Proceeding International Conference on Mathematics, Science, and Education (ICoMSE). Malang State University.
Malang
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The Importance of Cognitive Psychology
in Mathematics Learning and Students’ Creativity
Wahyudi
1, a), St. Budi Waluya
2, b)1Fakultas Keguruan dan Ilmu Pendidikan, Universitas Kristen Satya Wacana Salatiga, Indonesia 2
Pendidikan Matematika, Pascasarjana Universitas Negeri Semarang, Indonesia
a)Corresponding author: yudhi@staff.uksw.edu
Abstract. Mathematic has an important role in human life, therefore mathematics must be taught well and correctly. The success of learning mathematics is influenced by several factors such as thinking ability, social interaction, and more. Cognitive psychology is one of the critical success factors in learning mathematic. Cognitive psychology is the study of how people perceive various shapes, how they learn language, why they remember some facts but forget others and think about information. Thus cognitive psychology is a branch of science that learns about how people see, learn, think about something as information, feel, and remember, learning language and others, where the brain will perform main function, that is thinking as mental activity. Mental activity itself related to the ability to remember and socio culture where the human brain receives information and store it as memory system that is useful in solving problem. The ability in problem solving depends on how the ability of thinking itself works. The good problem solving ability with many alternatives shows a high degree of creativity.
INTRODUCTION
This The role of mathematics is so great in human life. Mathematics is the servant of science, queen of science and language of science (Gauss, 1963: 366). This role that makes mathematics is called as the basic science which underlying other science. According to Anthony & Walshaw (2009: 147) the mathematics has a very broad scope, it has a key or an important role in human life to face various areas of life either personal, social, or wider community. Seeing its great role in human life, it is necessary to learn mathematics properly since elementary school.
Zevenbergen (2004: 22) argued that there are three theories that influence how students can learn and understand mathematics correctly. It is the cognitive theory that focuses on students thinking process, socio-cultural theory as a social environment in learning mathematics, and social theory (socio critical theory). Zevenbergen (2004: 23) and Ojose (2008: 26-27) argued that cognitive psychology provides an important role in mathematics, especially in the cognitive development of students. As Piaget's research results provide a significant impact in learning including learning mathematics. Stages of cognitive development of children provide direction to the teacher to be able to teach mathematics correctly. In addition Piaget's views on the assimilation and accommodation process provide insight into how students gain their knowledge (Zevenbergen, 2004: 22; Hudojo, 1988: 48-49).
Constructivism also provides an overview of students' mathematical knowledge because they reflect their physical and mental actions. Learning mathematics is a social activity so that there is a dialogue and interaction in learning and constructs mathematical knowledge, Zevenbergen (2004: 23). In constructivism, language and dialogue become important in the learning environment so that they can communicate with learning partners and group members in constructing the mathematical concept, Zevenbergen (2004: 23-24).
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The Importance of Cognitive Psychology in Mathematics Learning and Students’ Creativity
end up providing a different interpretation with what the teacher wants. In any case, the mathematical communication process in this case does not work well. In addition to language and communication, the learning environment also influences the success of students in learning including learning mathematics (Zevenbergen, 2004: 25; Orton, 2004: 195-196).
Some of the things described above are part of cognitive psychology. Looking at some of these examples shows the importance and influence of cognitive psychology in mathematics. This is in line with research conducted by Laski, Reeves, Ganley & Mitchell (2013: 63-64).
This study aims to describe the importance of cognitive psychology from theory and real practice in mathematics learning and students' creativity. This research provides insight to us that teachers need to learn about the results of cognitive development research, because it will provide insight for teachers about the development of students, what is needed in learning so that they can prepare the learning well and can teach the well prepared lesson so that students can understand mathematics correctly and avoid misconception.
METHOD
This is a qualitative research using literature study as the research approach. The participants of this research were 29 students taking the basic mathematics concept. Six students were taken to have further interview. The research data was collected by doing literature study, conducting tests and interviewing the participants. To analyse the data, researcher used triangulation method, i.e. comparing the result of literature study, tests and interview.
