Developing Mathematics Teaching

Currently, an interesting Mathematics learning can be created by teachers using variation methods. The discussion this time will further discuss about the differences of two methods of teaching. Both methods are traditional method and progressive method. The differences are based on four main levels. They are spiritual level, the normative level, the formal level, and material levels. Consider this.

In the spiritual level, consisting of the spiritual itself, ways of live, and  vision of the future. Based on this level, traditional teaching method gives the education just as an obligation. As a result, students are burdened to learn because it has no awareness of the importance of learning. But, in progressive teaching, students have an awareness because teachers do not provide the liability but the motivation for the more advanced.

At second level, normative level, there are law, decree, education system, paradigm of education, and theories of education. On traditional teaching, position of teachers only teach knowledge to students. Students receive science as an empty vessel. Students are passive learner. For that, it needs reform of paradigm. This is represented by the progressive method. Methods progressive view of teachers as facilitators and students as a seed. Students are expected to build his own knowledge.

Formal level presented curriculum, syllaby, and the book. In Indonesia, we know KTSP (Kurikulum Tingkat Satuan Pendidikan), one of Indonesia curriculum that had been semi-progressive. It is actually could reform traditional curriculum to a progresive curriculum. Regarding the curriculum, we need to realize, as a candidate of mathematics teacher, if have case the same result, same objective, same steps, same thoughts, same facility, same time, but different students, including traditional methods. Coupled with only the orientation of the final value. This method is less precise applied current. Progressive method offers a solution to the differences in student characteristics on the assessment process. It make active student by student competence oriented with different facilities, different objective, different time, and different result.

The last is material level. This is consist by class, student, teaching, book, and building. In the traditional class, teacher just doing expository method. In this method, the teacher just explaining, giving example, giving problem, and giving task repeatedly. Text book oriented applied by the teacher. Students are pure mathematics. Contra with traditional method, progressive teaching have a fundamental, there is no the best way to education. Teacher can use various method at the class. Teacher can make book by find inovation to develop their knowledge and teaching method.

Well, That’s all discuss about the differences between traditional and progressive method teaching. Overall, as a candidade of mathematics teacher, we can choose progressive teaching method as appropriate method currently.

The Nature of Student Learn Everything

As a mathematics education student, we must feel happy because only few of young people have chance who concerning to the mathematics education. Then, as consequences, we need to empower or give supporting ourself. We should never be disappointed. We must wake up. After that, we must make certain that we are walking in the right track. It have the impact to our goal. When we have gain our goal, we should support our competence. We can use many facilities that available around. Besides, we also need support from our family. The most urgent is we need understand both ourselves and everythings around us. If we didn’t understand, we could be blind and empty. Blind meaningfull there it nothing destination. We  must fill our comprehension by hard struggling in our life. Then, we would not get blind and empty.

In life, we strive for understand ourself. It means we must understand about the our situations and our characteristics. Everybody have different characteristics. Now,
we are adult students. We should aware our situations. As a student, actually we can’t always depend on our lecturer.  Presently, we can improve our ability and knowledge by search knowledge from everything, everywhere.

For teaching, as a candidate of mathematics teacher, something important engage with the younger is the different way of thinking between us and them. If we are teaching, but students are learning. We should show modern teaching who make active student. It like mathematics iceberg. In the future when learning process, teacher should prepare something to teach. There are Lesson Plan and Student Work Sheet. Teacher also need to understand the role of interaction. Interaction happened by subjective knowledge and objective knowledge of mathematics. The urgent is how to guarantee student are able knowledge of mathematics. It means that we should revision knowledge.

In Deep Thinking about Mathematics Education

Mathematics education? Now, we are a student of mathematics education. As prospective teachers of mathematics, we should indept thinking about mathematics education.

