) (Susanto, 2011: 65). At each
Polya’s settlement step, one will experience a
thought process based on the assimilation and accommodation framework. In learning mathematics with problem-solving, students are certainly faced with a problem both open and closed issues. Polya (1973) suggests four stages of problem-solving in mathematics, namely: (1) understanding the problem, (2) making a plan, (3) implementing the plan of resolution, and (4) looking back at the complete solution. Mathematical learning that utilizes the use of open questions provides an opportunity to further explore students' thinking skills comprehensively. According to Takahashi (2006), the open-ended problem is a problem that has many solutions or settlement strategies. The current math learning is still procedural. Students are not yet accustomed to solving non-routine problems so high-level thinking skills such as their mathematical problem-solving skills have not been trained. Though this ability is required by students to be able to develop, to understand the concepts, and to be able to solve mathematical problems. Furthermore, we should use the PISA results to improve the quality of our mathematical education and learning. Based on the PISA survey, it shows that students are weak in geometry, especially in understanding space and shape. One of the causal factors is that students are poorly trained in solving problems with characteristics such as questions on TIMSS and PISA. Based on the above ideas, the PISA model is very suitable to know how far the thinking process of students in solving the open-ended problems PISA model. In solving math problems, everyone has different ways and styles of thinking because not everyone has the same ability to think. From here, Adversity Quotient (AQ) is considered to have an important role in solving the problem. According to Stoltz (2000), AQ is one's intelligence in coping with and overcoming adversity. To illustrate, Stoltz (2007: 18) borrows the terminology of mountaineers into three parts: climber, camper, and a quitter. Thus, Stoltz (2007: 139) divides AQ into three categories: (1) high AQ (climbers) is a group of people who always strive to reach the peak of success, continue to survive and struggle against various obstacles, (2) medium AQ (campers) is a group of people still have a desire to respond to the challenges that exist, but they quit because they feel that it can no longer be easily desperate and (3) low AQ (quitters) is a group of people who lack the will to accept challenges in life, preferring dodge, easy to despair, easily give up tend to passive and lack of determination to reach the peak of success. Based on the description above, this research is
needed entitled “
Student Thinking Process In Solving Open-Ended Problem Of The PISA Model Of Space and Shape Contents Based On
Adversity Quotient
(AQ).
2. Research Methods
In this research type of research which is used is descriptive research with a qualitative approach. In this study, there are three students who are selected as research subjects of each category of high AQ (climber), medium (camper) and low (quitter) in class VIII-C. The research instruments which are
Linda Kusumawardani, IJSRM Volume 05 Issue 12 December 2017 [www.ijsrm.in]
Page 7675 used in this research are a researcher, Adversity Response Profile (ARP), test, interview guide, and validation sheet. The researcher is the main instrument that can not be replaced with other instruments because researchers act as planners, gatherers, analysts, interpreters and eventually they become reporting research results. Whereas, others are supporting instruments. Data collection is begun by providing an Adversity Response Profile (ARP) questionnaire that is used to group students into three categories: climber, camper, and quitter students. The ARP used is a valid instrument to measure people's response to adversity. The next step, giving the three open-ended problems of PISA model to three students who have been selected in each category. Prior to the three subjects, the open-ended model of PISA must be tested for validity and reliability test in order to obtain valid and reliable research results and it is obtained from valid and reliable instruments. Test validity is given by validation questionnaires to one lecturer S2 and two lecturers of mathematics education of Universitas Jember while the reliability test is given by the whole problem that is to be done by one class student in the different class that is class VIII-A SMP Negeri 2 Jember. From the results of validity and reliability test, it is obtained that the problem is valid and has the high reliability that can be used in research. The final step is an in-depth interview to find out the students' thinking process in solving the open-ended problems of PISA model. The researcher analyzes the data by exposing data from test results and interviews that have been done. This analysis is the main objective of the study, which aims to describe students' thinking processes with high AQ (Climber), medium AQ (Camper) and low AQ (Quitter). This analysis is done per step by using Polya's stage. In this research, it is used triangulation method and triangulation investigator. Triangulation method is done by comparing information or data between test and interview result. Then, the triangulation of investigators conducted by requesting the help of other observers who always attend when the research is conducted.