RESULTS AND DISCUSSION
According to Sternberg (2012:3) “Cognitive psychology is the study of how people perceive, learn, remember, and think about information. A cognitive psychologist might study how people perceive various shapes, why they remember some facts but forget others, or how they learn language”. According Matlin (2009:2-3) “Cognitive psychology is influenced by research in cognitive neuroscience and artificial intelligence. Cognitive psychology is also part of an active interdisciplinary area known as cognitive science”.
From these two opinions, it can be concluded that the definition of cognitive psychology is a branch of science that learns about how people see, learn, think about something as information, feel, and remember, learning language and others where the brain will perform its main function, that is thinking as a mental activity. Thus cognitive psychology is closely related to the workings of the human brain. Because closely related to the workings of the human brain, the learning process of a person is closely related to cognitive psychology.
All information received by the brain does not just pass by or directly responded as an action but there is something to be saved. The work of the brain that must store information or entered data is called memory system. How the memory system works depends on one's ability to remember and store the information. An example given by Matlin (2009: 95) below.
Try each of the following mental multiplication tasks. Be sure not to write down any of your calculations. Do them entirely “in your head.”
1. 7 x 9 = 2. 74 x 9 = 3. 74 x 9 =
If we have to remember the multiplication of the problem in our brain then not everyone can remember it in a short time. Similarly, we are asked to do arithmetic-related problems, read complex sentences, work on reasoning tasks, or solve complex problems. Often we forget in what way to solve the problem, even though it has been studied, even though we had ever done it. For example, a student is given the following questions: Michael and Michelle travel through the same road and same time departing from two different cities, Tegal and Solo. Michelle left from Solo at 06.00 WIB to Tegal, her speed is 60 km/h and Michael's speed is 80 km/h from Tegal to Solo. If the distance between Solo to Tegal is 280 km, when and where they will meet on the way?
Proceeding International Conference on Mathematics, Science, and Education (ICoMSE). Malang State University.
Malang
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distance that can be taken every hour for each kid in order to determine the time they meet. In this way they could determine the time which is they both met after walking for 2 hours. The other two students use different ways, they use their memories that is related to the equation of motion of objects. Based on the memory of the two students, they use the equation s = v.t where s is the distance, v is the speed and t is the required time. But only one student is able to manipulate equations so that they can solve the problem. One student cannot solve the problem until the end, it can be caused by a limited memory related to it, or the student has no idea to solve it. This example provides an overview of the role of memory, representation and object manipulation to solve math problems.
Another part of cognitive psychology is the attention and consciousness. Attention is one of the components of human's mind (Sternberg (2012: 7). Attention becomes something important in a learning process including learning mathematics. When a person's attention is disturbed during their activity, it will most likely to affect the result. (Matlin 2009: 211) For example if a student draws a trip map from home to college, he tries to use mental imagery and cognitive maps that he has. At the time of drawing, this student is invited to chat or asked something continuously, then his attention (there is a distraction in the form of audio) which disturbed their attention and consciousness. This divides their attention and awareness so the drawing won't be done well. With the distraction, the work of the brain won't be maximal and will affect the results done by the organs in charge.
The brain becomes a very important human organ. The brain is the organ that controls our thoughts, emotions, and motivations and has the highest hierarchy of positions (bosses) and its work will also listen to and obtain information from other organs before a decision is made into act (Sternberg 2012: 42; Matlin, 2009: 13). The field of science that studies this part is called Cognitive neuroscience. This field of science is a field of study that connects the work of the brain and other aspects of the nerve system to process information or incoming data and will ultimately decide the actions or behaviours to be act out.
An optimal brain work will give a person a chance to have a good working memory, remind the good and even able to even pour back the memory that has been stored in verbal information or in the form of visual or drawing and writing. With conditions like this, someone will be able to learn many things well including learning mathematics.
