Abstract
Students, teachers, schools, facilities and all of things that have role in education, are different with last generation. When I asked my uncle about what he learned when he was at school, he said that he learned about addition, division, multiplication, and also subtraction. His teacher also taught about how to use abacus but he could not use it. I asked to my friend. He studied mathematics in University. He told me that he doesn’t understand about philosophy of mathematics but he already understands about algebra, logic, trigonometry and etc. So, there are many differences about the material that was learned now and before. It means that the methods of teaching-learning process have to adapt the developing era. It will be able to apply when the teacher change the paradigm and not only use the traditional methods for their way to facilitate their students. An innovative method is more effective to be applied because this method can increase their ability. For example they can improve communication between student, interaction between student and teacher, logical thinking, and so many others.
I. Introduction
What are the aims of educations? Is it just for making the students rich of knowledge? Or make them have positive attitude? When the students are rich of knowledge, but they don’t have positive attitude to make it real, it will be same like big empty box. And when they have positive attitude but they don’t have knowledge, it is like a bird without wings.
II. Developing the Scheme of Uncovering the Phenomena of Psychological Aspects of Mathematics Learning.
A. Scheme
Scheme is divided into three parts. First is form. Individual, group, organization, nation, and international are called form. The second is method. Method is the way that is used to transfer, to say, to give something for another people. In this case, method is the way that is used by teacher to deliver knowledge and also give understanding; there are many values that come from mathematics problem to students. There are many methods that have been used. Like using games, using mathematical aids, using traditional dance in learning symmetric concept, etc. The goal of using different methods is making the student understand easily with the material that will be given. Method is usually used to observe something, then to note or write the hypothesis and then to ask or act or participate when there is a problem that does not understand, yet. If there is no question or all of problems have been had solving, it will be held an evaluation, a study, an investigation, a research, a survey to know how deep the students understood about the material. The way to check it is held TEST or EXAMINATION. And the last is substance. Substance is the material itself. Substances of mathematics are number, formula, abstract problem, real problem, and many others.
B. Uncovering
Uncovering is activities to describe, to make description, to explain, to make therapy, to reflect, to build or construct the world of Psychological of Mathematics education or learning and finally to build the character of the students.
C. Phenomena
Phenomena are anything that can be perceived as an occurrence or fact by the senses. There are four grades of phenomena. See the figure.
Material phenomena are concrete phenomena.
The third is Formal Phenomena. Normative Phenomena are horizontal relationship, between human being.
And the last is Spiritual phenomena. Spiritual phenomena are vertical communication with God.
A. Psychological Aspects
General psychology is science that learn about behavior of norm, adult, cultural human. There are 4 aspects that can be identified of soul symptom. There are introduction (cognitive), feeling (affective), connation, and psychomotor (combination of three aspects before).
When we talk about psychology in mathematics, there are many aspects that affect the teaching-learning process. First is attention. Attention that comes from student who want to learn mathematics. They have to focus with the material that will be delivered by the teacher and attention that comes from teacher who must be able to detect what the difficulties that is found. Second is motivation. Student motivation is willingness to learn, study, and know more deep about mathematics. Student motivation will come if the student feels that they have to conquer the mathematics problem. Teacher motivation is willingness to make the student be smart, diligent, have positive behavior, and make them to improve their skills. So, they can survive in their life. Third is active. Teacher has to accompany student, give mathematical value that have correlation with their life, make student improve their skills, so they can survive, and so many others. How about student? They must have braved to ask, act, share, solve mathematical problem. Student not only waiting the teacher to give them material, but they have to look for the actual problem so they can get more experiences by their selves.