Well, firstly, we should understand the differences between younger and adult. If younger, they need something where concrete (concrete materials). In other side, younger have more think. They can think abstract object. For example, we can compare the number 7 and 5. When we describes the number 5 is greater in size than the number 7,  the younger will think that number 5 is greater in value because it was bigger. Younger just thinking something real. Different from younger, adult have ability to think about the values ​​contained in the numbers.

That is the reason why mathematics is different. The material learned in school and university levels differ because of differences in the character the ability to think of the pupils and students. At the first experience, while attending school, the material being taught according to the daily, real happening. Continued in college, the material being taught an abstract, consisting of definitions, axioms, theorems, and proofs.

Related to learning mathematics that have different characteristics, required educational innovation. In general, Ebbutt and Straker (1995: 10-63) defines school mathematics as the nature of mathematics, as follows:

1.      Mathematics as search activity patterns and relationships implication of this view of learning. Here the teacher gives students the opportunity to conduct discovery and investigation patterns to determine the mathematical relationship to make conclusions.

2.      Mathematics as a creativity that requires imagination, intuition and invention. The implication of this view of learning is to encourage initiative and provide an opportunity to think differently, encourage curiosity, the desire to ask, the ability to refute and ability estimates. Of particular interest to teachers is not suggesting a solution using only one method.

3.      Mathematics as problem solving activities (problem solving). The implication of this view of learning is to provide mathematics learning environment that stimulates the emergence of mathematical problems, solving mathematics problems using his own way, and encourage students to think logically, consistent, systematic and develop a system of documentation / records.

4.      Mathematics as a means of communicating. The implication of this view of learning are encourage students know the nature of mathematics, encourage students to make an example the nature of mathematics, encourage students to explain the nature of mathematics, encourage students to give reason the need for math activities, encourage students to discuss issues mathematics, and encourage students to read and write mathematics, respect students' mother tongue in talking about mathematics.

Ebbutt and Straker (1995: 60-75), gave his view that the potential for students can be developed optimally, assumptions about the characteristics of learners and subject implications for learning mathematics are given as follows:

1.      Pupils will learn math if they have motivation.

2.      Pupils learn mathematics in its own way.

3.      Pupils learn mathematics either independently or through collaboration with his friend.

4.      Pupils need a context and in different situations in learning mathematics.

That some material needs to be underlined by prospective teachers. The materials presented by Mr. Marsigit have many benefits and appropriate for education today. Provisions to be a teacher have been covered to one.

Parallelogram Area

Consider the following parallelogram.

a. Calculate the value of x. And then, calculate the length of AB.
b. Calculate the area of the parallelogram.

Quoted from : Exercise No 3, page 305
(Marsigit. 2009. Mathematics I for Junior High School. Jakarta: Yudhistira.)

Solution:
a. Base on the properties of parallelogram, the opposite sides are equal and parallel to each other. So, we can calculate the value of x.
                    AB = CD
              4x - 15 = 2x + 3
              4x - 2x = 3 + 15
                     2x = 18
                       x = 9

After we calculate the value of x, we can determine the length of AB.

                     AB = 4x - 15
                     AB = 4.9 - 15
                     AB = 36 - 15
                     AB =  21

Hence, the value of x is 9 cm and the length of AB is 21 cm.


b. The base of parallelogram ABCD is AB = 21 cm.
The height of parallelogram ABCD is DE = 10 cm.
Therefore, we can calculate the area as:

                       L = base x height
                       L = AB x DE
                       L = 21 x 10
                       L = 210

Hence, the area of parallelogram ABCD is 210 cm²

From Traditional Teaching To Progressive Teaching

In Indonesia, many pupils think that mathematics as a dangerous lesson which threatens. This pupils assumption who think that mathematics as a difficult subject makes mathematics to less and less enthused. Thus, understanding of Indonesian pupils about mathematics is worse.

