Adanya kecenderungan sekolah-sekolah membentuk kelas-kelas unggulan atas dasar prestasi akademik dewasa ini patut dikaji ulang. Apakah kecenderungan itu didasari atas pertimbangan yang sejalan dengan tujuan pendidikan kita ataukah karena pertimbangan lain sesuai dengan permintaan pasar yang bersifat sesaat? Terlepas dari mana yang benar, fenomena yang muncul dalam sistem persekolahan yang ada sekarang ini cenderung memperlakukan siswa secara kurang adil dan kurang humanistis. Siswa pandai diberi label unggul dengan segala fasilitas yang diberikannya, sementara siswa yang di kelas tak unggul memperoleh label kurang dan predikat negatif yang lain. Siswa pada kelompok unggul berkompetisi secara keras dan cenderung individualistik. Sementara siswa di kelas tidak unggul merasa tidak mampu, frustasi dan selanjutnya menerima keadaan itu. Persoalan lain yang menunjukan aspek kompetitif dan individualistik dalam pendidikan kita adalah model pembelajaran langsung (model pembelajaran konvensional). Pada pembelajaran konvensional, guru menjadi pusat pembelajaran, berperan mentransfer dan meneruskan (transmit) informasi sehingga siswa tidak perlu mengkonstruksi ide-idenya. Tingkat partisipasi siswa sangat terbatas karena arus interaksi didominasi oleh guru. Bentuk penugasan dalam pembelajaran ini bersifat individual. Sebagai konsekuensinya, evaluasi yang diterapkan dikelaspun juga individual. Dalam hal ini, guru perlu menyusun dan melaksanakan kegiatan belajar mengajar dimana siswa dapat aktif membangun pengetahuannya sendiri. Hal ini sesuai dengan pandangan kontruktivisme yaitu keberhasilan belajar tidak hanya bergantung pada lingkungan atau kondisi belajar, tetapi juga pada pengetahuan awal siswa. Keberhasilan dalam proses pembelajaran dipengaruhi oleh dua faktor yaitu faktor internal dan faktor eksternal. Faktor internal yaitu faktor yang berkaitan dengan diri siswa, diantaranya adalah kemampuan, minat, motivasi, keaktifan belajar dan lain-lain. Sedangkan faktor eksternal adalah faktor dari luar diri siswa, diantaranya adalah model pembelajaran. Model pembelajaran memiliki andil yang cukup besar dalam kegiatan belajar mengajar. Kemampuan menangkap pelajaran oleh siswa dapat dipengaruhi dari pemilihan model pembelajaran yang tepat, sehingga tujuan pembelajaran yang ditetapkan akan tercapai. Terdapat berbagai macam model pembelajaran yang dapat dijadikan alternatif bagi guru untuk menjadikan kegiatan pembelajaran di kelas berlangsung efektif dan optimal. Salah satunya yaitu dengan menggunakan model pembelajaran kooperatif. Wagitan (2006) menyimpulkan bahwa pembelajaran kooperatif dapat menjadi salah satu alternatif karena banyak pendapat yang menyatakan bahwa pembelajaran aktif termasuk kooperatif mampu meningkatkan efektivitas pembelajaran. Pembelajaran kooperatif mengutamakan kerjasama antar siswa untuk mencapai tujuan pembelajaran. Menggunakan pembelajaran kooperatif dapat mengubah peran guru, dari yang berpusat pada gurunya ke pengelolaan siswa dalam ke

1. Cooperative Model
in Teaching Linear Programming
at Senior High School
Writer: S u g i m a n
Presenter: E n d a n g L i s t y a n i
Mathematics Education Department
FMIPA UNY

2. The Presentation will start …

3. SMUN 4 Yogyakarta
The school of piloting
The piloting team discussed
the preparation with the
teacher at the guess room
of the principal office

4. Contents
1. Introduction
2. Purposes
3. Linear Programming
4. Cooperative model
5. The Role of Teacher and Student
6. Result of The Instruction
7. Making Conclusion

5. 1. Introduction
 Competent-Based Curriculum need new
teaching approach (CTL) and model
(Cooperative)
 Students should be trained in discussing
and sharing ideas
 Contextual problem is one of the important
part as starting point of any instruction.