3. Result and Discussion
The results of the AQ questionnaire analysis of 36 students are obtained by 3 students classified as climbers, 15 students as campers, and 1 student as quitters. Furthermore, the researcher selects students from each AQ category to be the subject of the study. The selected subjects in each category solve three open-ended problems of PISA model based on Polya's step which will be analyzed the thinking process. Here is a description of students' thinking process with high AQ (climber), medium (camper) and low (quitter) in solving three problems which are given in accordance with the Polya's solving stage. Analysis of thought processes is based on the results of written tests and interviews in solving problems of the PISA model. The results of the analysis show that each subject is different in the thinking process. a.
Thinking Process of Climber Students (S1) in Solving Mathematical Problems of PISA Model
Figure 1:
Answer result Climber students (S1) in step 3, implementing the plan of resolution S1 in solving open problems will experience a series of thought processes in accordance with the
Polya’s solving step. At
understanding the problem, S1 experiences high assimilation on each issue capable of deciphering what is known, what is unknown, and what is asked spontaneously and correctly. However, in problem 2, S1 slightly experiences disequilibrium. This is visible when S1 works on the problem, S1 seems silent for a moment and experiences confusion in understanding the intent of the problem but it did not last long. In addition, S1 experiences accommodation while trying to understand the intent and linkage of information with the given problem and producing
Linda Kusumawardani, IJSRM Volume 05 Issue 12 December 2017 [www.ijsrm.in]
Page 7676 the correct answer. This shows that in understanding the problem, S1 integrates a new stimulus through the establishment of a new scheme to adapt to the problems at hand. Thus, S1 also uses the accommodation thinking process in understanding the problem. At the planning stage, S1 feels high assimilation by writing down the answers as she knows when she matches during the interview, S1 gives the correct answer also using the accommodation thinking process. S1 is able to make a connection to the problem of the given PISA model. Thus, it has been able to devise a plan to solve the problem when he is investigated through interviews, S1 is able to give the reason smoothly and correctly until finally there is equilibrium. For example, S1 mentions the concept by using the square rectangle formula, but she tries to match the number of seeds on the problem, the result is less appropriate. Then, he does by making the dots as seeds on the smaller size permissions and finally gets the right answer. From here, S1 changes the existing scheme in his mind to be modified with the information that she gets in the matter. Furthermore, she is able to do the calculations correctly to get the correct answer from the problem. The situation occurs because the provided stimulus is compatible with the scheme that has been formed in her mind.
Figure 2:
Answer result Climber students (S1) in step 3, implementing the plan of resolution
When she is interviewed, S1 experiences accommodation when she is asked to provide reasons for choosing these steps until finally, she gets the correct answer. In addition, she can also answer the initial steps that must be done correctly to find a variety of alternative answers to the given problems until there is equilibrium. From the initial reply given, she is able to express other answers, such as looking for measures related to rectangles, trapezoids, and parallelogram, searching for a maximum number of viewers by changing the sizes used and she can search for a smaller area of land given. Initially, S1 cannot write down the solution neatly. However, she is investigated during the interview, S1 is able to explain fluently even though S1 is initially less skilled at communicating what he has thought, even though it is actually true. However, it can be overcome because he is trying to explain well what is on his mind. Thus, S1 uses the process of assimilation and accommodation thinking in implementing the plan of resolution. At the look the back, there is a thought process experienced by S1. It is able to recheck the solutions that are obtained through recalculation and can ensure that the results that are obtained are correct. S1 is no longer experiencing disequilibrium because S1 has already understood the desired intent in step 4 even in school learning activities, check back step is rarely done. Thus, at the step of rechecking, S1 is through a high assimilation process to the equilibrium state. When she is interviewed and asked whether she feels confused and has difficulty in the step of checking again, the S1 answer is not confused because there is already a description of it, based on step 3. Thus, S1 uses a high assimilation thinking process at the recheck stage. b.
Camper Student Thinking Process (S2) in Solving Mathematical Problems PISA Model

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