Developing Mathematics Teaching

There are four level to developing Mathematics teaching :

- Material level

    The basic level is material level, like class, teaching content, book, building, and students. In traditional teaching, there is one method or we call it expository method. Teacher is as subject to give, to explain, to give task to student, and student as an empty glass that should to fill.  In progressive or innovative teaching, there is no the best way to educate. Innovative teaching is use various method and contextual. Student as younger learner should

- Formal level

     The next level in development is formal level, included curriculum and syllabus. There is difference between curriculum in the traditional teaching and innovative teaching. Traditional teaching is based on teacher’s competence, but innovative teaching is based on student competence.

- Normative level

     That included in normative level are law, education system, paradigm of education, and theory of education. Theory of education in traditional teaching, student as empty vat and there is transfer of knowledge from teacher. It should reform or move to innovative teaching. In innovative teaching, student is like a seed and teacher should be dynamist to construct student’s knowledge. In Indonesian system education, national examination is final assessment. It is need to investigate because there is some deceitfulness.

- Spiritual level

     Spiritual level is the highest level in teaching development. That included in spiritual level are future, spiritual and religion, vision or goal, and way of life. In traditional teaching, there are opinion that with different student, same ways, same method, same Mathematics, same time, same facility, same object, and same teacher, will give same thinking and same result. In fact, there are defference thinking and defference result. So, with different student, different ways, different method, different Mathematics, different time, different facility, and different object, will give different result.

Effective learning reachable if student:

- Have motivation

- Do collaboration with other

- Unique

-  Know the context of problem (contextual)

IMPORTANT THINGS IN LEARNING

People never satisfied about what that they get. We always find something better what we get. To get better things, we always learn and study to research. Some important things in learning :

- Empower Yourself

Be assured with your ability. If we trust and believe in yourself, then automatically will maximize our ability.

- Do Not Dissolve in Disappointment

We definite ever fail somthing. When we fail, get up and fix it. We must have more spirit to improve our step to achieve success next time.

- Make Sure That You Are on The Right Track

After have a confident and enthusiastic, make sure that we are confident the steps that we take. Confidence will help us in maintaining our consistency in achieving the goals and ideals. You need to understand yourself, inside and outside. You need to identify your strengths and weakness. Then, your will improve abilities and reduce your weakness.

- Do Transformation

We are always changing, from kids to be adult people. Our thigking must be change to adult too. You need to transform yourself follow the period development, but do not to bevictim of the period development. So, our thinking must also develop better .

- Interaction

One important thing is to improve our ability to interact with others. Interaction and communication is very important for a teacher in delivering knowledge to the student.

- Awareness

Environmental awareness needs to be trained. A teacher must be sensitive in dealing with the environment because every student has a different character.

- Utilization of Environmental

We need make convincing that we have facilities to support our goal achievement. Facilities available must be used wisely.

- Renew Knowledge

One way to increase and broaden knowledge is by update and doing that knowledge in life. The knowledge will be stored long in our minds by the application.

The learning result is different among one person and other. Result that we get depent by what level of our effort to achieve our goal. So, let us improve our knowledge with spirit to learn.

Source : English Lecture

INDEEP THINGKING ABOUT MATHEMATHICS

We should be happy because we now study in Mathematics Education. From the semester to semester, the faster, the higher, and the more Mathematics we learn. Mathematics Education is different from level to level, but it’s interrelated. Psicologycaly, I think we are definitely different from students of elementary school, junior high school, or senior high school. We are adult people. So, our thingking must be adult too.

For example, kids will say that straw is a line, but adult people will say that straw is a tube. Kids learn Mathematics base on concret material, whereas adult people learn Mathematics with abscraction. It’s because we know that Mathematics is thingking object.

Every age level has a different ability so the result of the study was different. Mathematics for school studied with take an example from dialy activity through concret material.

Ebbutt, S. and Straker, A. (1995) write some formula of Mathemtics for school :

1.      Mathematics is a search for patterns and relationships

For kids, easier to learn Mathematics through understanding and recognizing patterns and the relationships which encounter things in everyday life. Then, Mathematics knowledge will survive in their memory.

2.  Mathematics is a creative activity, involving imagination, intuition and discovery

Mathematics is a means of creative thinking. Students are required to solve a problem. In solving these teachers should not limit students to certain methods. During the students understand and apply methods accurately and correctly. It’s make the students to think creatively, involve imagination, intuition, and discovery.

3.  Mathematics is a way of solving problems

Mathematics can be used in solving mathematical problems and everyday problems. A teacher may help the student by providing problems encountered daily, helping students to understand step by step, motivate students to keep the spirit of learning, and help students enjoyed lessons Mathematics.

4.  Mathematics is a means of communicating information or ideas
language is an important aspect in the delivery of learning Mathematics.

Language is an important aspect in the delivery of learning Mathematics. Many things which we get through appropriate communication. Therefore, a teacher needs to improve ways of communication, so the students understand the material provided.