Based on these facts, it takes innovative teachers. Teachers should change the mathematics paradigm of pupils from the difficult lesson becomes easy lesson. These days, teachers are required to be able to teach in a progressive, not traditional teaching. This some steps for teaching that is suitable for today:

1. Teachers as facilitators.
Different with traditional teaching that makes the teacher as a center of learning, in progressive learning, teachers are positioned as a facilitator. Teachers are assisting and supervising pupils in learning. Hence, active learners is very necessary. Pupils will actively ask the teacher. So, for pupils who are less active, the teacher is required to motivate their pupils. This is where the encouragement of teachers can enhance pupils' desires.

2. The number of learning resources.
Learning resources can come from anywhere. Teacher isn’t always standing in front of the class. Pupils can acquire knowledge from his own experience. From his experience, it is hoped science would be more understandable.

3. Change obligation to the needs and awareness.
This is needed pupils who have false paradigm, so teacher should give an explanation to the pupils. In traditional teaching, giving homework is usually regarded as an obligation. In fact, homework is a need for pupils to study at home. Teachers are expected to change the attitude of pupils who are less aware of the importance of mathematics, be aware and take mathematics.

4. Change the value orientation into process orientation.
Give pupils an understanding of that value is only the size of the final result. The most important is the process of achieving the many benefits.

Well, that's a few steps that can be done by a mathematics teacher who want to succeed. So, slowly but surely, the pupils' understanding of mathematics will be increased.

How To Prepare I Myself as A Successfull Student of Mathematics

Success came to me when I consciously decided to success. As a student of mathematics education, I want to be not only a teacher but also a professional teacher. Here are some more ways to prepare a successfull student of mathematics education . We can begin with the basic. A student should have self development. Self development can make people be better. Self-development consists of somethings, that desire, vision, and responsibility. Every people should have it.
Then, the process of self-development depends on the motivation, attitude, knowledge, skills, and experience. For more details, we will explain one by one from the process.
1.Motivation
Motivation is a process that explains the intensity, direction, and persistence of an individual to achieve their goal. The highest motivation comes from religion. Islam as a religion that I embrace, teach us to always strive in earnest, working hard. Beside, we should worship with praying to God.
2.Attitude
Attitude is so important, it can be more important than physical characteristics and mental health in a personality. Attitudes reflect a person's personality. As an Indonesian who is identical with friendly, then we should be friendly with everyone. So, the attitude which should be shown as a student is positive attitudes that sync with the goals. Continuously that can make habits.
3.Knowledge
Knowledge in here can be defined as knowledge of life. That is about how to translate life and our lives. The aims to improve the quality of life.
4.Skills
Skills acquired outside formal education. Someone have proficient skills after repeated trial.
5.Experience
Experience is the best teacher. We must have many experiences, both good experiences and bad experiences. However, keep in mind, the experience is not only reserved to yourself but also others. If the experience that we have also distributed to others, it includes a high level.
Finally, it all depends on each individual. What are the steps will be selected. Success is a chance. Who can take a chance, they will achieve success. My goal is to become a professional teacher will come with my confidence. Keep spirit and do the best...

A Story, First Meeting of English Courses

Friday, February 18, 2011, the first meeting of English courses. Change of schedule from morning to afternoon, was make us a little wait. But, no problem, that's the struggle.

At 1:00 pm, all students of mathematics education 2010 was ready for English courses. However, our class which is scheduled was used for faculty activities. In addition, the lecturer had not come. So, we were in uncertainty.

After waiting several minutes, the lecturer had come. The lecturer asked some students to search a class. We found 307. This class at the old building, little noisy, and rather hot because there was no air conditioning.

This courses have started, the lecturer introduced himself. His name is Mr. Marsigit. Then he spoke of education that has been achieved. Mr Marsigit said that "I've been bored with going abroad. " Wow, even though I've never traveled overseas. I want to go abroad and study there. I hope I can achieve it.

My impression on first meeting the English language course was fun. Mr Marsigit looks friendly and humorous. We laughed a lot in this class. In addition, Mr. Marsigit gave many motivations to us. I became more excited for college. Thank you ... Thank you ... Thank you ...