Pembelajaran Matematika Berbantuan Kalkulator : Studi Kasus Penggunaan Kalkulator Texas Instrumen TI 89 pada PBM Matematika Di SMK MUHAMMADIYAH IV YOGYAKARTA

Pembelajaran Matematika Berbantuan Kalkulator :

Studi Kasus Penggunaan Kalkulator Texas Instrumen TI 89 pada PBM Matematika

Di SMK MUHAMMADIYAH IV YOGYAKARTA

Presented By National Seminars
"National Seminar on Science and Mathematics Education: The Role of
IT / ICT in Supporting the Implementation of Competent-Based Curriculum "
Education at the University of Indonesia, Bandung
August 25, 2003

By:
Drs. Marsigit MA

(Lecturer at the Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, State University of Yogyakarta)
And
Retno Siswanto S.Pd.
(Mathematics teacher at SMK Muhammadiyah Yogyakarta IV)

 

Reviewed By : Eka Sulistyawati



Organized by
Faculty of Mathematics and Natural Sciences, Indonesia University of Education (UPI Bandung)
In Cooperation with
Japan International Cooperation Agency (JICA)
And
Directorate General of Higher Education (DGHE)

Abstrack

This research aims to identify and develop the use of Texas Instruments TI 89 calculator in the PBM Math Class I SMK IV Muhammadiyah Yogyakarta. In SMK Muhammadiyah IV Yogyakarta, case studies discussion of equations and inequatlities.

This case study noted some of the result include : 1) graphic calculator can used to match the graphic image, match answers to the set of solution and provide a real experience of graphic images, 2) method to solve the problem equations and inequalities can be viewed as a command, symbolic manipulation and graph on the calculator, 3) graph calculator useful to indicate the answers that were previously calculated without a calculator and accelerates mathematics problem solving.

The obstacle experienced by students in the use of graph calculators among others, difficulties in pharaphrase sentences into the language of mathematics calculator and expressing any appear calculator screen into mathematical sentence.

A.    Preface

In developed countries calculator to get an important role in the process of learning mathematics. This is indicated by the use of calculators in mathematics learning from education basic to higher education. The important of a calculator is to bridge the arithmetic and algebra (tenoch E.Cedillo;2002:1).

In the process of learning mathematics teachers need the ability to have a scheme learning. With the scheme teachers are expected to have systematic in learning mathematics. So that, the learning mathematics will be systematic and structured. Types of calculators had great development. Judging from utilization calculator consist of two types. That are namely ordinary calculators and scientifics calculators. Which pressed more previous sign that more is done. For example in the calculation of 2+4 x 8, according to the ordinary calculator 6x8=48. Yet according to mathematical rules, the first multiplication resolved, so it should be 2+(4x8)=2+32=34. While the scientific calculator widely uses by junir high school students, teachers, or students university to help the counting function. Scientific calculator has a way work that follows the rules work in mathematics. Examples in the calculation of 2+4x8, according to a scientific calculator, multiplication first done so 2+4x8=2+32=34.

An example of a scientific calculator is a graphic calculator. Graphic calculator has its own advantages than regular calculator. The advantages lies in the ability of the calculator in solving mathematics quickly and display them in graphical form. Another advantages of graphic calculator can create program that can solve mathematics problem.

B.     Case Study

A sign that the person is have learned that there change in behavior on the person that may be caused by changes in the level of knowledge, skills, and attitudes.(Azhar Arsyad;2000:1). In implementing learning process, teachers should be able to serve the learning activities students, so the learning activities students become effective and dynamic. Teachers should place ourselves as servants for students in learning activities. So that the teachers have duty to encourage, guide and facilitate learning for students to achieve goal. (Slameto:1995:97)

To give services to students, a teacher cannot regardless of the method of learning. There are several methods of learning which can be selected by the teacher. Discussion method is a vehicle for teachers to give opportunity to the students (group of students) to debate scientific hold in order to collect opinions, make inferences, and develop various alternative solutions to a problem. The learning process would be more effective if students involved in a real experience with the use of five senses well. (Oemar Hamalik,1989:9). So the learning process is the process of communication between teachers and students with certain conditions which would be more effective with experience with the use of five sense.

While the calculator can be viewed as a tool in learning. The calculator can be viewed as a tool in learning. The calculator according to the Dictionary of Electronics (Wasito;1996:83-94) is a special tool to perform arithmetic with the preparation of data and instructions are included to it. Most of these tools require the intervention arms, which can be used to implement calculation logic and digits. The benefits that can be explored from the use of calculators in Strategi Pembelajaran Matematika Kontemporer (2001:241-244) are : a) help to understanding mathematic concepts, b) help more strength the skills computation, c)develop high level thinking skills, d)improve problem solving skills, and e) make the solution problem more be realistic.

