Observation Report 2 MIN 1 eng
2nd Instructional Design of PMRI:” Straw, Matches, and Measurement of Length“
Achmad Dhany Fachrudin1
Ummy Salmah2, dan Sitti Busyrah3
International Master Program on Mathematics Education (IMPoME 2012)
email: [email protected], [email protected], [email protected]
I. Introduction
Mathematics is one of difficult lessons for most students. It can be seen that many
students do not like mathematics. This difficulty actually arises because of a lack of
understanding of mathematical concepts to students. Moreover some findings suggest that
teaching mathematics gives a lot of emphasis on procedural skills and led students only to
understand mathematics without reasoning (Yuwono, 2007). In the classroom, most
teachers still use the conventional learning, which a mathematical concept is only delivered
for granted without being associated with the experience of students, while mathematics
requires them to think logically, carefully, and accurately.
Basically, mathematics will be meaningful if the learning associated with the real
world of students. In order to make mathematics more meaningful, students should be
given the chance to reinvent mathematics under the guidance of adults (Gravemeijer;
1994). This is supported by the opinion of de Lange (1995) that, the process of reinvention
should be developed through the exploration of a variety of real-world problems. Therefore,
in the learning process, teachers should not be the learning centre, but the students. So that
students could not be seen as passive receiver of ready-made mathematics. Therefore,
PMRI that relates math concepts with real-world of students is considered appropriately to
be applied.
On this occasion, researchers developed instructional design for material of
measurement with length measurement as the sub material. This instructional design would
be applied to Grade 2 of Madrasah Ibtidaiyah Negeri 1 Palembang. It was developed with
reference to the approach of PMRI. By using PMRI approach, this lesson began with
problems from the environment the students themselves. In this lesson, researchers used
matchsticks and straws as non-standard instrument to measure some of the objects around
them, such as tables, benches, windows, and mathematics books.
Here are the stages carried out by researchers in the implementation of the study on
the measurement of the length in Grade 2 of Madrasah Ibtidaiyah Negeri 1 Palembang.
II. Instructional Design
As for the stages being performed is the Preliminary design (analysis of the
curriculum and the determination of learning objectives and indicators), continued with the
implementation/testing of design (teaching experiment) and a reflection of learning that has
been performed (retrospective analysis) that will be described as follows.
1. Preliminary Design
At this stage, the initial steps undertaken by researchers was conducting an
analysis of the curriculum to determine the material to be taught, formulating objectives
and indicators that will be achieved in this process, determining appropriate context in
accordance with the material to be taught, as well as drawing up a learning instruments
such as lesson plan and student worksheet which was used in the learning activities in
the classroom later.
Based on the results of the discussion with the mathematics teacher (Mrs.
Tartila), the material that would be taught was the measurement of the length with basic
competence that is using standard and non-standard measurement tools of length which
are often used. The indicator that will be accomplished was to measure the length of the
objects by using standard and non-standard units. In order to support learning activities,
the teacher together with researchers designed lesson plan and student worksheet which
were appropriate with to the material to be taught, as well as composed learning
scenarios by applying the PMRI approach.
Preparations of the lesson plan, student worksheet and learning scenario that
will be applied in the classroom were carried out a few days prior to the implementation
of learning process. The discussion was carried out twice. On the first discussion,
teacher and researchers designed the appropriate learning scenario and chose the
appropriate context to teach the concept of length measurements. At this early stage of
the discussion teacher and researchers agreed to use the context of measuring height as
a bridge to make students understand the concept of length measurements. On the
second discussion, the draft of lesson plan and student worksheet has been discussed,
similarly, with the initial learning scenarios have been discussed before. Mrs.Tartila as
the teacher provided some input and revision on the lesson plan and student worksheet
which researchers arranged before. After this discussion, the learning scenarios, which
have been discussed, divided students into several activities as follows
a. Activity 1: Students are introduced to the context which is related to the
context of length measurement
In this activity students are reminded about the height measurements which
they usually do in daily life in order to direct the students to the concept of
the length measurement. What people usually do when measuring the height
and what tools are commonly used.
b. Activity 2: Students are invited to measure the length of the objects around
them by using straws and matchsticks.
In this activity, students are invited to measure some of the objects in the
class, such as mathematics books, desks, chair, and window. As the nonstandard measurement instrument, we provided straws and matchsticks. By
using both these objects, they measure the four objects that have been
provided one by one and write down their length on the worksheet that had
been distributed to each group.
c. Activity 3: Students compared the length of those objects by using straws
and matchsticks.
