Reflection 3

" REFLECTION 3 " 

by : Elsa Winda Prastiana 

( 09313244015 /  International Mathematics Education )

At April 9^th 2012, Mr.Marsigit showed video about property of numbers. That video explain about all property of numbers.

1.      The reflextive property of Equality.

A number is equal to it self

Symbolicly : A = A

2.      The symmetric property of equality.

If one value is equal to another, then that second value is the same as the first.

Symbolicly : if A = B then B = A

                                    3 = X then X = 3

3.      The transitive property of equality.

If one value is equal to a second, and the second happens to be the same as a third, then we can conclude the first value must also equal the third.

Symbolicly : if A = B and B = C then A = C

4.      The substitution property of equality.

If one value is equal to another, then the second value can be used in place of the first in any algebraic expression dealing with the first value.

Simbolicly : If A = B then B can be substituted A for any expression

                  If B = A then A can be substituted B for any expression

5.      The additive property of equality.

We can add equal values to both sides of an equation without charging the validity of the equation.

Symbolicly : if A = B then A + C = B + C

                                                        C + A = C + B

6.      The cancelation law of addition.

Symbolicly : C + A = C + B
If we cancel C in the both side B, the final equation A = B

7.      The multiplicative property of equality.

We can multiply equal values to both sides of an equation without charging the validity of the equation.

Symbolicly : A = B (times C in both side)

                               AC = BC

                                CA = CB

8.      The cancelation law of multiplicative.

Symbolicly : AC = BC (both side divide by C)

                                 A = B

9.      The zero – factor property.

If two values that are being multiplied together equal zero, then one of the values, or both of them must equal zero.

Symbolicly : if AB = 0 , there are 3 possibility :
                                     A = 0

                                                             B = 0

                                                            A and B = 0

10.  The law of trichotomy.

For any two values, only one of the following can be true about these values :

Ø  They are equal

Ø  The first has a smaller value than the second

Ø  The first has a larger value than the second

Given any numbers A and B :

                        A = B

                        A < B

                        A > B

11.  The transitive property of inequality.

If one value is smaller than a second, and the second is less than a third, then we can conclude the first value is smaller than the third.

Simbolicly : if A < B and B < C we can conclude A < C

12.  Properties of absolute value.

Symbolicly :  
1. |A| ≥ 0
2. |-A| = |A|
3. |AB| = |A| |B|
4. |A/B| = |A|/|B|  ; (B ≠ 0)
 

                                                            

Properties of numbers :

A.    Closure.

1.      The closure property of addition.

When you add real numbers to other real numbers, the sum is also real.

Addition is a”closed” operation

If A and B is real number, then A+B = a real number.

2.      The closure property of multiplication.

When you multiply real numbers to other real numbers, the product is a real number. Multiplication is a”closed”  operation

If A and B is real number, then A B = a real number

B.     Commutativity.

1.      The commutative property of addition.

It does not matter the order in which numbers are added together.

Symbolicly : A + B = B + A

2.      The commutative property of multiplication.

It does not matter the order in which numbers are multiplied together.

Symbolicly : A B = B A

C.     Associativity.

1.      The associative property of addition.

When we wish to add three (or more) numbers, it does not matter how we group them together for adding purposes. The parentheses can be placed as we wish.

Symbolicly : (A+B)+C = A+(B+C)

2.      The associative property of multiplication.

When we wish to multiply three (or more) numbers, it does not matter how we group them together for multiplication purposes then parentheses can be placed as we wish.

(A.B).C=A.(B.C)

By the way, commutativity & associativity can’t apply substraction & division.

D.    Identity.

1.      The identity property of addition.

There exists a special number called the “additive identity” when added to any other number. Then that order number will still “keep its identity” and remain the same.

Symbolicly : A+0 = A

                    0+A = A

2.      The identity property of multiplication.

There exists a special number, called the “multiplicative identity” when multiplied to any other number, then that other number will still “keep its identity” and remain the same.

Symbolicly : A . 1 = A

                    1 . A = A

So, 0 is the unique additive identity.

       1 is the unique multiplicative identity .

E.     Inverse.

1.      The inverse property of addition.

For every rela number, ther exists another real number that is called its opposite. Such that, when added together, you get the additive identity (the number zero).

Symbolicly : A + (-A) = 0

                   (-A) + A = 0

2.      The inverse property of multiplication.

For every real number, except zero there is another real number that is called its multiplicative inverse or reciprocal, such that when multiplied together, you get the multiplicative identity (the number one)

Symbolicly : A . 1/A = 1
                  1/A . A = 1

Zero has not multiplicative identity.

