International Perspective on Developing Method to Uncover Psychological Phenomena of Learning Mathematics

By: Yudha Prihadi
10313244026

International perspective is the process of opinion and viewpoint that incorporates analysis and concerns from different parts of the world. Many times this multinational viewpoint originates from various national interests, which have outstanding concerns with one particular subject.

One of tehe problem in International perspective is to developing method in learning Mathematics. Exactly, it is not easy to developing methods in learning Mathematics in school. In this case, teacher becomes a major role in the process to developing this Mathematics learning method. Teacher not only focused on the output of the learning process but also teacher must focused in the process of learning. The method that given by teacher is very influental on the students’ psychological development. Nowadays, there are many existing method in teaching-learning Mathematics, but it make an educator or teacher feel confused, which method that suitable to be applied to students in learning Mathematics. This is very useful in meeting the demands of an international perspective.

Each method of learning Mathematics has drawbacks and advantages which vary according to era. An educator should be able to be open minded to the developing existing methods and take any positive point in each method. In traditional and modern Mathematics learning just focused on the mechanistics, structural, and empiric. New Mathematics can cover all of approach in Mathematics learning method which is focused on realistic. There are four important steps in realistic learning, such as introduction, creation, reason and explanation, and clossing. Introduction, students are given a problem and they are told to recognize and understand the problem. Creation, students are allowed to develop their creativity such as using symbols or develop formulas to solve the problem. Reason and explanation, students were  asked to provide feedback and explanation to the statement of the problem. Clossing, the teacher end the class  by giving a conclusion and application life squad from the material. In each steps must be given a reflection. Reflection is useful to interpret everything has been done before and to add their experience in learning Mathematics.

The role of a teacher is to develop teaching materials. They are not allowed to use only single way in delivering the materials. Teachers also have to think creatively in the teaching of Mathematics to enhance  students’ Mathematical thinking. Before starting to teach, teachers have to prepare many things in the learning process so that learning process goes according to plan. Teaching learning scheme is needed to help  teacher to delivered the material in a class. There are ten schemes, they are:

1.      Lesson Plan

Lesson plans are very useful to give references and limitation for the teacher to provide learning materials. Lesson plans are also useful for reducing or anticipate material that elapsed during the learning process, so all material can be delivered to students as well. With this lesson plan the teacher will be easier in delivering course material in sequence, from simple problems to more complex problems.

2.      Apperseption

Apperception means consciously observations about everything that is in itself a comparative basis and foundation to accept a new idea. So  a teacher must be open minds to the new ideas, so that their knowledge can flourish.

3.      Small group discussion

Small group discussions are useful in developing students’ ability in interact among the students. Small group discussion will help students to learn independently and  develop students' thinking ability and their confidence.

4.      Various Methods

Learning methods can vary greatly reduce the saturation of students in learning Mathematics. So here the teacher is also required to think creatively in varying methods of learning.

5.      Various Interaction

Various interaction mean at the time of learning, a student should be able to interact not only with teachers and friends only. Teachers create small groups that vary and the group is not permanent, but changing all the turn of the material. That way the student is not only able to interact with  certain students but also they  can be required to interact with other students in the class.

6.      Various Media

Instructional media are indispensable in any learning process and strongly supports the learning process. The media must be tailored to the learning materials provided at that time and should be interesting. This learning media should always be varied so that students do not quickly get bored.

7.      Student Reflection

Student reflection aims to give a meaning of the learning that has been given. Student reflection is usually done at the end of the lesson by the teacher. This is done so that students can take the meaning of the learning that done at that time.

8.      Scheme of Achieving

Each student achievement in mathematics learning process should be respected.  Form of praise or reward. This is done to continue to encourage and motivate students to learn Mathematics. If there are students who have achievement below the average, a teacher must always appreciate these achievements and  always motivated to be more advanced.

9.      Student Conclussion

Student conclussion aims to measure how much students understand the material that has been  given before. At the end of the lesson students are asked to summarize what they have learned at that time. Whether they understand or not the material that has been given. Student conclussion is used to stimulate students to make it easier to conclude a case.

10.  Student Worksheet

Student worksheet aims to measure how  students understand the material that has been given before. The student  worksheet usually  contains problems related to material that has been given previously. Usually worksheet contains levels of different issues, it aims to adjust the level of students that have different abilities too. Student worksheet should be made by the teachers themselves, because they are familiar with the conditions or the ability of each student.

