This paper-based applet adopts the Java version entitled ‘Beads on Chain’. To access this, you may visit: http://www.fisme.science.uu.nl/toepassingen/00747/
Number pattern, or commonly known as ‘bilangan loncat’ by the lower grade students in Indonesian primary school, is first taught in the third grade.
The ‘beads on chain’ applet is actually a very good manipulative to stimulate students’ understanding on this concept. However, internet connection which does not support most Indonesian elementary schools has been an undeniable challenge. Therefore, preserving the paper-based version could be an alternative.
I have tried out the ‘Colourful Necklace’ to learn number pattern with a number of Grade III-D students of SD Pusri Palembang.
At first, I invited 2 students to play during the breaktime. Hearing that I would play with them, some other students came closer and got involved. It shows how this tool first impressed and be positively responded by the students.
To begin with, I told them the way to make a colourful necklace. Here, I emphasized that a similar pattern is important to make the necklace more beautiful. So, we first placed two yellow beads, then one brown, then yellow, and then blue again. Next, I tested them for the following sequence to ensure that they understood the problem. Finally, we got the first two sequences of alternating beads colour.
I, then, told them that I would love to use 32 beads for my necklace and I was worried about the colour of the last bead will be. The students were mostly confused and tried to gamble the answers. After a little repeating with emphasis to the questions, several students tried to think.
Solving this way, the students were arguing each other, explaining their strategies to find the answers, or debating someone’s opinions (recognizing the error).
A student tried to explain her answer (Left)
The students’ answer (Right)
The idea came when students pronounced the alternating colours of the necklace (yellow, yellow, brown, yellow, blue, yellow, yellow, brown, yellow, blue, etc). A student tried to list the colour and put on the ordered number below the colour. Finally, he could find that the bead in the 32nd order is yellow.
Another student, Keyla, could identify the pattern without listing. The following is the conversation script between me (O) with Keyla (S).
S : Well, this is yellow, yellow, brown, yellow blue. Yellow, yellow, brown, yellow, blue. Yellow, yellow, brown, yellow, blue.
O : Yeah. So, what colour would be in the 32nd order?
S : Yellow
O : How do you know?
S : We could count on this until 10. After this, there must be another yellow, yellow. The counting could be continued.
O : Oh. So, this is for the 11st, right?
S : Yes. Now, we add another yellow, brown, yellow, blue. And then we add. So, we have 15 now.
O : Good. Go on!
S : It means that if we go through this pattern twice, then we got 20.
O : And then?
S : It means, later on we will have 30 here. If we add 2 more beads, then it would be the 32nd. The colour would be yellow since the it alternates regularly.
From the conversation, we could see how she proposed her own solution and found the correct answer. Her reasoning also made sense and was understandable by other students.
After her explanation, I tried to give additional questions for different order. Almost all the students found it easy to determine the colour.
The overall activities convinced me how a game interact students to learn mathematics indirectly. The game which was started with only 2 students were becoming more and more crowded at the end.
The students were very enthusiastic in getting involved in the activity