In this activity, students are asked to compare measurement results that they
have done with the use of straws and matchsticks.
d. Activity 4: Students measured some objects by using ruler.
In this activity, students are asked to measure the objects on previous
activities by using a ruler. In addition, students are given a problem, i.e.
measuring the length of the money Rp 2,000 by using two pieces of a ruler
which have provided in their worksheets. The first ruler is a ruler intact
(starting from 0), whereas the second ruler is a ruler which its scale was
from 1. This is done to bring understanding about the concept of length
itself.
Here is the iceberg instructional design of this learning material:
Using ruler (standard
measurement) to measure object
Length of straw
=....... length of
matchstick
Measuring the length of
objects around us
Figure 1. Iceberg design in Length Measurement Material
2. Teaching Experiment
Math lessons in class 2A MIN 1 Palembang start at 11.55 am on Wednesday,
after the lesson Penjaskes. Mrs. Tartilah (here in after are written as teacher), teacher
assistant and research team divided class into 6 groups. Furthermore, teacher initiated
the learning by asking students about their activities related to measurement or
measurement activities they have ever seen. The students enthusiastically answered
these questions. Among them are those who answer the door or window measurements
performed handyman when building a house or school. Then the teacher asked what
objects are used craftsman. One answered meters, and some others answered ruler.
After that, the teacher asked the students to come forward to measure the board and seat
height using a ruler (Figure 2). The teacher lure students with a question, what can be
done to measure something without using a ruler or other measuring devices? Some
students answer using span or footsteps. Then, teacher conveyed to the students that
they will measure objects using another unit of measurement namely matchstick and
straw.
Figure 2. Student measured the length of whiteboard
The Activity of Measuring Object by Using Matchsticks and Straws
In this activity students measured objects around them as table length, seats height,
window width, and length of mathematics textbooks by using matchsticks and straws under
teacher's guidance (Figure 3). The aim of this activity was students are able to do the
standard iteration count how many times a matchstick or a straw to measure these objects
and then compare them.
Figure 3. Students measured objects by using matchsticks or straws
Some students have difficulty in the process of measuring seat height by using
matchsticks. There's even given up do not do it. However, once we help, they finally
know how to measure the seat height by using matchsticks. The results of measuring
the length of the table, the width of the window, seat height, and length of math
textbooks, either by using matchsticks or straws, all written in a table that has been
provided in the worksheet.
Then, each group wrote their measurement results on the board and exposed it to
the class (Figure 4). At this exposure, there were some groups that do not regard the
current presentation. Moreover, the teacher did not use vary answers of every group as
class discussion.
Figure 4. Presentation of each group
The Activity of Measuring Object by Using Ruler
After all the representatives from each group presented their work, teaching and
learning mathematics followed by conducting measurements of objects using standard
unit, which is a ruler. Students were given the second worksheets, which contains the
instructions for measuring a thousand banknotes by using two types of rulers; normal
ruler and broken ruler (no zeros). This worksheet was used to know the extent of
student understanding about measurement concepts they have learned.
Figure 5. Students measure the length of a thousand banknotes by using two types
of ruler
In these measurements, some students still make mistakes as in the picture above.
Students also have a variety of reasons related to differences in banknote thousand
length using two rulers.
3. Retrospective Analysis
Retrospective analysis is conducted by the teacher and researchers after teaching
and learning process is completed. This activity’s purpose is to analyze and reflects the
learning process that has been completed. These are about the problems occurred during
the learning process. Further, this activity’s purpose is also to analyse the pupils’
thinking, working, and answers.
According to the observation that we have done, overall the implementation of
learning is good enough. However, there are some pupils that did not focus and played
during the lesson. The teacher seemed she could give the guidance although sometimes
she met some difficulties because of the pupils.
The first attention of the research team during the taching and learning process
is based on instructional design that has been created, teacher should began the lesson
by introducing the contextual examples or problems about the measurement to the
students, but teacher gave questions directly to students about the kinds of measuring
instrument, then give context or examples of measurements in daily lives. This is
happened because the teacher has been introduced previously about the measurements
to the students so teacher felt the children already know and be able to answer these
questions. However this is not influence whole of the learning process.
On the measurement of the activity using the non-standard measurement,
apparently there are still many pupils who are not yet able to measure using non
standard measurement that has been prepared. On the other hand, there are groups who
have recognised a way to measure but there is still an error in measurement, for instance
they measure table by using a matchstick wrongly (Figure 6). Consequently, the result
of measurement is inexact. Therefore, researchers and teacher gave a little guidance to
assure that all groups about how to measure correctly.