From the ten schemes above we can know how to prepare a good learning of mathematics. Teachers should always take into consideration the development of their students, not just focus on the final exam only. Most important is the process. And there are four things that support this process, such as teacher thinking, development model, interaction between student and teacher, and Mathematical strand.

PSYCHOLOGICAL ASPECT OF MATHEMATICS LEARNING

by: Yudha Prihadi 

Abstract

Many students think that mathematics is difficult. But it is really wrong. It is depend on  the delivery of the material in accordance with the needs of students. Teachers should understand what students need and how to overcome the problems that arise in the learning process. Success or failure of a learning does not only depend on the teacher, but students and their environment is also very influential in this process, and there are many aspects that influenced.

A.                Introduction

Mathematics is not just a study of numbers, it is not about calculations or applying formulas. Mathematics can be described as a field of creation through accurate and logical thinking." Mathematics has a long, rich history and continues to grow rapidly. Mathematics, on the other hand, has made considerable contributions to the advancement of other academic fields. In fact, mathematics is often described as the foundation of scientific studies.

Sometimes, Mathematics is regarded as a scourge in learning at school. Many students often meet difficulties in learning Mathematics. Several factors influence this. Not only the teachers who play an important role in addressing this problem, both students and the environment is also very influential in addressing this problem.

B.                 Psychological Aspect of Mathematics Learning in School

Many students assume that Mathematics is so hard, but they are make a big mistake for think like that. In fact, Mathematics is so easy to study. An important aspect of how we perceive objects or people has to do with what we think they are or should be (Morris 1973). How Mathematics is perceived depends on what students themselves think Mathematics is. Because students are limited in what they can perceive, they are highly selective in whether they choose to perceive and that which is relevant to them. Different people will react differently even when they are from the same physical environment. They would not always have the same experiences, hence perceptions in Mathematics. Attitudes therefore relate to the way we act or react. The way we perform our thinking (perceptions) is what results in our attitudes. Our actions therefore depend on our attitudes.

To determine the success or failure of students in learning mathematics, we need to take a look on some important aspects of psychology, such as:
the nature of Mathematics, students, students differences, teacher and classroom learning environment. This the further explanation:

1.      The Nature of Mathematics

Mathematics is the study of quantity, structure, space, and change. The mathematicians look for patterns, to formulate new conjectures, and establish the truth through a rigid method of deduction mathematics from axioms and corresponding definitions. Mathematics systematically built and developed as a system, definitions,  and  axioma to built a new theorem.

Teach mathematics is not easy because in facts show that students have difficulties in learning mathematics (Jaworski, 1994 in Depdiknas 2003). In mathematics teaching-learning process, teacher should be adjust for student’s psychology, age, and based on their world.

As a candidate of mathematics teacher, we must know what is school mathematics. School Mathematics  is a Mathematics that has sorted out and adjusted to the stage of student’s intellectual development. It’s used to developing student’s thinking skill. In teaching Mathematics, teacher usually starting from the concrete to the abstract object. However, although the object of Mathematics is abstact, but the ability of  students are still in the concrete operational stage, so to understanding the concepts and principles, the students are still needed experience through concrete objects (Soedjadi, 1995:1). Ebbutt and Straker (1995:10-63) said school Mathematics is

1.      Mathematics is a search of pattern and relationship

The implication of this view of learning are give students the opportunity to conduct discovery and investigation patterns to determine the relationship, give an opportunity for students to have an experiment with many  ways,  encourage students to discover the existence of sequence , difference, comparison, grouping, and give a general conclusions.

2.      Mathematics as problem solving activities

The implication of this view of learning are help students to solve Mathematics problem using their own way, helping students to think creatively in solving problems (When we used the formula for the specific problem and how to apply this formula?), and  develop students' competency in problem-solving.

3.      Mathematics as a creativity that requires imagination, intuition and invention.

The implications of this view learning are give the initiative to the students to think differently with other, to encourage the curiosity of all things that are useful, dare to refute and value the opinions of their friends, and can be creative in solving any problems in mathematics.

4.      Mathematics as a means of communicating

The implication of this view of learning are to help students to recognize the properties in mathematics, as a means of communicating with one another in discussing about mathematics, encourage students to make examples of the nature of mathematics,  encourage students to explain the nature of mathematics, and encourage students to justify the need for math activities.

2.      Students

A student is person who is actively enrolled in a accredited educational institution and who is expected to spend a minimum aggregate of given hours per week in a classroom or similar institutional setting during the term of enrolment.

