THE SOUNDTRACK OF LIFE

Mathematics can we practice from a song. It is also more fun! Believe it! Why? Because we can express our emotion and our expression. Do you know? From a song, we can show our creativity. That is that Mr. Marsigit give to his students include me. We were given some mathematics songs.

Song: Do you know about math

It is tell us what mathematics is. There are many chapters in mathematics. For example : multiply, memorizing pi, take limits, to simplify, graphing utility, trigonometry, limits, logarithm, exponential, etc. From that song we know that learn mathematics is fun.

Song: Perimeter

From this song we can learn how to measure perimeter of a shape. It can be circle, triangle, squares, rectangles, parallelograms, trapezoidal, kite, etc.

Song: Mean, median, and mode

From this song we learn about statistic. We can practice how to find median, mean, and mode. Mean is the average of the data. To find mean, it is to add up the numbers in the data, then divide the total by the number of items. Then median is the middle value, to find it, we must look arrange the numbers in order from the lowest to the highest values. The middle number is the median for an odd number of items. The average of two middle numbers is the median for an even number of items. Mode is the value that often arise, to determine it just find the number that repeats most often.  If there is no number that repeats most often, there is no mode.

Song: The math song

It is song from Bruno Mars with title The Lazy Song. That song is made with fun style. So, it can interest student. We can practice more easy.

Then some videos from Mr. Marsigit. That video show about derivative, integer, and angle.

Derivative is slope of tangent line at point (x, f(x)) ((x+h),f(x+h)), h is change of x. Slope = (y2-y1)/(x2-x1). Definition of derivative F’(x)= limh→0 (f(x+h)-f(x))/h. So, derivative is a slope. Derivative is limit a slope, limit change. Then, try find f’(2) from f(x)= 4×2-8x+3. Substitute f(2) and f (2+h)to the function. Then, simplify and factory.

Integer is whole number, not fractional or decimal. Whole numbers that greater than zero are called positive integers, It is on the right of zero in the number line. Whole numbers less than zero are called negative integers, it is on the left of zero in the number line. In the integer, there are place number, such as unit place, tens place, hundred place, thousand place, etc.

Angle. There are several kinds of angles: acute angle, the angle whose measure is less than 90⁰. The angle brackets, which the measure is 90^0. Obtuse angle, the angle whose measure is greater than 90⁰. Straight angle, the angle whose measure is180⁰. Two angles that complement each other is total of the measure is 90⁰. Two angles that supplement each other is total of the measure is 180⁰. Vertical angles are two angles that the places are opposite each other. Angle bisector is a ray that splits an angle became two congruent angles. Perpendicular lines are intersecting lines that from right angle.

That’s all…. So, we can say that practice mathematics is fun. Sing your own song and show your expression. Be creative student!

TEACH MATHEMATICS, TEACH OUR LIFE

Stadium General

Monday, March 12th 2012, 1 p.m.

By Prof. Mohan Chinnappan, Ph.D

Last Monday, I had to join a stadium general at Seminar Room floor 2, MIPA. It was also task from my lecturer, Mr. Marsigit. There was presented someone from Australia that was Prof. Mohan Chinnappan, Ph.D. I must make a report after I attended the stadium general. During the stadium general, I try to listen carefully and write that I can understand. It was very pleasant because from him I can know about education from other country especially about mathematics education.

Many things that Prof. Mohan Chinnappan, Ph.D. explained to participant. First, about mathematical thinking like the theory of Shigeo Katagiri. It include 3 matters.

Mathematical thinking consist of:

1.      Mathematical attitude

2.      Mathematical method

3.      Mathematical content

Then, an analogy between mathematics and tailor. Before the tailor sew the cloth, he make draw what will he sew. He does it in order to make easy when he sew the cloth. So, there is no mistake and his job will finished well. We can say that the sailor make a pattern. From that pattern, he can work well. Now, like the sailor, mathematics also have pattern. That pattern has function when we learn mathematics. So, pattern and relationship in mathematics include:

1.      Problem solving

2.      Communication

3.      Investigation

The next explanation is about religion knowledge and mathematics knowledge. There is a question. What is the relationship between natural knowledge and religion knowledge? To answer it, Prof. Mohan Chinnappan, Ph.D. give example of some matter.

1.      Relationship between praying and mathematics. Before and finish the lesson we are praying.

2.      Zakat is depend on our property. To count how much we must give zakat, we can use mathematical operation. Every kind property that we have, it is has different calculation. So, we need mathematics.