Figure 6. pupils’ mistake in measurement
Because we gave a lot of matchstick to each group to measure using nonstandard measurement, they tend to perform measurements by arranging a match on
their objects of measurement (Figure 7). In this activity, almost all of the groups used
the same method that was arranging the matchstick on the object that was being
measured, then count the number of matchsticks needed. But when they had some
trouble when they measured the height of the Chair, that was because the matchsticks
cannot be arranged in a stand position.
Figure 7. pupils’ measuring method
In the measurements using a straw, pupils used almost the same as they use when
measuring by using matchsticks. But a little bit different because the number of straw
given to each group is limited.
After looking at the pupils’ answers on worksheet, most of pupils write down
the measurement results with the integers, but it turns out there are some groups that are
already familiar with decimal. When the measurement result does not meet exactly in
one unit, for example when one of the groups measured the table by using a matchsticks
that the size of the table is not appropriate 11 units of matchsticks, they write down the
result by 11.5. But some other groups who only wrote 11 units of matchsticks.
Figure 8. the difference of pupils’ answer
On the activity of the measuring using the standard measurement, most of pupils
still had not been able to use and read the scale of ruler correctly. We could notice it by
finding a mistake of their answers in their worksheet. Of the two rulers provided, the
first ruler’s scale is started from 1 (ruler 1) and the second ruler’s scale is started from 0
(ruler 2), students write a different answer when measuring the length of an object
(paper money of Rp. 1000). When using the ruler 1, they wrote down the answers is 15
cm, but when using the ruler 2 their answers is 14 cm. However, there is still one group
that got the correct answer (14 cm), which was answering with the same answer when
using two different rulers.
Figure 9. the difference of pupils’ answer in second activity
In General, all of IRME’s characteristics were already concluded in the teaching
and learning process, although still insufficient. One of them is due to the
understandings about the design of leaning between the teacher and the researchers. For
instance, after completing the worksheet the teacher asked the pupils to collect the
worksheet. whereas we should let pupils to had it, so that they could remember their
answers during the presentation and discussion in the class. In addition, the teacher did
not give the guidance to the pupils to find the conclusion on the worksheet, which was
indicated by there exist of some groups that still have not fill in the answers in the
conclusion part yet of the worksheet, but the teacher asked them to collect the answer.
Another problem occurred during the teaching and learning process was the
noisy condition of the class. Also there were some students who did not want to
cooperate with their group. On the other hand, one pupil was reading comics in the
class when she had finished her task given by the teacher (Figure 10). The teacher said
that this is an issue that happened in more often on the kids who are like playing and
less like working with their friend to finish their task. Learning conditions, which began
in the 12.00 am and after sports lesson, also give much effect to the concentration of the
pupils. Most of the pupils were getting tired, so they wanted to go home quickly and did
not focus during the teaching and learning.
Figure 10. pupil read a comic
Actually, the lesson would be better if at the end of it, teacher gave an individual
practice to ensure the pupils understanding. However, because a lot of time spent on the
activity of learning before, at the time teacher did not give the individual practice. But,
Pupils seemed to understand about how to read the scale on the ruler.
III. Conclusion
Based on the description above, we can conclude that the pupils can learn about the
measurement by using a span, step and certain objects arround their lives beside using the
standard measurement tool such as a ruler. In addition, the non-standard measurement was
used in this learning as an introduction to the pupils so that they can get a better
understanding about the standard measurement. Finally, at the end of learning process
pupils can conclude that to measure using standard measurement tool like a ruler, we do not
need to only pay attention to the number of a ruler’s scale, but by calculating the number of
the scale.
Generally, the teaching and learning that had been conducted satisfied the five
characteristics of IRME. These are measurements used in the daily lives like the one carried
out by the craftsman and the tailors (the use of context), learning media such as matchsticks
and straws (the use of models), activity of measurements and pupils’s involvement in
determining the conclusion
(use of students’ contributions), presentation and group
discussion (interactivity) and addition (intertwining). The process of mathematizing that
occurred in teaching and learning process can be described on the iceberg below.
Measure using ruler as a standard
measurement tool
Measure using matches and straws as a nonstandard measurement tools
Measurements in daily life
References:
Gravemeijer, K.P.E. 1994.Developing Realistic Mathematics Education . Disertasi Doktor,
Freudenthal Institute.