Whereas, adult people learn Mathematics through the definition and proof. That's the difference between Mathematics Education for school and Mathematics Education for adult. So, We must thingking deeply about Mathematics because we now study in Mathematics Education. Do not give wrong perseption to our student in the future.

There are some characteristics student that learn Mathematics :

1.      That student learn Mathematics efectively if have good motivation.

If we have good motivation, we will do supporting learning activity continuely.

2.      That student learn Mathematics individualy.

Student must be able to find solution by themself.

3.      That student learn Mathematics incolaboration with other.

Student also must learn Mathematics with other. So, they can discusse that they can’t find the solution by themself only.

4.      That student learn Mathematics in context.

Student must knowing the context of the problem. So, they can apply their knowledge to their life.

It’a all above to have concept to our mind that learning can’t be represented.

MATRIKS

Manipulasi Matriks

     Membuat matriks magic variable A.

A = magic(3)

A =

     8     1     6

     3     5     7

     4     9     2

     Sekarang masing-masing elemen A akan ditambah dengan 2

A+2

ans =

    10     3     8

     5     7     9

     6    11     4

     Mencari tranpose matriks A yang dilambangkan dengan A apostrof.

A'

ans =

     8     3     4

     1     5     9

     6     7     2

     Contoh perkalian matriks.

Pertama, kita harus menentukan matriks baru yang diberinama matriks B, lalu lakukan perkalian matriks A dengan matriks B.

B = 2*ones(3)

B =

     2     2     2

     2     2     2

     2     2     2

A*B

ans =

    30    30    30

    30    30    30

    30    30    30

     Kita juga dapat mengalikan masing-masing elemen yang bersesuaian matriks A dan matriks B dengan menggunakan operator (.*).

A.*B

ans =

    16     2    12

     6    10    14

     8    18     4

Operasi Dasar Matriks

     Pertama, buat matriks sederhana a dengan 9 elemen.

a = [1 2 3 4 6 4 3 4 5]

a =

     1     2     3     4     6     4     3     4     5

     Lalu, tambahkan 2 pada masing-masing elemen.

b = a + 2

b =

     3     4     5     6     8     6     5     6     7

     Untuk, membuat grafik, lakukan perintah plot dan grid on untuk memberi kisi.

plot(b)

grid on

     Grafik lain yang dapat kita buat dengan MATLAB.

bar(b)

xlabel('Sample #')

ylabel('Pounds')

     Kita juga dapat mengganti simbol yang kita pergunakan dalam penggambaran grafik dengan menambahkan jenis simbol dan jenis garis yang ingin dipergunakan setelah matriks yang akan digambar, contoh:

plot(b,'*')

axis([0 10 0 10])

     Apabila akan membuat matrik baru, masing-masing baris matriks dipisahkan tanda (;).

A = [1 2 0; 2 5 -1; 4 10 -1]

A =

     1     2     0

     2     5    -1

     4    10    -1

     Dengan mudah kita dapat membuat transpose matriks A dengan langkah:

B = A'

B =

     1     2     4

     2     5    10

     0    -1    -1

     Lalu lakukan perkalian matriks A dengan matriks B.

Catatan: MATLAb dapat menjalankan operasi bila matriks dalam ukuran yang sama.

C = A * B

C =

     5    12    24

    12    30    59

    24    59   117

     Mengalikan masing-masing elemen matriks A dan B yang bersesuaian menggunakan (.*).

C = A .* B

C =

     1     4     0

     4    25   -10

     0   -10     1

     Untuk mencari invers matrik, menggunakan perintah sebagai berikut.

X = inv(A)

X =

     5     2    -2

    -2    -1     1

     0    -2     1

     Kita ketahui bahwa perkalian matriks dengan inversnya menghasilkan matriks identitas.

I = inv(A) * A

I =

     1     0     0

     0     1     0

     0     0     1

Sumber : Help dalam MATLAB

MATHEMATICS EDUCATION

          Methematics Education is a meaningfull thing. It’s have deep mean in our life. As a mathematics education’s student is important to love mathematics. We love mathematics, it’s why we are study mathematics now. If we love everything that we do, we will enjoy it. If we enjoy whatever we do, we will get positif thing.

         The problem that we hae as mathematics student is how to promote mathematics education to be innovative teaching. It’s should we have thinking about, because in the future we will to be a teacher, mathematics teacher.

          Change traditional teaching to be innovative teaching isn’t easy. Traditional teaching base on teacher explanation. Student have no time to improve theire ability and the lesson had prepared by curriculum. Whereas, innovative teaching can make the student be autonomouse. Student can improve their ability because they we can do exercise by theirself, but passive student will left behind. Student is like a seed. They will grow up because of many factor, teacher factor, student factor, and environment situation. So, communication between student, teacher, and the envinonment is important.