6. 2. Purposes
 To improve teacher’s ability in using
cooperative model
 To promote the use of Cooperative
teaching model at high school
 To improve the quality of class instruction
processes
 To develop cooperative model appropriate to
Indonesian culture
 To prepare the dissemination of the results
to non-piloting teachers

7. 3. Linear Programming
Why Linear Programming (LP)?
 It is close to daily life of almost all students
 LP problem is easy to connected with real
problems already faced by students
 It involves various of mathematical
concepts and symbols
 It challenges students to overcome
Let’s watch the problem given by teacher.

8. Contains
Per Capsule
Fluin (Gram) Fluon (Gram)
Aspirin 2 1
Bicarbonate 5 8
Codeine 1 6
Price Rp. 400,00 Rp. 600,00
Doctor say to cure a influenza, a patient must
take at least 12 gram aspirin, 74 gram
bicarbonate, and 24 gram codeine.
Referring to the above table, how many Fluin and
Fluon can cure with the minimum cost?
Selected Problem (Receipt Problem)

9. 4. Cooperative model
 Cooperative doesn't mean competitive nor
individualistic
 John Dewey (1916): Class should be the
representation of real social; teacher should
encourage democratic and scientific process
 3 stage: Thinking (individually), pairing or
grouping, and sharing (classically)
 Slavin ( 1986): cooperative is better than
competitive or individualistic
To be continued

10. Phase:
1. Teacher explains the goal of the instruction
and motivates all students.
2. Teacher gives useful information related to
the content of instruction
3. Teacher organizes student grouping
4. Teacher urges and helps student to solve
the problem
5. Teacher evaluates student activity and
achievement

11. 5. The Role of Students and Teacher
 Students learn to be
more creative and
active in solving
problem
 Student should help
each other in group
 Student should share
his ideas with others
 Gifted student should
help his weak group
mate
 Teacher gives chance to &
pushes students in developing
their ability by themselves
 Teacher arranges heterogeneity
in small grouping
 Teacher asks the clever student
to teach his group mate
 Teacher asks student to present
his result and make conclusion

12. Teacher introduces the
daily life problems such
that students are interested
in and motivated
Teacher distributes a paper
sheet to each students. The
paper consist of one
selected problem
Starting lesson

13. Students solved the problem individually. Meanwhile
teacher monitored students’ activity. Teacher held
some discussions with the students.
Students work individually

14. Grouping
Having had understand
what should they do,
then they worked in
group

15. Work in group
Situations of class
Teacher helped the
group to understand
the problems

16. Students were discussing about what the problem is.
Group Discussion 1

17. Group Discussion 2

18. Teacher’s Activity in the Group
Teacher was
delivering the
questions
Teacher was
delivering a few
directions

19. Teacher’s Activity in the Group

20. Collaborative Situation

21. Preparing Presentation

22. Presentation 1
Student’s presentation of
group one Teachers encouraged
students to ask some
questions

23. The problem of first presentation
Using the the point with fractional
coordinate to test minimum problem

24. Discussion 1

25. Presentation 2
1. Second presentation
2. Teacher asked the students
whether they have some
questions
The first presenter defend
her opinion of her wrong
answer

26. Making Conclusion 1
Students make
conclusion
A student made incorrect
conclusion: “ Minimum point is
the nearest point from O.” So
teacher asks others to think this
incorrect conclusion.

27. The Student Conclusions about LP
1. Mathematics is very useful to cover daily
life problems
2. When we get any fractional points, we try
integer points near the fractional point and
must in the region to test maximum or
minimum values

28. Giving Homework

29. 6. The Results
 The students felt happy and enjoyed the
instruction with cooperative model
 Thinking individually before grouping is very
effective in small group discussion process
 All groups can solve the problem
 Presentation from selected group makes
class discussion is much more effective
 The teacher is able to implement the
cooperative model approach

30. 7. Making Conclusion 2
 Based on their activities in group
discussions and class presentation, the
students can make conclusions.
 Incorrect conclusion can become a very
good moments in instructions
 The students are aware of the importance of
mathematics in their daily life

31. Evaluation System
1. Based on the students’ activities and
discussion process
2. Group results
3. Home works
4. Post test

32. Problems
 If the planning is not good, the cooperative
model can not be effective

33. Thank you very much for
your attention
Sugiman
Endang Listyani