On above example, it was about someone who used memory, representation and manipulation; they will eventually solve the given mathematical problem. This ability is called the problem solving ability. The solving process involves identifying problems, defining problems, formulating problem solving strategies, organizing/gathering problem solving information, allocating resources, monitoring, and evaluating (Sternberg 2004: 460). Slightly different from the Polya (1945) solving steps (in Tall, D, 2002: 18) the problem-solving process is done in 4 stages of understanding the problem, preparing the plan, executing the plan, and looking back. As an example of the problem given above:
Michael and Michelle travel through the same road and same time departing from two different cities, Tegal and Solo. Michelle left from Solo at 06.00 WIB to Tegal, her speed is 60 km/h and Michael's speed is 80 km/h from Tegal to Solo. If the distance between Solo to Tegal is 280 km, when and where they will meet on the way?
Students are able to identify the problem that is the time and distance when the kids met. From the identified problems, they will determine the solving plan (some use their memory with equations of motion, there are also plans by drawing using image representation and manipulation). The plan is later implemented to get the results; the final part is that they recheck their work. When students choose and work on problem-solving options, their creativity in problem solving can be identified using several ways with new approaches, new perspectives. Judging from the demands of the activities undertaken in the problem-solving process, it appears that there is a creative activity in managing and solving the problem (Orton, A., 2004: 25; Tall, D., 2002: 18; Sternberg 2004: 480). If someone has good problem solving skills then have good creativity as well. Thus the problem-solving ability requires creativity so that the problem can be solved with many solutions.
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The Importance of Cognitive Psychology in Mathematics Learning and Students’ Creativity
Creativity is the result of students' creative thinking has been incorporated as one of the major components in 21st century education (Mann, 2005). Therefore, the contemporary curriculum emphasizes the development of creative thinking skills for students (Vale, I. & Barbosa, A., 2015; Sternberg, R. J., 2006). Creative students can be built by the role of creative teacher as well (Aktaş, M.C., 2016: 43). Currently the learning of mathematics has undergone a change that was originally it is centred on the teacher, now it is centred on student activity (more of the student activity) (Orton, A., 2004: 1-2).
Creativity can focus on the process and also on creative products. Creativity can also be interpreted as a continuous action, as a process of bringing something new into something. Every individual has a creative potential in a particular (special) case of Gardner (1993). It is also expressed by Leikin (2008) that a person has a creative potential in certain things eg in the field of mathematics.
Based on the opinion of these experts, it shows that creativity has a very important role in human life. This ability can be achieved through problem-solving process with interesting problems in learning. By making the students to stay creative in solving problems, it will improve their ability to make decisions and their reasoning abilities. The example in the question given at the beginning gives an overview of how the student takes the decision in choosing a problem-solving strategy and the solving step that must be done. This requires a good reasoning ability to be done by students. So the choices taken are the most efficient way and solution.
To be able to build students' creativity, it is required a learning that is able to provide opportunities and chances for students to develop their creativity in solving problems. Mathematics is close to humans, mathematics is part of human culture (Hersh, R., 1997: 22-23). Ernest said that mathematics is part of social reality (Hersh, R., 1997: 228). Based on the opinions of these experts then to learn mathematics must be linked with the context of human life and human culture so that mathematics memorable, imagined, represented, manipulated and assembled in cognitive maps so that learners learn mathematics without having burdened with mathematical formula so much.
CONCLUSION AND SUGGESTION
Mathematics has an important role in human life must be taught to students properly and correctly. One of the factors that can make students is able to learn and understand mathematics well and correctly is cognitive psychology. Cognitive psychology is a branch of science that studies about how people see, learn, think something, feel, remember, and learn the language where the brain will perform its main function that is thinking as a mental activity. Students' cognitive psychology helps them to recognize the students, understand what affects brain work so that the teacher is able to help students to use their brain work well.
Mathematics is close to human activity and is part of human culture. Therefore this study suggested that learning mathematics should be linked to the context of human life and human culture. Then to learn mathematics must be linked with the context of human life and human culture so that mathematics memorable, imagined, represented, manipulated and assembled in cognitive maps.
Full attention and consciousness will help a person to receive and process and store information in the brain as well as to solve encountered problems. The ability to solve problems involving the brain work, memory, representation and manipulation, it is also called problem solving ability. Problem solving will vary greatly when the creativity is high. This problem solving ability and creativity get people to make decisions and to reason.
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Proceeding International Conference on Mathematics, Science, and Education (ICoMSE). Malang State University.
Malang
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