Maximization of Water Productivity and Yield of Two Iceberg ...
The ICEBERG Approach of Learning Fractions in Junior High School
39
The ICEBERG Approach of Learning Fractions in Junior High School: Teachers’ Reflection Prior Lesson Study Activities APEC-Chiang Mai International Symposium IV 1 – 6 November 2010 By Marsigit Yogyakarta State University Indonesia 10/20/2014 Marsigit, Indonesia
Transcript of The ICEBERG Approach of Learning Fractions in Junior High School
The ICEBERG Approach of Learning
Fractions in Junior High School: Teachers’
Reflection Prior Lesson Study Activities
APEC-Chiang Mai International Symposium IV
1 – 6 November 2010
By
MarsigitYogyakarta State University
Indonesia
10
/20
/201
4M
ars
igit, In
do
ne
sia
HERMENEUTICS OF LIFE
10
/20
/201
4M
ars
igit, In
do
ne
sia
Iceberg Approach in Realistics Mathematics
(Moerlands, 2004 in Sutarto, 2008)
10
/20
/201
4M
ars
igit, In
do
ne
sia
ICEBERG VOLCANO
West Indonesia
10
/20
/201
4M
ars
igit, In
do
ne
sia
MOUNT OF KRAKATAU
10
/20
/201
4M
ars
igit, In
do
ne
sia
Mount of M E R A P I
10
/20
/201
4M
ars
igit, In
do
ne
sia
10
/20
/201
4M
ars
igit, In
do
ne
sia
Pheno
menon
Ammus-
ing
Disaster
10
/20
/201
4B
y M
ars
igit, In
do
nesia
MATHEMATICS
Ammus-
ing
Disaster
10
/20
/201
4B
Y M
ars
igit, In
do
nesia
10
/20
/201
4B
y M
ars
igit, In
do
nesia
PROBLEM OF MATH TEACHING
IN INDONESIA1
0/2
0/2
01
4
Traditional Innovative
Teacher
Students Constructive Teaching
BY
Ma
rsig
it, Ind
on
es
ia
PROBLEM OF MATH TEACHING
IN INDONESIA1
0/2
0/2
01
4
FORMAL
MATH
SCHOOL
MATH
Teacher
Students Constructive Learning
By M
ars
igit, In
do
nesia
PHENOMENOLOGY(HUSSERL)
10
/20
/201
4M
ars
igit, In
do
ne
sia
Idealized
Abstracted
MathPhenomenaEpoche
The Nature of School Math1
0/2
0/2
01
4M
ars
igit, In
do
ne
sia
Inside your
MIND
(Superserve)
Outside your MIND
(Subserve)
3
The Nature of Mathematics1
0/2
0/2
01
4M
ars
igit, In
do
ne
sia
Inside
Your
MIND
(Unique)
Outside your MIND
(Plural)
The Nature of School Math1
0/2
0/2
01
4M
ars
igit, In
do
ne
sia
Inside your
MIND
(analytic/co
herence)
Outside your MIND
(synthetic/
Correspondence)
3+2=5
3 book + 2 book = 5 book
3 pencil + 2 pencil = 5 pencil
3 book + 2 pencil = 5 ?
3 book + 2 pencil = 5 ?
The Nature of School Math1
0/2
0/2
01
4M
ars
igit, In
do
ne
sia
Inside your
MIND
(abstract)
Outside your MIND
(concret)
X=30
The Nature of School Math1
0/2
0/2
01
4M
ars
igit, In
do
ne
sia
Inside your
MIND
(Realistic Math:
Vertical)
Outside your MIND
(Realistic
Math:Horizontal)
1
½
¼
HERMENEUTICS OF
THE ICEBERG APPROACH
SCHOOL
MATHEMATICS(EBBUT AND STRAKER, 1995)
1. Mathematics is a search for PATTERN and
RELATIONSHIP
2. Mathematics is PROBLEM SOLVING activity
3. Mathematics is a mean of INVESTIGATION
4. Mathematics is a mean of COMMUNICATION
10
/20
/201
4M
ars
igit, In
do
ne
sia
10
/20
/201
4M
ars
igit, In
do
ne
sia
Iceberg Approach in Realistics Mathematics
(Moerlands, 2004 in Sutarto, 2008)
10
/20
/201
4M
ars
igit, In
do
nesia
10
/20
/201
4M
ars
igit, In
do
nesia
10
/20
/201
4M
ars
igit, In
do
ne
sia
10
/20
/201
4M
ars
igit, In
do
nesia
10
/20
/201
4M
ars
igit, In
do
nesia
10
/20
/201
4M
ars
igit, In
do
nesia
10
/20
/201
4M
ars
igit, In
do
ne
sia
10
/20
/201
4M
ars
igit, In
do
ne
sia
10
/20
/201
4M
ars
igit, In
do
ne
sia
CONCLUSION
The teachers need to have clear
picture of the NATURE OF
SCHOOL MATHEMATICS,
REALISTICS MATHEMATICS,
and CONSTRUCTIVE
TEACHING
10
/20
/201
4M
ars
igit, In
do
ne
sia
The teachers need to organize
presentation, demonstrate and
interconnected relationships
between division, fractions,
decimals, and percents (e.g.,
physically divide a whole into
five equal pieces)
10
/20
/201
4M
ars
igit, In
do
ne
sia
The teachers need to develop skills on using
concrete materials (i.e., manipulatives)
before proceeding to semi-concrete
materials (e.g., pictorial representations)
before proceeding to abstract problems
(e.g., numerical representation)
10
/20
/201
4M
ars
igit, In
do
ne
sia
The teachers need to develop
methods to uncover the
variations of all problem types
lead the students to make
generalizations (e.g., that all
fractions represent parts of a
whole)
10
/20
/201
4M
ars
igit, In
do
ne
sia
The teacher need to develop
various methods of teaching,
various learning resources,
and various
interaction/communication
10
/20
/201
4M
ars
igit, In
do
ne
sia
The teachers still have problems in
developing concept acquisition of
fractions from mathematical world
orientation to formal form of
fraction.
10
/20
/201
4M
ars
igit, In
do
ne
sia
Material model of fraction and
searching the relationship
help the teacher to develop
method to encourage
students to solve the
problems of acquisition of the
fractions.
10
/20
/201
4M
ars
igit, In
do
ne
sia
THANK YOU
10
/20
/201
4M
ars
igit, In
do
ne
sia
