7/25/2012
Teachers’ Simulation on Developing Problem
Solving-Based Mathematics Textbook in
Vocational Senior High School Mathematics
Teaching in Indonesia
Marsigit, Indonesia
To be presented at
APEC- Ubon Ratchathani International Symposium 2011: Innovation on
Problem Solving Based Mathematics Textbooks and E-textbooks
Ubon Ratchathani, 2-5 November 2011
Thailand
By
Marsigit and R. Rosnawati
Department of Mathematics Education, Faculty of Mathematics and Science,
Yogyakarta State University Indonesia
Email: marsigitina@yahoo.com
Weblog: http://powermathematics.blogspot.com
7/25/2012
Marsigit, Indonesia
Teachers’ Professional
Development in
Indonesia
LEGAL FRAMEWORK OF EDUCATION REFORM IN INDONESIA
1999-2002
1945 National Constitution (UUD) Amendment
2003-2007
UU 20/2003
Law Number
20 year 2003 on
Sistem Pendidikan
Nasional
beserta
2 PP dan
4 RPP turunannya
National
Education
System
followed
2005-2007
UU 14/2005
Law Number
14 year 2005
Guru dan Dosen beserta 2 RPP turunannya
on Teachers and Lecturers
3
Fasli Jalal
3
THREE PILLARS OF EDUCATIONAL POLICY IN
THE STRATEGIC PLAN OF
THE MINISTRY OF NATIONAL EDUCATION 2005-2009
1. Equity and Expansion of Access to
Education ;
2. Improvement of Quality, Relevance,
and Competitiveness ;
3. Improvement of Good Governance,
Accountability, and Public Image.
Quality Education, Accountable, Low-cost, Equally
4
accessible, Affordable by majority of citizens of the
country
Fasli Jalal
NUMBER OF TEACHERS BY LEVEL OF SCHOOL AND THEIR
EDUCATION BACKGROUND
Education Background
No.
Level of
Schooling
D1 -D2
D3
Number of
Teacher
5
<= Senior
High
> Bachelors
Degree
(S1+S2+S3)
1
Kindergarten
110,742
41,822
3,097
18,768
174,429
2
Primary School
512,144
670,076
32,927
239,659
1,454,806
3
Junior
Secondary
76,178
97,924
95,381
398,532
668,015
4
Special Ed
School
1,666
3,121
803
4,564
10,154
5
Senior
Secondary
16,391
10,661
33,254
259,850
320,156
6
Vocational
School
5,172
4,183
23,942
122,464
155,761
722.293
827.787
189.404
1.043.837
Total
2,783,321
Fasli Jalal
A model of Continuous Professional
Development (CPD) for Teachers and
Education Personnel
2.783.321
Teachers
258.047
SCHOOLS
6 x 441
6 x 441
4x4 x 33
MGMP J.S.S MGMP S.S.S MGMP V.S.S
District
Province
MGMP Sp.S
6
JSS
SSS
VSS
Sp.S
3 x 441
MKKS
1 x 441
MKPS
Teacher
Principal
Supervisor
Association Association Association
Scientific
Forum
Scientific
Forum
BlockGrant
BlockGrant
30 LPMP
13 State LPTK, 19 FKIP State Univ.
237 Private LPTK
12 P4TK
= Junior Secondary School
= Senior Secondary School
= Vocational Secondary School
= Special School
MGMP = Working group for teachers at secondary school level
MKKS = Working group school principals at secondary school level
MKPS = Working group for superintendents/ supervisors at
secondary school level
Fasli Jalal
7/25/2012
Marsigit, Indonesia
The Aims
of Mathematics Teaching
at
Vocational Senior High School
in Indonesia
7/25/2012
Marsigit, Indonesia
The Aims of Mathematics Teaching
at Vocational Senior High School in Indonesia
Marsigit, Indonesia
To understand the concepts of
mathematics, to explain their
relationship, to develop
mathematical algorithm, to apply
mathematics in more flexible,
accurately, efficiently through
problem solving activities.
