Minggu, 18 Maret 2012

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 21st 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 3rd 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 25th term of the square numbers is n^2 = 25^2 = 625

Tidak ada komentar:

Posting Komentar