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.
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.
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 non-standard 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.
(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:
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
Using ruler (standard measurement) to measure object
Length of straw =... length of matchstick
Measuring the length of
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.
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
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
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.
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
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
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.
References:
Gravemeijer, K.P.E. 1994.Developing Realistic Mathematics Education. Disertasi Doktor, Freudenthal Institute.
Yuwono, Ipung. 2007. Pembelajaran Matematika Realistik. Malang: UM Press. Measurements in daily life
Measure using matches and straws as a non-standard measurement tools