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------------------------------------------------------------------------------------(1)
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The Aims of Mathematics Teaching
at Vocational Senior High School in Indonesia
-----------------------------------------------------------------(2)
Marsigit, Indonesia
To develop logic on mathematical
characteristic and patterns, to
manipulate mathematics in order to
get generalization, to prove
mathematical formula, to explain
mathematical ideas and
mathematical concepts.
7/25/2012
The Aims of Mathematics Teaching
at Vocational Senior High School in Indonesia
-----------------------------------------------------------------(3)
Marsigit, Indonesia
To solve mathematics problems
through understanding the
problems, developing mathematical
models, solving mathematical
models and predicting the results of
the solution.
7/25/2012
The Aims of Mathematics Teaching
at Vocational Senior High School in Indonesia
-----------------------------------------------------------------(4)
Marsigit, Indonesia
To communicate
mathematical concepts and
ideas using the symbols,
tables, diagrams, or other
media.
7/25/2012
The Aims of Mathematics Teaching
at Vocational Senior High School in Indonesia
-----------------------------------------------------------------(5)
Marsigit, Indonesia
To develop attitude in appreciating
the use of mathematics in daily life
including curiosity, attention,
motivation in learning mathematics,
diligent and self confident in solving
the problems.
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Marsigit, Indonesia
Developing Problem Solving-Based
Mathematics Textbook in Vocational
Senior High School Mathematics
Teaching in Indonesia
SOME ASPECTS OF
TEXTBOOK DEVELOPMENT
3.
4.
Marsigit, Indonesia
2.
Policy for textbooks publication
Developing the textbook for teachers
Developing the textbook for students
Distributing and providing the
textbooks
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1.
Teachers’ Competencies
of Developing Textbooks
SYSTEMIC
EXPERIENCES
MOTIVATION THEORY
ATTITUDE
PRACTICE
INDIVIDUAL
EXPERIENCES
Marsigit, Indonesia
COMMUNITY
EXPERIENCES
Marsigit, Indonesia
Finding the Volume of a Cone
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The Case of Posing the
Problem
CASE 2
Marsigit, Indonesia
CASE 1
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The Case of Preparing the
Draft of Problem Solving
Based Mathematics Text
Book
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Marsigit, Indonesia
Teachers’ Simulation on
Developing Problem SolvingBased Mathematics Textbook
THE PROCEDURE FOR THE
2.
3.
4.
5.
6.
7.
Whole-class Lecturing
Reviewing the Developed Text Books
Small Group Discussion
Teachers’ Presentation
Whole-class Discussion
Teachers’ Filling in the Questionnaire
Teachers’ Reflection
Marsigit, Indonesia
1.
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SIMULATION
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Marsigit, Indonesia
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Marsigit, Indonesia
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Marsigit, Indonesia
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Teachers’ Perception on Good
Textbook for Vocational Senior
High School Mathematics
Marsigit, Indonesia
Teachers’ Perception on Good Textbook for
Vocational Senior High School Mathematics
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Marsigit, Indonesia

7/25/2012
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It should motivate the students to learn mathematics
It should develop students’ oriented teaching learning of
mathematics
It should support of achieving learning objective
It should employ flexible teaching learning method
It should facilitate students’ need to learn mathematics
It should facilitate the students to do exercise mathematics
It should dealing with the students’ difficulties in learning
mathematics
It should consist of summary
It should as a communicative writing
It should develop the cognitive schema of learning mathematics
It should be as a students’ learning oriented
It encourage the students to solve mathematics problems
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Polya’s Notion of Problem Solving
Procedure as a Tool for Teachers’
Simulation
Marsigit, Indonesia
7/25/2012
Marsigit, Indonesia
In relation with the strategies of problem solving
that can be developed in the textbook, teachers’
perceptions consist of 10 aspects, as they were
outlined by Polya and Pasmep (in Fajar
Shadiq:2004:13) :
 Trial and Error
 Make diagram
 Try for simple problem
 Make Table
 Find the pattern
 Break down the goal
 Consider possibility
 Logical Thinking
 Reverse Order
 Identify impossibility
Teachers’ Simulation
Aims of Math
Teaching at VSHS