F.      Distributive.

1.      The distributive law of multiplication over addition.

Multiplying a number by a sum of numbers is the same as multipliying each number in the sum individually, then adding up our products.

Example : 5(7+3) = 5(10)

                              = 50 …….(1)

                  5(7)+5(3) = 35+15

                                   = 50 ……(2)

                  1&2 is same

The formula : A(B+C) = AB+AC

                        (A+B)C = AC+BC

2.      The distributive law of multiplication over subtraction.

The formula : A(B - C) = AB - AC

3.      The general distributive property.

Example : 2(1+3+5+7) = 2.1+2.3+2.5+2.7

                                      = 2+6+10+14

                                      = 32

The formula :a(b_1+b_2+b_3+b_4+…+b_n)
             ab_1+ab_2+ab_3+ab_4+…+ab_n

4.      The negation distributive property.

If you negate (or find the opposite) of a sum, just “change the signs” of whatever is inside the parentheses.

The formula : -(A+B) = (-A)+(-B)

                                    = -A-B

“ REFLECTION 2 ”

By : Elsa Winda Prastiana

09313244015

At previous meeting, Mr. Marsigit showed some video about mathematics education. Among other things about Word Problems. In video 1, we can learn how to solve word problems use an acronym BUCK$ to solve word problems. BUCK$  is Box the question, Underline the info needed, Circle the vocabulary, Knock out un-needed info. We use the BUCK$ system to simplify, organize and solve the problem. Academic Vocabulary very important to solve word problems. Then in Video 2, also explained again about to solve word problems in mathematic. In this case, some of basic things to think about where training how to solve the word problem is to figure out what is the fact and what is being else for.   

From video 3, we learn how to solve puzzles and riddles otherwise known as word problems using two variables. An example the problem is a first number plus twice a second number is 23. Twice the first number plus the second number is 31. Find the number. Then we solve this, suppose the first number is x and the second number is y. From the information, we can get the equation x + 2y = 23 and the second equation is 2x + y = 31. From equation 1 we get x = 23 – 2y. Then, we substitute the value of x in the second equation. We get 2(23-2y) + y =31. Then, we calculate 46 – 4y + y = 31. After that we get -3y = -15. So, the value of y = 5. Then we find the value of x is 13. Finally, we get the first number is 13 and the second number is 5.

In video 4, we learn about properties of log. Properties of logarithms is :

a.      log_b x=y ↔ b^y=x.

b.  log_10 x=log x ;log_e x= ln x

c.  log_b (M ∙N)= log_b M + log_b N

d.  log_b M/N= log_b M - log_b N

e.  log_b x^n= n log_b x

      From the properties above, we can solve this problem : 

1.   log_10 100=x. The value of x is 10^x=100. So, x = 2.

2.  log_2 x=3. The value of x is 2^3=x. So, x =8.

3.  log_7 (1/49)=x  ↔ 7^x=1/49
                               ↔ 7^x= 1/7^2
                               ↔ 7^(x)= 7^(-2)
                               ↔ x= -2

“ REFLECTION 1 ”
By : Elsa Winda Prastiana
09313244015

At March 19th 2012, Mr.Marsigit showed some videos about mathematical content. That videos purpose to employ VTR to learn English for Mathematics Education. In video 1, we learn about derivative notation.  We know that notation for derivative is f’(x) is read f prime of x. We also can say y’, because f (x) and y are interchangeable. Finally, we get dy/dx . Key word in derivative is slope of tangent line at point. We can get slope of a line = (y2-y1)/(x2-x1). From the definition of derivative, we get f'(x)=lim(h→0) (f(x+h)-f(x))/h. Derivative just not limit of a slope it is also limit change in values of f(x) over change in x or instantaneous rate of change.

In the next video, we learn about angle. Angle is made up of two rays connected at the same point. First ray drawn to form an angle is called initial side. Second ray drawn to form an angle is called terminal side. Vertex is point where initial and terminal sides meet. Two ways to measure an angle :
1. By the direction terminal side goes in
    If terminal side rotates in counter clockwise direction then positive angle.
    If terminal side rotates in clockwise direction then negative angle.
2. How far the terminal side rotates from the initial side
When measuring an angle we want both the initial and terminal sides on top of one another on x-axis, vertex of two rays at the origin of graph. When an angle’s vertex is at origin of graph and initial side is on positive x-axis the angle is in standard position. X-axis is positive on right side of y-axis and negative on other side but y-axis is positive above x-axis and negative below it.
Two measure an angle in radian and degrees.
   