The students’ condition is very influential on success or failure of a process of learning Mathematics. Many things are influential in this process. Mathematics learning can be said to be effective or successful if:

1.      Students have motivation to learn mathematics

To motivate the student  we can  encouraged the studens to think about pleasant things. But not all students can be motivated  with the same things, because they come from different backgrounds and family.

2.      Students can work/study together with other

In this case students are expected to be able to cooperate and exchange their ideas  or help each other to solve problems, and it can help them to communicate with each other.

3.      Students learn Mathematics individually

 Students are not all alike. Each one sees the world in a way that makes the most sense to him/her such individualized perceptions shape what students think, how they make decisions, and how they define what is important. The perceptions also determine students' natural learning styles. In this case, students are expected to be able to develop their potential as they wish. Besides that, they are also expected to be more independent in solving their own problem in Mathematics.

4.      Students learn Mathematics contextually

3.      Students Differences

            The important things that teacher must be know that there are differences between their students. Not all students same. Each students has their own differences. The effective learning is when the teacher can respond the special needs of each students. This is the differences between each students. In Psychology, individual differences  means how someone different in thinking, feeling and acting. In addition, perception and intelligence of each student are very different. Therefore, a teacher is not allowed to be too imposing a teaching method to students. They should be given freedom in choosing how to solve a given problem. That way they will not feel compelled to learn.

4.      Teacher

A teacher is a person with multiple roles in the learning process. His role goes beyond the traditional roles of planning and assessing. He is ultimately responsible for what goes on in the classroom environment. He is expected to effectively educational needs of his students.

Nowadays, teachers must change their perspective in the Mathematics theacing-learning process. Today is very different from earlier times, student can not be forced to study or think about Mathematics. They must have their own motivation to learn, so the output can be realized.

In the old paradigm, students are regarded as an empty barrel that every day should be filled and refilled continuously. In the other words, the knowledge every day transformed from teacher to students continuously. But there is no reciprocity between the two. Students do not have the opportunity to develop their talents, because every day they only get the input and output can not be realized.

But in the new paradigm, students are regarded as individuals who have seeds and will grow into a better individual. The functions of a teacher include diagnosing, mediating, and facilitating in the classroom. This means that the teacher has to diagnose students' prior knowledge before bringing in new knowledge. As a facilitator, the teacher has to structure learning in such a way that good learning experiences are brought to the fore. This is done organizing activities that help students to actively participate in their own learning. As a mediator, the teacher should help in narrowing the gap between students' views about real scientific or mathematical knowledge. Teachers would be expected to accept changes in their interactions with students and support students as their roles change too. The role of teachers therefore will be that of facilitating and mentoring.

That's the reason why teachers have to change the paradigm from the old to new. Because at this time students are expected to be more able to develop their talent in accordance with the desire and talent they have, not by forced and without feel scared or uncomfortable with their teacher.

5.      Classroom Learning Environment

In Mathematics teaching-learning process, classroom environment is very influential in student development. The nature of the classroom environment and social interactions can make a difference in how students learn and achieve their goals. It has been revealed that learning outcomes and students' attitudes toward learning were closely linked to the classroom environment (Entwistle and Entwistle 1991, 2003).

Studies of Classroom Environments have demonstrated that perceived classroom environment can help predict student learning. For example, Haertel, Walberg and Heartel (1981) found that student environment improved in those classes, which students felt had greater and less cohesiveness, satisfaction and goal direction and less disorganization and friction. In order for the teaching of Mathematics to be effective, there is need to be a sound learning environment or "backdrop" as well as an effective program instruction and assessment. These two elements must go hand in hand and not necessarily distinguishable. This learning environment for Mathematics has many elements that will enhance learning. An affective Mathematics Learning environment is an environment that:

-          Value prior knowledge

-           make connections between that knowledge, the world of the students, and the stands and actions of Mathematics;

-          encourages the establishments of a community of Mathematics learners

-          focuses on important Mathematical concepts or big ideas,

-          explore excepts through problem solving

-          is supported by strong roles and of teachers, principal, senior administrator

-          is supported by the home

The learning environment as community of learners who feel that their knowledge and thoughts are valued, who feel safe to take risks in trying to solve problems and who are comfortable talking about their understanding of Mathematics.

C.                Conclussion

Both students and teachers interact in determining the success in learning mathematics at school. In addition, the methods used by a teacher greatly influence the development of their students. A good classroom environment and teachers are creative in managing the classroom can also enhance students' motivation in learning mathematics.