Good Problem Solving
Based Text Book
Marsigit, Indonesia
THEORY
(Polya’s Notion)
Existing Math
Text Book
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Marsigit, Indonesia
The Results of
Simulation
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Marsigit, Indonesia
TRIAL AND ERROR
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It needs of manipulating concrete objects
It is useful to find the mathematics pattern
It is a speculative method
It is construct theories
It needs teaching aids
It involves drawing activities
It is useful for the teacher to motivate the
students to solve mathematics problems
 It is useful to find the formulas
 It involves mathematical activities
 It based on individual ways and
experiences
Marsigit, Indonesia
 It is useful to solve the problems
 It is useful to get the best solution
 It means of finding the method of solving
the problems
 It is useful to get the right answers
 It should under the teacher’s guidance
 It means of step by step solution
 It is useful to learn any possibility of
existing solution
 It is useful to find the wrong answers
 It is useful to identify the related concept
(it needs pre-requisite)
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Marsigit, Indonesia
MAKING DIAGRAM
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 It is useful to relate two or more
mathematical ideas
 It is useful to organize possibilities
 It is useful to produce summaries
 It is useful to compare mathematical ideas
 It is useful to classify the data
 It is useful to visualize mathematics
procedures
 It is useful to make rough notes
 It is useful to the prove the formula
 It is useful to produce further diagrams
 To make diagram is to solve the problems
 It is useful to indicate the degree of
achievement
Marsigit, Indonesia
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It is useful to record the data
It is useful to illustrate the situation
It is useful to get mathematical concepts
It is relevant to realistic mathematics
It is useful to illustrate the solutions of
problems
It is useful to solve the problems easily
It is useful to show students’
competencies
It employs various diagrams
It is useful to record experiment activities
It is useful to interpret the data easily
It is useful to communicate/share
mathematical ideas
It is as a teaching media
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Marsigit, Indonesia
TRYING THE SIMPLE PROBLEMS
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 It is useful to make mathematics concepts
more realistic
 It is useful to comprehend mathematics
competencies
 It is useful for the teacher to facilitate
his/her students
 It is useful to make the students
understand about mathematical procedures
 It needs to be supported by the use of
teaching aids
 Trying the simple problems need
observation activities, recording, and
conclusion
 It is useful to make the abstract
mathematics be more concrete one
Marsigit, Indonesia
 It should from the simple problems
to the complex one
 It is useful to get prerequisite
understanding
 It is a mathematical method
 It needs of applying the formula
for the solution of the simple
problems
 It is useful to breakdown the
complex problem into the simpler
one
 The simple problem should be
taken from daily life
 It is useful to evaluate the students’
competencies
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Marsigit, Indonesia
MAKING THE TABLES
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 It is as the method to solve
the problems
 It needs students’ skill to read
the table
 It is closely related to
experiment activities
Marsigit, Indonesia
 It needs to be supported by
the using of teaching aids
 It is useful to summarize the
data
 It is as a tool to solve the
problems
 It needs students’ skill to
make the table
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Marsigit, Indonesia
FINDING THE PATTERNS
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Finding pattern is a natural way of life
It is an abstract method
It is relevant with experiment method
It is repeated procedure
It consists of possible other small patterns
The students should find it
The students can use one pattern to find
other pattern
The pattern makes mathematics be more
meaningful
It is more effective way to solve
mathematics problems
It consists of mathematical concepts
The pattern is a repeated certain change
It is useful to find the characteristics of
mathematics problems
Marsigit, Indonesia
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 It is a continuing process from the
previous step to the next step in order to
solve the problems
 It should be supported by the use of
Students Work Sheet
 It can be an individual activity
 It should lead to the finding of the
formula
 It is the method to solve the problems