From the third video, we learn about Trigonometry. Trigonometry is arranged from triangle and meter. From the triangle, we can get about sinus, cosinus and tangent. The formula of Sinus is opposite/hypotenus , Cosinus is adjacent/hypotenus and Tangent is opposite/adjacent. Usually, we can remember it by acronym SOH CAH TOA. In the next video, we learn about inverse function. From this video, we know how to get inverse from a function and how we sketch the graph. Then, in next video we learn about integer. Integer numbers is whole numbers and their negatives. Integer numbers can divide be 3 kinds. First, positive numbers. The second is zero and the third is negative numbers. In the sixth video, we study about factoring polynomials. How we can factorize the polynomial.

Assignment 1 English

Elsa Winda Prastiana

09313244015 

International Math Education ‘09

Exercise No.1 Page 95 Mathematics for Junior High School 2

1.Determine the line equation through point (0,0) and has gradient :

a.12

b.16

c.-3

Solution :

a.m=12

 Since the line through point (0,0) then generally the line has equation y=mx. Given m=12, thus the line equation is y=12x.

b.m=16

 Since the line through point (0,0) then generally the line has equation y=mx. Given m=16, thus the line equation is y=16x.

c.m=-3

 Since the line through point (0,0) then generally the line has equation y=mx. Given m=-3, thus the line equation is y=-3x.

Exercise No.3 Page 95 Mathematics for Junior High School 2

2.Find the equation of a line through point (0,0) and is perpendicular to a line whose gradient of -1/6 .

Solution :

Since, general equation of line a is y =mx. Known the line a is perpendicular with another line with gradient of -1/6. Since the multiple gradient result of the two perpendicular line is -1, then the line gradient of a is 6. So, the line equation of a is y=6x.

Exercise No.2 Page 115 Mathematics for Junior High School 2

3.The price of 2kg of oranges and 3 kg mangos is Rp 38,000.00. Determine the price of 1 kg of orange if known that 1 kg of mango is Rp7,000.00

Solution :

Change the given information in the word problem into mathematical expression. For instance, let 1 kg orange in a and 1 kg mango in b. Accordingly, 2kg of oranges in 2a and then 3kg of mangos is 3b. Therefore we will get an LETV of 2a+3b=38.000. Fom the information we know that b=7.000. Subtitute b=7.000 to the equation of 2a+3b=38.000, thus resulting

↔2a+3(7.000)=38.000

↔2a+21.000=38.000

↔2a=38.000-21.000

↔2a=17.000

↔a=8.500

So, the price of 1 kg of orange (a) = Rp 8.500,00

Exercise No.1 Page 45 Mathematics for Junior High School 3

4.In the afternoon, the length of student’s shadow that has 150cm high is 50cm. If at the same time, the length of the tower’s shadow is 10cm, what is the height of the tower ?

Solution :

The student’s height is 150cm, the length of the student’s shadow is 50cm, and the length of tower’s shadow is 10m (1000cm). The height of the students corresponds to the height of the tower. The length of student’s shadow corresponds to the length of the tower’s shadow so that he proportion the corresponding sides is : 

(the height of the tower)/(the height of the student)=(the length of the tower's shadow)/(the length of the student's shadow)

Let the height of tower is h cm, so by using the proportion in similarity, we get :

h/150=1000/50 ↔ 50h=1000×150

                    ↔ 50h=15.000

                    ↔ h=15.000/50

                    ↔ h=300

So, the height of the tower is 300cm=3m.

Exercise No.2 Page 189 Mathematics for Junior High School 1

5.In a shelve, there are Mathematic books, Indonesian Language books, and Physics books with the ratio of 4∶2∶3. Determine the numbers of Physics books and Mathematical books if the Indonesian Language books is 6 books. 

Solution :

The ratio among Mathematic books, Indonesian language books, and physics books is 4∶2∶3. The number of Indonesian Language books is 6 books. 

The number of Indonesia Language books =  (ratio of indonesia language books)/(total ratio)×total books

6                 =  2/9  ×total books

6× 9/2         = total books

27                 = total books

From that we know that the total number of books is 27 books.

