The ICEBERG Approach of Learning Fractio
The ICEBERG Approach of Learning
Teachers’Fractions in Junior High School:
Reflection Prior Lesson Study Activities
1 /2 /2
1
4 APEC-Chiang Mai International Symposium IV M a rsi
1
- – 6 November 2010 g
it, In d o n e sia
By
Marsigit
Yogyakarta State University
Indonesia
H ERMENEUTICS OF LIFE
Iceberg Approach in Realistics Mathematics (Moerlands, 2004 in Sutarto, 2008)
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1
4 M a rsi g it, In d o n e sia
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VOLCANO Indones ia
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AU T A KRAK OF MOUNT
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I P A R M E of nt Mou
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10/20/2014 Marsigit, Indonesia Ammus
- ing Disaster
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By Marsigit, Indonesia
- Disaster
Ammus ing
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BY Marsigit, Indonesia
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By Marsigit, Indonesia
ROBLEM OF
ATH
EACHING
P
M
T
I N
I NDONESIA
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1
4 Traditional Innovative
Teacher BY Marsigi t, Indo nesia
ROBLEM OF
ATH
EACHING
P
M
T
I N
I NDONESIA
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1
4 FORMAL
MATH SCHOOL MATH
Teacher By Mar sigi t, Indone s ia
HENOMENOLOGY P
USSERL
(H )
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1
4 Idealized M a rsi g it, In d o n e sia
Abstracted Math The Nature of School Math
Inside your
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MIND Outside your MIND
/2
1
4
(Superserve) (Subserve)
M a rsi g it, In d o n e sia
3 The Nature of Mathematics
Inside Outside your MIND
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Your (Plural)
/2
1
4 MIND M a
(Unique)
rsi g it, In d o n e sia The Nature of School Math
Inside your Outside your MIND
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MIND (synthetic/
/2
1
4
(analytic/co Correspondence)
M a
herence)
rsi g it, In d o n
3 book + 2 book = 5 book e
sia
3 pencil + 2 pencil = 5 pencil 3+2=5
3 book + 2 pencil = 5 ? 3 book + 2 pencil = 5 ? The Nature of School Math
Inside your Outside your MIND
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MIND (concret)
/2
1
4
(abstract)
M a rsi g it, In d o n e sia
X=30 The Nature of School Math
Inside your Outside your MIND
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MIND (Realistic
/2
1
4
(Realistic Math: Math:Horizontal)
M a
Vertical)
rsi g it, In d o n e sia
1 ½
ERMENEUTICS OF
H
T HE
ICEBERG A PPROACH
SCHOOL
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MATHEMATICS
/2
(E S , 1995)
4 M a rsi g
1 BBUT AND TRAKER
1. Mathematics is a search for PATTERN and
it, In d o
RELATIONSHIP
n e sia
2. Mathematics is PROBLEM SOLVING activity
3. Mathematics is a mean of INVESTIGATION
4. Mathematics is a mean of COMMUNICATION
Iceberg Approach in Realistics Mathematics (Moerlands, 2004 in Sutarto, 2008)
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1
4 M a rsi g it, In d o n e sia
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Marsigit, Indonesia
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Marsigit, Indonesia
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Marsigit, Indonesia
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Marsigit, Indonesia
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Marsigit, Indonesia
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Marsigit, Indonesia
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Marsigit, Indonesia
10/20/2014 Marsigit, Indonesia
10/20/2014 Marsigit, Indonesia
C ONCLUSION
The teachers need to have clear picture of the NATURE OF SCHOOL MATHEMATICS, REALISTICS MATHEMATICS, and CONSTRUCTIVE TEACHING
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4 Mars
igit , Indones ia
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1
4 The teachers need to organize M a rsi
presentation, demonstrate and
g it, In d o
interconnected relationships
n e sia
between division, fractions, decimals, and percents (e.g., physically divide a whole into five equal pieces)
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4 M
1 The teachers need to develop skills on using
concrete materials (i.e., manipulatives)
a rsi g it,
before proceeding to semi-concrete
In d o
materials (e.g., pictorial representations)
n e sia
before proceeding to abstract problems (e.g., numerical representation)
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1
4 The teachers need to develop M a rsi
methods to uncover the
g it, In d o
variations of all problem types
n e sia
lead the students to make generalizations (e.g., that all fractions represent parts of a whole)
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1
4 The teacher need to develop M a rsi g
various methods of teaching,
it, In d o n
various learning resources, e
sia
and various interaction/communication
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4 M a
1 The teachers still have problems in
developing concept acquisition of
rsi g it, In
fractions from mathematical world
d o n e sia
orientation to formal form of fraction.
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1
4 Material model of fraction and M a rsi g
searching the relationship
it, In d o n
help the teacher to develop e
sia
method to encourage students to solve the problems of acquisition of the fractions.
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OU Y K