Yuwono, Ipung. 2007. Pembelajaran Matematika Realistik. Malang: UM Press.
Achmad Dhany Fachrudin1
Ummy Salmah2, dan Sitti Busyrah3
International Master Program on Mathematics Education (IMPoME 2012)
email: [email protected], [email protected], [email protected]
I. Introduction
Mathematics is one of difficult lessons for most students. It can be seen that many
students do not like mathematics. This difficulty actually arises because of a lack of
understanding of mathematical concepts to students. Moreover some findings suggest that
teaching mathematics gives a lot of emphasis on procedural skills and led students only to
understand mathematics without reasoning (Yuwono, 2007). In the classroom, most
teachers still use the conventional learning, which a mathematical concept is only delivered
for granted without being associated with the experience of students, while mathematics
requires them to think logically, carefully, and accurately.
Basically, mathematics will be meaningful if the learning associated with the real
world of students. In order to make mathematics more meaningful, students should be
given the chance to reinvent mathematics under the guidance of adults (Gravemeijer;
1994). This is supported by the opinion of de Lange (1995) that, the process of reinvention
should be developed through the exploration of a variety of real-world problems. Therefore,
in the learning process, teachers should not be the learning centre, but the students. So that
students could not be seen as passive receiver of ready-made mathematics. Therefore,
PMRI that relates math concepts with real-world of students is considered appropriately to
be applied.
On this occasion, researchers developed instructional design for material of
measurement with length measurement as the sub material. This instructional design would
be applied to Grade 2 of Madrasah Ibtidaiyah Negeri 1 Palembang. It was developed with
reference to the approach of PMRI. By using PMRI approach, this lesson began with
problems from the environment the students themselves. In this lesson, researchers used
matchsticks and straws as non-standard instrument to measure some of the objects around
them, such as tables, benches, windows, and mathematics books.
Here are the stages carried out by researchers in the implementation of the study on
the measurement of the length in Grade 2 of Madrasah Ibtidaiyah Negeri 1 Palembang.
II. Instructional Design
As for the stages being performed is the Preliminary design (analysis of the
curriculum and the determination of learning objectives and indicators), continued with the
implementation/testing of design (teaching experiment) and a reflection of learning that has
been performed (retrospective analysis) that will be described as follows.
1. Preliminary Design
At this stage, the initial steps undertaken by researchers was conducting an
analysis of the curriculum to determine the material to be taught, formulating objectives
and indicators that will be achieved in this process, determining appropriate context in
accordance with the material to be taught, as well as drawing up a learning instruments
such as lesson plan and student worksheet which was used in the learning activities in
the classroom later.
Based on the results of the discussion with the mathematics teacher (Mrs.
Tartila), the material that would be taught was the measurement of the length with basic
competence that is using standard and non-standard measurement tools of length which
are often used. The indicator that will be accomplished was to measure the length of the
objects by using standard and non-standard units. In order to support learning activities,
the teacher together with researchers designed lesson plan and student worksheet which
were appropriate with to the material to be taught, as well as composed learning
scenarios by applying the PMRI approach.
Preparations of the lesson plan, student worksheet and learning scenario that
will be applied in the classroom were carried out a few days prior to the implementation
of learning process. The discussion was carried out twice. On the first discussion,
teacher and researchers designed the appropriate learning scenario and chose the
appropriate context to teach the concept of length measurements. At this early stage of
the discussion teacher and researchers agreed to use the context of measuring height as
a bridge to make students understand the concept of length measurements. On the
second discussion, the draft of lesson plan and student worksheet has been discussed,
similarly, with the initial learning scenarios have been discussed before. Mrs.Tartila as
the teacher provided some input and revision on the lesson plan and student worksheet
which researchers arranged before. After this discussion, the learning scenarios, which
have been discussed, divided students into several activities as follows
a. Activity 1: Students are introduced to the context which is related to the
context of length measurement
In this activity students are reminded about the height measurements which
they usually do in daily life in order to direct the students to the concept of
the length measurement. What people usually do when measuring the height
and what tools are commonly used.
b. Activity 2: Students are invited to measure the length of the objects around
them by using straws and matchsticks.
In this activity, students are invited to measure some of the objects in the
class, such as mathematics books, desks, chair, and window. As the nonstandard measurement instrument, we provided straws and matchsticks. By
using both these objects, they measure the four objects that have been
provided one by one and write down their length on the worksheet that had
been distributed to each group.
c. Activity 3: Students compared the length of those objects by using straws
and matchsticks.