So the number of Math books = (ratio of math books)/(total ratio)×total books 

                                                = 4/9×27 = 12 books

The number of Physics books = (ratio of physics books)/(total ratio)×total books

                                              = 3/9×27 = 9 books

Resume English for Mathematics Education I_week III

“ PERSOALAN PEMBELAJARAN MATEMATIKA DI SEKOLAH”

Oleh : Dr. Marsigit, M.A

Ikhtisar oleh : Elsa Winda Prastiana (09313244015)

Blog : elsawinda.blogspot.com

Minggu, 25 September 2011

Top of Form

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Development of mathematical models of learning through action research to overcome the difficulties of service of teachers to give students a positive impact, but in actual experience obstacles both technical, academic, and socio-cultural. Business teachers in meeting the academic demands of a wide range of students, encourage students to improve achievement of low achievers, encourage students to learn actively, and encourage students to learn through collaboration, can be done by:

a. Developing the Student Worksheet

b. Formation of study groups

c. Development of methods class discussions / group

d. Development of teaching aids and educational media.

In the effort to develop a model of learning can be concluded:

a. Teachers are still having difficulty in meeting the various demands of academic students.
b. Teachers have developed a scheme to encourage students to improve achievement of low achievers
c. Teacher has managed to create conditions so as to encourage students active learning; but still have  difficulty in develop the scheme.

d. Teacher has managed to create conditions to encourage students to learn through 

     cooperation; but still have difficulty in developing the scheme.

e. Teachers have tried to develop a method of discussion, problem solving and training  and the provision of tasks; but still have trouble in developing the scheme.

In general, teachers have sought to develop learning methods in accordance with the purpose of action research; but teachers experiencing technical difficulties, and academic fundamentals. Technical difficulties of teachers in developing teaching methods that have not require tools or learning the necessary facilities. Academic difficulties of teachers in developing teaching methods are not yet perceived incompatibility of the teachers' mathematical learning model with the meaning of the learning model according to the theory referred to.

Suggestions for teachers: Teachers can make efforts to increase the quality of learning mathematics through the development of ways / methods to meet the various needs / demands of academic students, encourage students to learn actively, encourage students to learn to cooperate, and try to start developing a learning tool using technology modern.

In developing methods of learning, the teacher suggested:

• planning a mathematics learning environment

• plan mathematical activities

• develop the role of teacher

• set the time to whom and when to perform activities mathematics together /

  not  together students 

• observe student activities

• evaluate yourself

• assess understanding, processes, skills, facts and results

• assess the results and monitor student progress

Not only the teacher's role is needed, but also the role of both school principals and fellow teachers are also needed for success in overcoming the problems in learning.

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REFLECTION ON THE TEACHING OF “THE MULTIPLICATION ALGORITM OF THE 3^rd  GRADE OF PRIMARY SCHOOL” THROUGH VTR

Oleh : Dr. Marsigit, M.A

Ikhtisar oleh : Elsa Winda Prastiana (09313244015)

Blog : elsawinda.blogspot.com

Minggu, 25 September 2011

VTR untuk pendidikan guru dan gerakan reformasi di Pendidikan Matematika, khususnya untuk mengembangkan studi pelajaran memiliki beberapa manfaat sebagai: ringkasan pendek dari pelajaran dengan penekanan pada masalah utama dalam pelajaran, komponen pelajaran dan peristiwa utama dalam kelas, dan kemungkinan masalah untuk diskusi dan refleksi dengan guru mengamati pelajaran (Isoda, M., 2006). Katagiri, S (2004) tercantum jenis pemikiran matematika sebagai sikap matematika, berpikir matematika yang berkaitan dengan metode matematika, dan berpikir matematika yang berhubungan dengan isi matematika. Ini identifikasi berpikir matematis dengan Katagiri dapat menjadi titik awal untuk mencerminkan proses belajar mengajar matematika di sekolah seperti untuk untuk mencerminkan ajaran "algoritma perkalian dari kelas 3 sekolah dasar" oleh Mr Hideyuki Muramoto, kemudian, VTR pelajaran ini akan ditargetkan untuk serangkaian kegiatan: pengamatan dan refleksi. Karakterisasi Pelajaran :

1.      Karakterisasi Pelajaran dari Rencana Pelajaran

Karakteristik awal pengajaran Muramoto adalah ditetapkan dalam Rencana Pelajaran seperti sebagai    berikut:

a.       Tema: pelajaran matematika kelas tiga yang mendorong kemampuan siswa untuk  menggunakan apa   yang mereka pelajari sebelumnya untuk memecahkan masalah dan membuat hubungan dalam rangka untuk memecahkan masalah dalam situasi belajar yang baru.

b.      Metode

c.       Tujuan

d.      Skenario Pengajaran

1)       Mengembangkan pengajaran yang membantu siswa untuk menyadari sambungan antara apa yang mereka pelajari sebelumnya dan apa yang mereka pelajari sekarang dan menggunakan pengetahuan yang dipelajari sebelumnya untuk mengatasi hambatan dalam situasi baru.

