USING FINGERS, SQUARES METHOD, AND MAKE-FOUR GAME TO TEACH THE CONCEPT OF COMMUTATIVE ADDITION FOR GRADE I STUDENT IN ELEMENTARY SCHOOL
By Fajar Arwadi
Observation Report at SDN 117 Palembang on 7 October 2010
Mathematics learning using Pendidikan Matematika Realistik Indonesia (PMRI), a.k.a the Indonesian version of Realistic Mathematics Education (RME) has developed well in some elementary schools in Indonesia. It is shown by the participation of many schools and their teachers and stakeholders involved in the implementation on PMRI in Indonesia. On this occasion, Sri Imelda, the student of Nusa Cendana University and I, the student of Makassar State University, made a teaching-learning process for grade I students in SDN 117 Palembang in order to give contribution as an observer and a researcher of PMRI. The lesson taught in the learning process is commutative addition of integer from 1 to 10. The main activity of the learning is make-four game.
b. The Goal of Observation
The formulation of observation goal is as follows:
- To create an enjoyable learning using PMRI
- To know the effectiveness of make-four game
- To make student understand the concept of commutative addition
c. The Process of Teaching-Learning at Class
In the commencement, teacher, represented by I, told a story “Andi has several friends” try to count how many friends Andi has if his friends are in the front of the classroom”. Then the teacher pointed some students, as illustration, exactly 14 students to come forward. Of all the 14 students, the teacher asked 6 students to sit and 8 students to stand up as illustrated by the picture below.
Then, the conversation between the teacher and students occurred as follows
Teacher : here the friends of Andi, some of them are sitting down and the others are standing up. Do you know how many friends sitting down Andi has?
Students : six sir
Teacher : how many friends who are standing up?
Students : eight sir
Teacher : you are right, now how many the total friends Andi has?
Students : (counting one by one) there are 14 friends
teacher : great
The next step, the teacher exchanged the group of students in the front of the classroom. The students who had sut down before were asked to stand up and vice versa. By doing the similar conversation like above, the students were also able to get the result 14 students. To solidify the understanding of students, the teacher used another way namely right-left fingers hand. The students can exchange, the model of their fingers which represent certain number from left finger hand to right finger hand or vice versa to catch the concept of commutative addition as shown in the picture below.
In the next step, to verify and to improve their ability about commutative addition, the teacher run make-four game, the game adapted from make-three game published by Kidscount website owned by Freudenthal Institute. However, the teacher just use the paper based of the game concerning that the internet connection at the school is not available. The materials and tools of the game are as follows:
- Carton paper
- Paper containing the addition of two integer numbers from 1 to 10 consisting of 10 columns and 10 rows which totally result 100 cells
- Number card containing integer numbers from 1 to 20
The picture and activity of students in make-four game as follows:
The rule of the game is the students take one card number randomly in a jar then they must find the addition of two numbers in one cell appropriating with the number in the written in the card number which has been taken before. If the students correctly determine the cell, they can circle the box. In the learning process, the teacher divided the students into four groups, namely A, B, C, and D in which group A played against group B and group C played against group D. In one game, the group which successfully make four circles in the cells vertically or horizontally, then the group is stated as the winner.
However, in the reality, it took a long time to get the winner. The teacher then determine the time limit of the game which is only 15 minutes and the winner is denoted by the number of circle each group has. The group having more circle is the winner. In doing cell selection, for instance, the card number taken by a student stating 15, then the possible combination are 5 + 10, 6 +9, 7 + 8, 8 + 7, 9 + 6 and 10 + 5. To facilitate the students who find difficulty, the teacher help students make illustration by drawing some squares, the number of squares is appropriate with the number in
the number card taken. For example, the number is 7
then the students can make a line among the squares
It can be shown that 7 squares is the result of the addition of two squares and five squares.
In the game, we see that the ability of students are vary. There are students who immediately make a circle and others need squares method first, as documented in the pictures below.
Gambar 1: a student taking card 9 circles cell 1 + 8
Gambar 2: a student draws squares
After running a game, we move to the more formal step namely student worksheet (LKS)working in which there are some questions stating a known number and instruction to determine the addition of two numbers resulting the known number e.g.
Fill the blank with correct number
In the working of LKS, all students correctly answered the questions, however the majority of them were not able to conclude the desired conclusion. However, mentally, they know that in addition of two numbers satisfies commutative property.
Here is the iceberg of the learning process
e. Conclusion and suggestion
The conclusion of this activity are:
- The teaching-learning process created enjoyable learning for students
- Make-four game was not suitable for students as its level of difficulty is high.
- Many students mentally conclude that addition of two numbers satisfies commutative property, although they couldn’t conclude it formally
The suggestions of this activity are:
- Teacher in elementary school begins the learning with concrete context.
- In implementing PMRI, the number of students must be at most 25 to create effective learning