 It moves from the simple problems to the
complex one
 It finds the rule
 It is the pattern of methods
 It is the pattern of problems
 It finds the relationship
 It finds the repeated procedures
 It leads to generalization
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Marsigit, Indonesia
BREAKING DOWN THE GOAL
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 It means breaking down the
procedures
 It means identifying the appropriate
procedures
 It is useful get the shorter procedures
 It is useful to make priority of doing
certain procedure
 It appropriates with small group
discussion
 It means classifying the mathematics
problems
 It means breaking down the problem
into the unit problems
Marsigit, Indonesia
 It means solving the problems step
by step
 It means getting the different goals
 To solve multiple problems
 It is supported by the use of
Teaching Aids and Students Work
Sheet
 It means solving a big (general)
problem through solving the smaller
(specific) problems
 It means solving the longer term
problem through solving the shorter
term problems
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Marsigit, Indonesia
CONSIDERING THE POSSIBILITIES
 It is useful to clarify the mathematics
problems
 It is useful to classify the mathematics
problems
 It is useful to anticipate the unpredicted
solution
 It is useful to predict the correct or wrong
answers
 It means of identifying all possibilities
 It means of considering the possibilities to
apply a certain procedure to a different
problem
 It is useful to examine the strong (more
effective) or the weakness (less effective) of a
certain procedure
 It is useful to provides non-routine problems
 It means the students’ creativities
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Marsigit, Indonesia
 It should be facilitated by the Students
Work Sheet
 The teachers need to uncover students’
thinking
 It is more related to experiment activities
 It is the possibility of students’ thinking
 It is the possibility of students’ different
answers
 It is useful to uncover the risks and
benefit of any activity
 The possibilities need to be recorded
 It means of the flexibility of mathematical
procedures
 It means of the possibility of the existing
solution
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Marsigit, Indonesia
THINKING LOGICALLY
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It is useful to think effectively
It is useful to think realistically
It is useful to think rationally
It is as an if-then thinking
It is useful to develop analyzed-based
thinking
 It is useful think contextually
 It is useful to develop experiencedbased thinking
 It is useful to relate problems that has
similar characteristics
Marsigit, Indonesia
It means of expressing logically
It is contextual
It is situational
It is about understanding
It is about logical based thinking
It is useful to think clearly
It is useful to think rigorously
It is useful to get prior experiences
thinking
 It is useful to think systematically
 It is useful to think coherently
 It is useful to think scientifically
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Marsigit, Indonesia
REVERSING THE ORDER
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 It is useful to learn different
procedures
 It is useful to examine the concepts
 It is useful to relate some procedures
 It means of predicting the results first
then thinking the procedure later.
 It means copying the procedures
Marsigit, Indonesia
 It is useful method to employ
prerequisite understanding
 It is useful method to produce the
reasons
 It is useful method to examine the
results
 It means reconstructing the
mathematics procedures
 It is useful to produce explanation
 It is useful to review the methods
 It is useful to reflects the process
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Marsigit, Indonesia
IDENTIFYING THE IMPOSSIBILITIES
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Marsigit, Indonesia
 It is useful to learn why a certain procedure doesn’t
work
 It is useful to clarify why a certain procedure is
work effectively
 It is useful for the teacher to observe his/her
students works
 It is useful for the teacher to motivate his/her
students to develop mathematical procedures
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Marsigit, Indonesia
CONCLUSION
7/25/2012
Marsigit, Indonesia
The problem solving based mathematics textbook in the
Vocational Senior High School can be developed based on
the criteria outlined by Polya and Pasmep that are:
(1) Trial and Error,
(2) Making diagram,
(3) Trying the simple problem,
(4) Making Table,
(5) Finding the pattern,
(6) Breaking down the goal,
(7) Considering the possibilities,
(8) Thinking Logically ,
(9) Reversing the Order, and
(10) Identifying the impossibility.
7/25/2012
Marsigit, Indonesia
THANK YOU