Mathematical Thinking (Shigeo Katagiri) n Stadium General

Name: Soleh uzain Class: Mathematic Education 2011 NIM : 11301241018 Mathematical Thinking (Shigeo Katagiri) 1.Mathematical Attitudes : a.Attempting to grasp one’s own problems or objectives or substance clearly, by oneself For example : 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? (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 35, number 5) b. Attempting to take logical actions For example : A six-sided dice was thrown 30 times. What is the expectation frequency of occurrences of the even spot side? (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 122, number 2) c. Attempting to express matters clearly and succinctly For example : Mother buys a watermelon. The perimeter of the surrounding watermelon is 62.8cm. (the watermelon is assumed as sphere). The volume of the watermelon is… (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 81, number 15) d. Attempting to seek better things For example : Find the sum of the first 15 terms of the series of 1+√3 + 3 + 3√3 + ....
(Mathematics 3 For Junior High School Year IX, Yudhistira, Page 209, number 3)

 2. Mathematical Thinking Related to Mathematical Methods a. Inductive thinking To conclude the general thing from the specific things. For example : Find the next three numbers of the pattern of 24,26,28,30,32, … (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 181, number 1) b. Analogical thinking for example: Find the ratio value and the 5th term of the following geometric sequences. 64,16,4,1,... (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 199, number 1) c. Deductive Thinking for Example: Expression of an means the repetition of multiplying by a i.e. showing multiplication, as much as n factors. an is an exponent. an = axaxax…xa n factor (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 151) d. Integrative thinking for example: The amount of students in the class is… (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 231, number 11) e. Developmental Thinking For Example: A building has a roof in the form of hemisphere with diameter 14 m. The roof is made of glass. If the price of the glass is Rp500,000.00 per m2, determine the cost of the entire roof surface. (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 75, number 4) f. Abstract Thinking for Example: If a and b are integer, and an=b, then a is n root of b, and it can be written as a=n√b (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 157) g. Thinking that simplifies For example .With the selling price rp2,200,000.00 a camera trader can reach 10% profits. The buying price of the camera is…90 divided 100 multiply 2200000 equal to rp1,980,000.00 (page 229) (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 229, number 4) h. Thinking that generalizes For example : The daily mathematics test score of a student in a certain period as shown in the table below, the mean can be calculated by the method below (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 109) i. Thinking that Specializes Example: Because the sum of the triangle’s sides is 180˚, hence it is applicable that: angleABC + angleBCA+ angle CAB = 180˚ (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 23) j. Thinking that symbolize Example : The height is given symbol “t”. (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 59) k. Thinking that express with numbers, quantifies, and figures Example Consider the following figure (Mathematics 3 For Junior High School Year IX, Yudhistira, Page 47, number 2) 3. Mathematical Contents a. Clarifying Sets of Objects for Consideration and Objects Excluded from Sets, and Clarifying Conditions for Inclusion (Idea of Sets) Example ; Consider the following figure. (page 47) b. . Focusing on Constituent Elements (Units) and Their Sizes and Relationships (Idea of Units) Example: How to rationalize the roots (page 163) c. Attempting to Think Based on the Fundamental Principles of Expressions (Idea of Expression) Example: There are several properties of positive exponent, for a is an interger, m and n are positive interger. 1. am xan=am+n 2.am:an=am/an=am-n (page 151) d. Clarifying and extending the meaning of things and operations, and attempting to thinkbased on this (Idea of operation) example: 23 x 25 = 2x2x2 x 2x2x2x2x2 = 2x2x2 x 2x2x2x2x2= 28 or 23 x 25= 23+5=28 (page 151) e. Attempting to formalize operation methods (Idea of algorithm) After the data is arranged from the smallest, the result is: 155 157 160 163 165 168 (page 111) f. Attempting to grasp the big picture of objects and operations, and using the result of this understanding (Idea of approximation) example. Line chart of the measuring of sombody’s weight. Consider the chart, in the year axis, the number 2004 shows scale 70 in the weight axis. Hence, in year 2004 his/her weight is 70 kg. (page 97) g. Focusing on basic rules and properties (Idea of fundamental properties) Example: Two circles have 11 cm and 3 cm radius with M and N in the center.If the distance between M and N is 17 cm, then the outer common tangent AB is... (page 235) h. Attempting to Focus on What is Determined by One’s Decisions, Finding Rules of Relationships between Variables, and to Use the Same (Functional Thinking) Example: Are there any relation between exponent and roots? (page 149) i. Attempting to express propositions and relationships as formulas, and to read their meaning (Idea of formulas) example. The formula of arithmetic sequence for the n-term is given as follow. Un=arn-1 where Un = the n-term, for n is natural numbers, a= the 1st term (U1), r= ratio. (page 197) Name: Soleh uzain Class: Mathematic Education 2011 NIM : 11301241018 The Reflection of Stadium General from Prof. Mohan Chinnapan, PhD Report of Stadium General, with Prof Mohan Chinnappan, PhD and mr. marsigit as moderator. theme raised at this event is Be Good Teacher with Mathematics. many faculty and students who did not get a seat because the participants who came exceeds the available seats. This shows how interesting and importance of this event for us. Prof Mohan Chinappan share some knowledge of mathematics and a good teacher. To be good teachers, we must know the contents properly. After knowing the contents, we must know how children learn the content. Each child is unique in the class, so one of the differences with the other students. A good teacher has a good method to keep students in touch with teachers. Talk about mathematics, mathematics is important, very important to get a job and can make sense in the world. Examples are the benefits of learning patterns in elementary school. This will help us to decide the quantity. Thus, this pattern is very important, because it can predict anything. And Mathematics also learn about numbers. Numbers help us to decide the quantity. Not only is the pattern, and numbers, but also learn about the count. When calculated, there are many patterns, you have to understand the knowledge and you need to know the contents properly. Then we come to the explanation of the source of mathematic knowledge. Prof. Mohan explained that mathematical knowledge rooted in religion, as in the teachings of Islam, we know that the Qur'an is the highest knowledge. In the Qur'an there is knowledge of mathematics and other sciences. As well as the Qur’an that cannot be changed, mathematics also cannot be changed, it is an exact science. Mathematics is the science that important. Mathematics is also found in the Hindu religion, like the basic system and decimal system. Zero. Zero is a number which sometimes becomes something that is nothing, but it's so difficult, if we do not have zero, because the number system does not mean anything without a zero. So religion is set with knowledge. At this point, Mr. Marsigit reminds us of previous lectures about the fourth stage of mathematics method, such as concrete mathematics, concrete models of math, formal models of mathematics, and formal mathematics. The conclusion 1. We need to always have relationalize of what kind of subject, topic, activity 2. The developing of teacher profesionality 3. The need to understand international paradigm, theories of math. 4. How to make use power of culture 5. Some aspect how to manage different competent.