2)       Sambungan antara pengetahuan yang telah dipelajari sebelumnya dan pelajaran baru

3)       Mewakili suatu situasi masalah dengan diagram.

4)       Mengembangkan pelajaran yang menggabungkan ide ini dan membantu siswa untuk menggunakan diagram untuk berpikir

Karakterisasi Pelajaran dari VTR

a. Masalah dari rekaman video

- Kualitas gambar yang relatif baik

- Kamera tunggal membuat pembatasan lansekap kelas

- Tulisan kecil di layar membantu untuk menangkap lebih gambar kelas
b. Komponen pelajaran

- Seluruh kelas telah mengurangi kompleksitas interaksi kelas menjadi

   pola sederhana atau linear dari interaksi antara guru dan siswa.
- Menyoroti ide-ide tertentu dari siswa tertentu telah mengabaikan ide siswa  

  lainnya
- Menyoroti aspek tertentu dari pemikiran matematika dari siswa-siswa  

  tertentu.
c. Mendorong dan mengungkap siswa berpikir matematika

- Guru usaha dalam mendorong dan mengungkap siswa berpikir matematika

  adalah cukup efektif.

- Upaya Guru dalam melayani siswa secara individual tidak efektif lagi.

- Beberapa siswa mampu melakukan pemikiran matematika

- Guru mampu mencapai tujuan pelajaran

- Berpikir Matematika dari siswa tertentu dapat menjadi model bagi orang   

  lain.

- Siswa yang berbeda, dalam alokasi waktu yang sama, apakah masalahnya

  sama dengan menggunakan metode yang berbeda untuk menumbuhkan

  hasil yang sama.

- Diskusi Siswa di antara mereka sendiri belum muncul.

- Keterlibatan siswa dalam manajemen kelas masih terbatas.  

- Guru telah efektif menggunakan alat bantu mengajar yang tepat.

Revitalisasi Pendidikan Matematika

Oleh : Dr. Marsigit, M.A

Ikhtisar oleh : Elsa Winda Prastiana (09313244015)

Blog : elsawinda.blogspot.com

Minggu, 25 September 2011

Top of Form

Teach mathematics is not easy because we find that students are also not easy to learn mathematics (Jaworski, 1994: 83). On the other hand found the fact that it is not easy for educators to change the style of teaching (Dean, 1982: 32). While we are required, as educators, to constantly adjust our teaching methods in accordance with the demands of changing times (Alexander, 1994: 20). Revitalization of mathematics education trying to put the important role of teachers to make math education more in line with the (returned to) educate in the sense of meaning in truth and nature of science which is the object of learning it self.

Cocroft Report (1982: 132) at least gives one solution. After a thorough investigation 'large scale survey' in Britain, learning mathematics should be offered an opportunity for teachers to use the choice of teaching methods that are tailored to student ability levels and material ajarnya as follows:

1. method of exposition by the teacher

2. method of discussion, between teachers and Students and between Students  and  students.

3. methods of problem solving

4. method of discovery (investigation)

5. basic skills training methods and principles.

6. methods of implementation.

Because the mathematics associated with all the knowledge of the human self, it is clear that mathematics is not neutral and value free. Thus mathematics requires a social foundation for their development (Davis and Hers, 1988: 70 in Ernest 1991: 277-279).Shirley (1986: 34) explains that mathematics can be classified into formal and informal, applied and pure. Based on this division, we can divide the activities of mathematics into 4 (four) types, where each has different characteristics:

a. formal mathematics-pure, including mathematics developed at the University and the mathematics taught in schools; 

b. formal-applied mathematics, namely that developed in and outside education, such as a statistician who worked in the industry.

c. informal-pure mathematics, ie mathematics which developed outside the educational institution; may be attached to the culture of pure    mathematics.  

 d. informal mathematics, applied mathematics that is used in all daily life,  including crafts, office work and trade. 

Dowling in Ernest (1991: 93), based on recommendations from Foucault and Bernstein, developed a variety of contexts mathematical activities. He divided the one-dimensional model into 4 (four) types: Production, Recontextualization, Reproduction and Operationalization. The second dimension of development includes 4 (four) types: Academic, School, Work and Popular.