B. Mathematics
The nature of mathematics education is mathematics that can be taught at school. It has many different point of view, like:
a. Mathematics is a search for patterns and relationship
As a search for pattern and relationship, mathematics can be perceived as a network of interrelated ideas. Mathematics activities help the students to form the connections in this network. It implies that the teacher can help students learn mathematics by giving them opportunities to discover and investigate patterns, and to describe and record the relationships they find; encouraging exploration and experiment by trying things out in as many different ways as possible; urging the students to look for consistencies or inconsistencies, similarities or differences, for ways of ordering or arranging, for ways of combining or separating; helping the students to generalize from their discoveries; and helping them to understand and see connections between mathematics ideas.
b. Mathematics is a creative activity, involving imagination, intuition and discovery
Creativity in mathematics lies in producing a geometric design, in making up computer programs, in pursuing investigations, in considering infinity, and in many other activities. The variety and individuality of children mathematical activity needs to be catered for in the classroom. The teacher may help the students by fostering initiative, originality and divergent thinking; stimulating curiosity, encouraging questions, conjecture and predictions; valuing and allowing time for trial-and adjustment approaches; viewing unexpected results as a source for further inquiry; rather than as mistakes; encouraging the students to create mathematical structure and designs; and helping children to examine others’ results.
c. Mathematics is a way of solving problems
Mathematics can provide an important set of tools for problems- in the main, on paper and in real situations. Students of all ages can develop the skills and processes of problem solving and can initiate their own mathematical problems. Hence, the teacher may help the students learn mathematics by: providing an interesting and stimulating environment in which mathematical problems are likely to occur; suggesting problems themselves and helping students discover and invent their own; helping students to identify what information they need to solve a problem and how to obtain it; encouraging the students to reason logically, to be consistent, to works systematically and to develop recording system; making sure that the students develop and can use mathematical skills and knowledge necessary for solving problems; helping them to know how and when to use different mathematical tools.
d. Mathematics is a means of communicating information or ideas
Language and graphical communication are important aspects of mathematics learning. By talking, recording, and drawing graphs and diagrams, children can come to see that mathematics can be used to communicate ideas and information and can gain confidence in using it in this way. Hence, the teacher may help the students learn mathematics by: creating opportunities for describing properties; making time for both informal conversation and more formal discussion about mathematical ideas; encouraging students to read and write about mathematics; and valuing and supporting the diverse cultural and linguistic backgrounds of all students.
When we talk about mathematics education, it has a relation between teacher and their method that is used. There are two ways and it has a significant differences. What are the differences? First way, most of teacher used this way, is traditional method. Traditional method is the method that the teacher as the main sources of the knowledge. In this case, student only get anything from teacher. You can see the figure bellow.
The picture shows that student is like a tree. They start from seed, and then grow up again and again until the seed become a tree with many leaves there and produce the fruits also. So, the roles of teacher are give motivation, accompany, and give a bridge to walk when they find problem. Not only give the win solution, but teacher has to always and always think creatively. Maybe any student who thinks that with their own way, they can solve the problem easily. But some of them think that it is not the shortest way. So, they can improve their thinking although it is on simple problem.
A. Learning
Activities to understand, share, study, discuss about something that is focused on context and experience of student. Then, they will make some conclusions and also communicate the result to other student. Activities like that are called learning.
Now, we are going to talk about learning mathematics. There are many factors to indicate when the learning mathematics process is effective, such as:
1. Students have motivation,
2. Students have collaboration with other in learning mathematics,
3. Students can learn mathematics individually,
4. Students can learn mathematics contextually.
I. Conclusion.
To develop the Scheme of Uncovering the Phenomena of Psychological Aspects of Mathematics Learning, we have to know what the meaning of the scheme itself, what things should be uncovered, what the psychological aspects that should be known, what mathematics education is and what the activities of learning mathematics. After we have known about them, we can plan the methods that will be used when we want to teach something. First material will be different with the second material in the way the teacher taught it.
II. References
http://www.google.co.id/image/263052_0_Kegiatan_Belajar_Mengajar on Sunday, October 16th 2011, 8 pm.
Marsigit. 2010. PHILOSOPHICAL AND THEORETICAL GROUND OF MATHEMATICS EDUCATION on marsigitmateri-workshop-qitepphilosophymatheduclesson-study-teamfinal.pdf
Sugihartono, dkk. Psikologi Pendidikan. Yogyakarta: UNY press.