3.      We can calculate inheritance.

4.      Zero = notion of nothing. It use for nothing. Decimal system become more complete.

5.      Basis number  system: 0, 1,2, 3, . . ., 9. We can not change the position of Al-Qur’an.

From that explanation, we can state that there is close connection between mathematics and religion.

Then, it is about culture in Indonesia. What is the culture of Indonesia in mathematics knowledge? Mathematics can be interpreted in Indonesian culture. From our culture, we can know how mathematics is used. When count the day dead in Java like “pasaran” days. For example is Pon, Wage, Kliwon, 7 days, 100 days, 1000 days, etc. It is just use modulo five.

The other is the construction of temple. Geometry construction is five steps and around the temple there is relief. Ramayana: 1 à earth

                                                   2 à couple

                                                   0 à the symbol of loss

There is also important about lesson study to teach. Lesson study include teachers as model, observers, and resource persons. Lesson study is based on students  learning activities.

In lesson study, we need to do three actions. First, detailed planning. Include material approach, how to present to the students, and the estimated constraints. Second, doing. Present the lesson, observing the activity of students, when students begin to learn, when students are getting bored, and what activities that support student learning and not support the learning. We must pay attention our student in the class and need to understand situation in the class. Third, reflection. In reflection, we do evaluation. From activities in the class, we can conclude many things. So, we can know if we do a mistake or there are something that we must be increased or decreased. Teacher must have strategy to teach his/her students. The lesson study can help teacher to solve the problem and make the teacher ready when face his/her students. So, we should involve lesson study in the class room.

The last session is discussion. There are some question from the participants.

- So many subject in the school because some society need many knowledge. So they must study more. To understand more knowledge, we need learn more subject. It is different with Indonesia. In Indonesia, the subjects are more than in Australia.

- In Australia, people can choose 5 subjects since 12 years old. For example science, mathematics, language, etc. It is also different. In Indonesia, students learn all subjects since in elementary school. Then in senior high school, there are three majors and also kind of school like SMA, SMK, etc.

- How to teaching mathematics in Australia? Use ICT, smart board, Internet to download and solve problem, and use laptop, etc. From Prof. Mohan Chinnappan, Ph.D. answer, we know that facilities in Australia are more good than in Indonesia.

- How to cope with children with skills below average?  

Based on the facilities on the school. Government also support the school. Teacher creates worksheets that correspond to student ability. Learning to do and learning to be.

- Character of education in Indonesia and Australia is different.

Australia: secular country and liberal democracy.

Indonesia: there is religion school for example Islamic school, Christian school. But public school do not support religion as many as in religion school.

For the closing, there are some conclusions:

- We need to be rational to the subjects and what kind of activity.

- Developing of teacher professionalism.

- Understand national curriculum and theory in mathematics.

- Attention to our culture and we have characteristics because our culture is important.

- How to manage the different competence in mathematics.

INTERPRETATION OF MATHEMATICAL THINKING FOR TEACHING MATHEMATICS

Teaching mathematics is not simple. It is needed some methods, creativity, and knowledge. It is also needed some experience from applying mathematics. To understand about it, then we should study about mathematical thinking. Mathematical thinking is said by Shigeo Katagiri in 2004. It include 3 matters. First, Mathematical attitudes. Second, mathematical thinking related to mathematical methods. Third, mathematical thinking related to mathematical contents.

Let see the explanation and the example about the 3 matters of mathematical thinking in Marsigit’s book, that is in Mathematics 3 for Junior High School Year IX.

1.    Mathematical Attitudes

Mathematical attitude is different with attitude toward mathematics. Mathematical attitude, they are more specific. Attitude toward mathematic, they are more general.

Attempting to Grasp One’s Own Problems or Objectives or Substance Clearly, by

Oneself

- Attempting to have questions

- Attempting to Maintain a Problem Consciousness

- Attempting to Discover Mathematical Problems in Phenomena

*Example: page 35 number 1

A frame of picture is in the form of rectangle by the size of outside edge 30cm x 20cm. if the edge of the picture frame is attached by additional frame of 5 cm wide, decide whether the outside edge of rectangle of the picture is similar with the inside edge of rectangle. Explain your answer.

Attempting to Take Logical Actions

- Attempting to Take Actions that Match the Objectives

- Attempting to Establish a Perspective

- Attempting to Think Based on the Data that Can Be Used, Previously Learned Items, and

Assumptions

*Example: page131 number 1.a and 1.b

A six-sided dice was rolled once. Find (a) the probability of obtaining the even-spot side or the odd-spot side. (b) the probability of obtaining the even-spot side or the side with spot greater than 3.