Ebbutt and Straker (1995: 10-63), provides guidelines for the revitalization of mathematics education in the form of basic assumptions and their implications for learning mathematics as follows:

1. Mathematics is the search activity patterns and relationships.

2. Mathematics is the creativity that requires imagination, intuition and discovery.

3. Mathematics is problem solving activities

4. Mathematics is a tool to communicate

5. Mathematics Teaching Materials include:

- Facts

- Concepts

- Skills algorithms

- Reasoning Skills

- Problem-solving Skills

- Investigation Skills

On the other hand, Ebbutt and Straker (1995: 60-75), gave his view that in order for the students' potential can be developed optimally, then the following assumptions can be used as a reference:

1. Students will learn if given the motivation.

2. Students studying in its own way

3. Students learn independently and through cooperation

4. Students need the context and circumstances that vary in their learning

Revitalization of mathematics education is an effort in the direction where the practitioners mathematics education are given the opportunity to conduct self-reflection, for then faced with multi-entry decision on the basis of the attitude of the in-depth study towards a new paradigm has to offer. That teachers are better able to realize the revitalization of the (educational) learning mathematics that fosters the creativity of students the teacher must pass the Phase Preparation Teaching, Learning Phase, and Phase Evaluation.

Wawasan Tentang Strategi dan Aplikasi Pembelajaran Matematika Berbasis Kompetensi

Oleh : Dr. Marsigit, M.A

Ikhtisar oleh : Elsa Winda Prastiana (09313244015)

Blog : elsawinda.blogspot.com

Minggu, 25 September 2011

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• Characteristics of School Mathematics
In order to meet the demands of learning mathematics educational innovation in general, Ebbutt and Straker (1995: 10-63) defines the mathematical school, hereinafter referred to as a mathematician, as follows:
1. Mathematics as search activity patterns and relationships.
2. Mathematics as a creativity that requires imagination, intuition and invention.
3. Mathematics as problem solving activities (problem solving)
4. Mathematics as a tool to communicate

• Characteristics of Student Learning Mathematics
Ebbutt and Straker (1995: 60-75), gave his view that in order for the students' potential can be developed optimally, subject to assumptions about the characteristics of learners and implications for learning mathematics are given as follows:
1. Pupils will learn math if they have the motivation
2. Pupils learn mathematics in its own way
3. Pupils learn math either independently or through collaboration with friends
4. Pupils need the context and the different situations in studying mathematics

• Hierarchy Aspects of Affective and Psychomotor

According to Paul (1963:519) the attitude of an individual's readiness for
react so relatively fixed dispositions that have been in had through experience that took place on a regular basis and direction. Krech (1962: 139) states that attitude is a system consisting of the cognitive component, feelings and tendencies to act. Attitude is the level of positive feelings or negatively directed to objects of psychology. Thus the mean attitude tendency of feeling toward the object of psychology that is a positive attitude and negative attitude whereas the degree of feeling in the mean as the degree of assessment of the object.

In addition to aspects of cognitive and affective aspects, aspects of motor skills also have a role that is not less important to know the students' skills in solving problems. In this activity students are asked to demonstrate abilities and skills do physical activities such as drawing a triangle, square painting, painting circles, etc.. To determine the skill level of students, evaluators can use the observation sheet.

• Competency-Based Mathematics Curriculum

A.    The Standard of Competency

The curriculum is designed to be in the process of learning mathematics, students are able to perform the search patterns and relationships; develop creativity with imagination, intuition and invention; perform problem-solving activities; and communicate mathematical thinking to others.

B.     Syllabus Format

Format syllabus is a form of presentation of the syllabus content consists of standard
competencies, basic skills, learning materials, descriptions of learning materials,
student learning experience of time allocation, and reference sources used, while
systematic presentation of the syllabus describes the sequence of parts of the syllabus.

C. Syllabus Preparation Steps Basic Capabilities-Based Currency Math Lessons

Step-by-step preparation of syllabus-based Basic capable eye Math lessons, a series of events that begins with the study philosophical development of mathematics education, including the preparation of scientific structures.

C.     Determination of Learning Materials and description

For all levels of education, mathematics learning materials include:
a. Facts
b. Concepts.
c. Reasoning skills

d. Algorithmic skills

e. Mathematical problem-solving skills

f. Skills investigation

E. Learning Development Unit

Component units of learning include: Identity Subject, Basic Capabilities, Learning Materials, Learning Strategy, Learning Media, Assessment / Assessment, Material Resources