In this activity, students are asked to compare measurement results that they
have done with the use of straws and matchsticks.
d. Activity 4: Students measured some objects by using ruler.
In this activity, students are asked to measure the objects on previous
activities by using a ruler. In addition, students are given a problem, i.e.
measuring the length of the money Rp 2,000 by using two pieces of a ruler
which have provided in their worksheets. The first ruler is a ruler intact
(starting from 0), whereas the second ruler is a ruler which its scale was
from 1. This is done to bring understanding about the concept of length
itself.
Here is the iceberg instructional design of this learning material:
Using ruler (standard
measurement) to measure object
Length of straw
=....... length of
matchstick
Measuring the length of
objects around us
Figure 1. Iceberg design in Length Measurement Material
2. Teaching Experiment
Math lessons in class 2A MIN 1 Palembang start at 11.55 am on Wednesday,
after the lesson Penjaskes. Mrs. Tartilah (here in after are written as teacher), teacher
assistant and research team divided class into 6 groups. Furthermore, teacher initiated
the learning by asking students about their activities related to measurement or
measurement activities they have ever seen. The students enthusiastically answered
these questions. Among them are those who answer the door or window measurements
performed handyman when building a house or school. Then the teacher asked what
objects are used craftsman. One answered meters, and some others answered ruler.
After that, the teacher asked the students to come forward to measure the board and seat
height using a ruler (Figure 2). The teacher lure students with a question, what can be
done to measure something without using a ruler or other measuring devices? Some
students answer using span or footsteps. Then, teacher conveyed to the students that
they will measure objects using another unit of measurement namely matchstick and
straw.
Figure 2. Student measured the length of whiteboard
The Activity of Measuring Object by Using Matchsticks and Straws
In this activity students measured objects around them as table length, seats height,
window width, and length of mathematics textbooks by using matchsticks and straws under
teacher's guidance (Figure 3). The aim of this activity was students are able to do the
standard iteration count how many times a matchstick or a straw to measure these objects
and then compare them.
Figure 3. Students measured objects by using matchsticks or straws
Some students have difficulty in the process of measuring seat height by using
matchsticks. There's even given up do not do it. However, once we help, they finally
know how to measure the seat height by using matchsticks. The results of measuring
the length of the table, the width of the window, seat height, and length of math
textbooks, either by using matchsticks or straws, all written in a table that has been
provided in the worksheet.
Then, each group wrote their measurement results on the board and exposed it to
the class (Figure 4). At this exposure, there were some groups that do not regard the
current presentation. Moreover, the teacher did not use vary answers of every group as
class discussion.
Figure 4. Presentation of each group
The Activity of Measuring Object by Using Ruler
After all the representatives from each group presented their work, teaching and
learning mathematics followed by conducting measurements of objects using standard
unit, which is a ruler. Students were given the second worksheets, which contains the
instructions for measuring a thousand banknotes by using two types of rulers; normal
ruler and broken ruler (no zeros). This worksheet was used to know the extent of
student understanding about measurement concepts they have learned.
Figure 5. Students measure the length of a thousand banknotes by using two types
of ruler
In these measurements, some students still make mistakes as in the picture above.
Students also have a variety of reasons related to differences in banknote thousand
length using two rulers.
3. Retrospective Analysis
Retrospective analysis is conducted by the teacher and researchers after teaching
and learning process is completed. This activity’s purpose is to analyze and reflects the
learning process that has been completed. These are about the problems occurred during
the learning process. Further, this activity’s purpose is also to analyse the pupils’
thinking, working, and answers.
According to the observation that we have done, overall the implementation of
learning is good enough. However, there are some pupils that did not focus and played
during the lesson. The teacher seemed she could give the guidance although sometimes
she met some difficulties because of the pupils.
The first attention of the research team during the taching and learning process
is based on instructional design that has been created, teacher should began the lesson
by introducing the contextual examples or problems about the measurement to the
students, but teacher gave questions directly to students about the kinds of measuring
instrument, then give context or examples of measurements in daily lives. This is
happened because the teacher has been introduced previously about the measurements
to the students so teacher felt the children already know and be able to answer these
questions. However this is not influence whole of the learning process.
On the measurement of the activity using the non-standard measurement,
apparently there are still many pupils who are not yet able to measure using non
standard measurement that has been prepared. On the other hand, there are groups who
have recognised a way to measure but there is still an error in measurement, for instance
they measure table by using a matchstick wrongly (Figure 6). Consequently, the result
of measurement is inexact. Therefore, researchers and teacher gave a little guidance to
assure that all groups about how to measure correctly.