Attempting to Express Matters Clearly and Succinctly

- Attempting to Record and Communicate Problems and Results Clearly and Succinctly

- Attempting to Sort and Organize Objects When Expressing Them

*Example: page 141 number 16

A cone has a slant height of 7cm and radius 3,5 cm. The surface area of the cone is …

Attempting to Seek Better Things

- Attempting to Raise Thinking from the Concrete Level to the Abstract Level

- Attempting to Evaluate Thinking Both Objectively and Subjectively, and to Refine

Thinking

- Attempting to Economize Thought and Effort

*Example: page 213 number 20

The sum of 8 – 4 + 2 - … - ¼ is …

2.   Mathematical Thinking Related to Mathematical Methods

It cover all of your past and present experiences in doing mathematics plus its theoretical review.

Inductive Thinking

Page 195 number 1.a:

Find the 21^st term of the following arithmetic sequences. a) 3, 7,11,15, …

Analogical Thinking

Bab 1 page 49  number 11:

The proportion between the length of two similar sides is 2:3.If the diagonal length of the small rectangle is 30 cm, so the length of the diagonal of the bigger rectangle is …

Deductive Thinking

Page 231 number 11:

In a class, 25 people join in basketball training, 35 people join in table tennis, and 15 people join both of them. If 3 people in the class do not join in any activities, the amount of students in the class is …

Integrative Thinking

Page 133number 5:

The mean of the art test score from a certain group of students is 75. After a new member join the group, the average turns into 73. The art test score of the new member is …

Developmental Thinking

Page 45 number 3:

Two flag poles have their length of shadow respectively x m and (x+12) m. If the length of the shorter pillar is 1/3 the length of the higher pillar, calculate x.

Abstract Thinking

Page 17 Example:

Show that ΔPQY congruent ΔRQY.

Thinking that Simplifies

Page 170 number 6:

(-a^-3)^3 (-a^5b^5)^2

Thinking that Generalizes

Page 179 number 1:

Find the sum of 2+4+6+8+ …

Thinking that Specializes

Page 47 number 5:

ΔDEF and XYZ are congruent. The length of YZ is ...

Thinking that Symbolize

Page 225 number 25:

The values of a and b of the sequence 41, a, 55, b, …

Thinking that Express with Numbers, Quantifies and Figures

Page 213 number 3:

In 5 weeks, Budi has been training to face the marathon competition. Each week he has to run twice time further than the week before. In the 3^rd week he runs 3km. Determine the total distance for Budi in five weeks training.

3.    Mathematical Thinking Related to Mathematical Contents

Clarifying Sets of Objects for Consideration and Objects Excluded from Sets, and Clarifying Conditions for Inclusion (Idea of Sets)

Page 15 Example:

Let ΔAB Congruent  ΔDEC as shown in the figure. Determine the congruent sides and angles of both triangles.

Focusing on Constituent Elements (Units) and Their Sizes and Relationships (Idea of Units)

Page 77 number 5:

An orange is sliced athwartly in equal size. It is found that the orange diameter is 7 cm (the orange is assumed as spherical shape). Determine the volume of the half of orange.

Attempting to Think Based on the Fundamental Principles of Expressions (Idea of Expression)

Page 169 number 1:

Rationalize the following roots. 1/2√5 - √3

Clarifying and Extending the Meaning of Things and Operations, and Attempting to Think Based on This (Idea of Operation)

Page 237 number 39:

A ladder has steps height from the ground of 15 cm, 25 cm, 35 cm. … If the ladder has 25 steps, the height of the last step from the ground is …

Attempting to Formalize Operation Methods (Idea of Algorithm)

Page 235 number 29:

The solution of 3x + 2y = -5 and 4x – y = 19 is p and q. The value of p + q is …

Attempting to Grasp the Big Picture of Objects and Operations, and Using the Result of this Understanding (Idea of Approximation)

Page 141 number 14:

A biscuit can has diameter 20 cm and height 10 cm. The surface area of the biscuit can is …

Focusing on Basic Rules and Properties (Idea of Fundamental Properties)

Page 155 Example:

Covert the following negative exponents into positive exponents. 1) 2^-5 answer is ½^5

Attempting to Focus on What is Determined by One’s Decisions, Finding Rules of Relationships between Variables, and to Use the Same (Functional Thinking)

Page 35 number 5:

At the TV screen, it was seen a monument of 10 cm high and 4 cm wide. If the real width of the monument is 10 m, what is the real height of the monument?

Attempting to Express Propositions and Relationships as Formulas, and to Read their Meaning (Idea of Formulas)

Page 185 Example number 2:

The 25^th term of the square numbers is n^2 = 25^2 = 625