Merriweather an Thrap (1999) stated that the use of graphic calculators in class can cause a student to be affected and involved in mathematics, and cab solce mathematics problems which these issues are not resolved at that time. Hambre and Desert in they research entitled Effect of held-held Calculators in Pre-College Mathematics Education(1986) concluded that : a)calculator should be uses in any learning of mathematics, b) the computers is helpful in improving problem solving skills, especially for students with low and high ability. Meanwhile, K.Kuech Robert in his research titled Using Digital Technologies in the Science Classroom to Promote Conceptual Understanding(2002) proff that: a) a dynamic atmosphere showing with a movement graph and students angaged in conflict kognitife, provides an opportunity discussion of additional information in the graphic calculator and improve understanding of the concept, b) equipment technology can be a means to speed up the meaning, reflect on and analyze the data and plugging, and c) equipment technology can be a means to improve the evaluation of hypotheses with the relationship between the diverse data.

C.    Research Results

The result can be translated into several sections. Some part is the process of implementing the use of graphic calculators in the process of learning mathematics, methods of solving problems equations and inequalities with graphic calculators, and student response toward the use of calculators in mathematics learning process.

1.      Several important orders from Texas Instruments calculator TI 89

a.       Solve command

Solve command is a command of the feature algebra. This command is uses to solve a problem. Example are :

By using the calculator then the students press the button :

 F2 à 1 à  (  à 2 à X à - à 1 à ) à - à 5 à = à ( àX à + à 1 à ) à - à 2 à, à X à) à ENTER

b.      Simult Command

Simult command is one command of the feature matrix. Solved based on the equations in the matrix. Examples of equation that can be finished is a system of linear three variables.

Determine the complection of set below :

2x+y+z=9……(1)
 x+2y-z=6……(2)
3x-y+z= 8……(3)

If using a calculator then students press the button :

 Catalog à S à down arrow à13 times à ENTER à 2nd à , à 2 à , à 1 à , à 1 à2^ndà 9 à1à,à2à, à (-) à 1 à 2à9à3à,à(-)à1à , à 1à2^nd à - à , à 2^nd à, à9 à , à 6 à , à8 à 2^nd à - à ) àENTER.

c.       Exspand Command

Exspand command is one of the feature algebra. Solved based on the translation process. Examples of problems that can be completed is a matter in determining the quadratic equation is known roots. Determine the roots of a quadratic equation whose roots-2 and 5.

Quadratic equation whose roots -2 and 5 is (x-x1)(x-x2)=0

With x1=-2 and x2=5 then obtained :

Calculations with a calculator : student press :
 F2 à 3 à ( àXà + à2 à) à ( àxà - à 5 à) à, à Xà) à ENTER

2.      Discussion of Two Variables Systems of Linear Equations techers give apperception about the theory linear equation two variables to explain the method to find the completion of set. The method is a graphical method, elimination method, the method of substitutional and determinant method. Similarly to the theory of orders calculator graphs that have been given in previous meetings. After the teacher gives apperception, teachers continue to provide practice questions. Students are formed into 8 group (one group consisting of 4 people) to do the exercise. With in these groups the effort to in depth discussion.

a)      Problems are done by students. Determine the set of equations following the solutions of the system.

1.      x+y=4  ; x-y=2

2.      2x+y=4            ; x-y=5

3.      x+y=5  ; x+3y=7

4.      2x+y=4            ; 7x+2y=17

b)      Work steps Problem

Example Number 1  assisted by Calculator 

a.       Opening APPS feature or application

b.      Inserting equation in the Y = Editor
The first equation of x + y = 4 to y = 4-x and the second equation x - y = 2 into y= x-2. After that we enter one by one equation in the calculator. First we put y = 4 - x by pressing the 4 - x ENTER.

c.       Present in graphic form

d.      Looking at the application of the calculator

D.    Conclusion
From research conducted, the conclusion, among others:

1.      Stages use calculators as a mathematic learning tool at SMK Muhammadiyah IV Yogyakarta, can be done as follows :

The first stage is the stage of understanding the significant of calculator graph. It is explained in basic and detail about the graphing calculator.

The second stage is the stage of understanding the theory and use of calculators graphs to solve problems about equations and inequalities.

The third stage, namely stage of entering data to graphs calculators.

The fourth stage is the stage interpretation of the graphic calculator screen and draw conclusions.

2.      Use of graphic calculator

From research conducted, nothing there are some aspects use the graphic calculator in learning mathematics as follows :

a.       Graphic calculator is useful to determine and match graphic images.

b.      Gaphic calculator is useful to determine and match solutions.

c.       Graphic calculators give real experience of graphic images.

d.      Settlement about equation and inequalities can be use the command, symbolic manipulation and graphics.

e.       Graphic calculator is useful to provide answers previously calculated without a calculator and accelerate the completion mathematics matter.

f.       The constraints experienced by students in using the calculator graph is a paraphrase sentences into the languages of mathematics calculator and disclose any appearance of the calculator screen to in mathematical sentences.