Figure 6. pupils’ mistake in measurement
Because we gave a lot of matchstick to each group to measure using nonstandard measurement, they tend to perform measurements by arranging a match on
their objects of measurement (Figure 7). In this activity, almost all of the groups used
the same method that was arranging the matchstick on the object that was being
measured, then count the number of matchsticks needed. But when they had some
trouble when they measured the height of the Chair, that was because the matchsticks
cannot be arranged in a stand position.
Figure 7. pupils’ measuring method
In the measurements using a straw, pupils used almost the same as they use when
measuring by using matchsticks. But a little bit different because the number of straw
given to each group is limited.
After looking at the pupils’ answers on worksheet, most of pupils write down
the measurement results with the integers, but it turns out there are some groups that are
already familiar with decimal. When the measurement result does not meet exactly in
one unit, for example when one of the groups measured the table by using a matchsticks
that the size of the table is not appropriate 11 units of matchsticks, they write down the
result by 11.5. But some other groups who only wrote 11 units of matchsticks.
Figure 8. the difference of pupils’ answer
On the activity of the measuring using the standard measurement, most of pupils
still had not been able to use and read the scale of ruler correctly. We could notice it by
finding a mistake of their answers in their worksheet. Of the two rulers provided, the
first ruler’s scale is started from 1 (ruler 1) and the second ruler’s scale is started from 0
(ruler 2), students write a different answer when measuring the length of an object
(paper money of Rp. 1000). When using the ruler 1, they wrote down the answers is 15
cm, but when using the ruler 2 their answers is 14 cm. However, there is still one group
that got the correct answer (14 cm), which was answering with the same answer when
using two different rulers.
Figure 9. the difference of pupils’ answer in second activity
In General, all of IRME’s characteristics were already concluded in the teaching
and learning process, although still insufficient. One of them is due to the
understandings about the design of leaning between the teacher and the researchers. For
instance, after completing the worksheet the teacher asked the pupils to collect the
worksheet. whereas we should let pupils to had it, so that they could remember their
answers during the presentation and discussion in the class. In addition, the teacher did
not give the guidance to the pupils to find the conclusion on the worksheet, which was
indicated by there exist of some groups that still have not fill in the answers in the
conclusion part yet of the worksheet, but the teacher asked them to collect the answer.
Another problem occurred during the teaching and learning process was the
noisy condition of the class. Also there were some students who did not want to
cooperate with their group. On the other hand, one pupil was reading comics in the
class when she had finished her task given by the teacher (Figure 10). The teacher said
that this is an issue that happened in more often on the kids who are like playing and
less like working with their friend to finish their task. Learning conditions, which began
in the 12.00 am and after sports lesson, also give much effect to the concentration of the
pupils. Most of the pupils were getting tired, so they wanted to go home quickly and did
not focus during the teaching and learning.
Figure 10. pupil read a comic
Actually, the lesson would be better if at the end of it, teacher gave an individual
practice to ensure the pupils understanding. However, because a lot of time spent on the
activity of learning before, at the time teacher did not give the individual practice. But,
Pupils seemed to understand about how to read the scale on the ruler.
III. Conclusion
Based on the description above, we can conclude that the pupils can learn about the
measurement by using a span, step and certain objects arround their lives beside using the
standard measurement tool such as a ruler. In addition, the non-standard measurement was
used in this learning as an introduction to the pupils so that they can get a better
understanding about the standard measurement. Finally, at the end of learning process
pupils can conclude that to measure using standard measurement tool like a ruler, we do not
need to only pay attention to the number of a ruler’s scale, but by calculating the number of
the scale.
Generally, the teaching and learning that had been conducted satisfied the five
characteristics of IRME. These are measurements used in the daily lives like the one carried
out by the craftsman and the tailors (the use of context), learning media such as matchsticks
and straws (the use of models), activity of measurements and pupils’s involvement in
determining the conclusion
(use of students’ contributions), presentation and group
discussion (interactivity) and addition (intertwining). The process of mathematizing that
occurred in teaching and learning process can be described on the iceberg below.
Measure using ruler as a standard
measurement tool
Measure using matches and straws as a nonstandard measurement tools
Measurements in daily life
References:
Gravemeijer, K.P.E. 1994.Developing Realistic Mathematics Education . Disertasi Doktor,
Freudenthal Institute.
Yuwono, Ipung. 2007. Pembelajaran Matematika Realistik. Malang: UM Press.