Pusat Penelitian dan Pengembangan Pendidikan Matematika Realistik Indonesia Sekolah Tinggi Keguruan dan Ilmu Pendidikan



1. Introduction

    Developing children number sense requires long time and hard effort. Teacher should facilitate children in such a way they can construct the big ideas that lies under number sense. Starting from counting, children may be guided through grouping strategy and then reach the unitizing concept.

    In this report, we will present the process of two students in constructing their mathematical understanding in numbers. They were Isa and Eli who joined the K-1 class in solving Taking Inventory context. This observation is aimed to analyze their learning process during working in the class until the whole class discussion. It is expected to give brief explanation about the shift of their understanding.

    2. Observation Question

      How do Isa and Eli grouping strategy reflect mathematical development?

      3. The reflection of mathematical development from grouping strategies

        Started from Isa and Eli activities in ‘Children at Work’ session, we looked the fascinating strategy that they used for solving the paper bag problem. Jodi as a teacher acted to be a guide here. She asked them more in order to bring their thinking to what she wanted. The strategies came out intentionally, Isa and Eli counted the paper by grouping of tenth. It made Jodi interest with their work, indeed.

        The amount of paper that Isa and Eli got was not the end of Jodi’s inquiry. She asked more to guide them into better understanding in number sense by asking them “How many” as a theme, such as “How many packs of ten? And how many loose one?” in 249. However, Isa and Eli only can determine the amount by counting the packs of ten bags one by one. Their strategies reflected their understanding about unitizing concept in the initial stage. They still could not recognize that 249 consist of 24 tenth (packs) and 9 ones (loose one).

        In the next phase, ‘Children at Work two days later’ session reflected Isa and Eli‘s further development of their mathematical thinking. Jodi gave them a problem that challenged them to make a prediction how many packs of ten bandages in 80 and 60 bandages. This problem was intended to make them determine mentally the number of packs of ten. They found it was difficult to do it until they came up with the idea that 20 things can be made into 2 packs. This fact showed the development of Isa’s and Eli’s comprehension in constructing the idea of unitizing.

        Meanwhile, from the last part of Isa and Eli activities, ‘Isa and Eli share their thinking’ session, it showed the next level of understanding in their thinking. Isa and Eli came up with their idea to separate the pack and the loose of bandages. When Jodi asked 60 bandages can be made into how many packs, Rachel came with her answer that it is 6 packs, but there was no feedback from Jodi, she was back to Isa and Eli. Eli also gave another example that 100 things could be made into 10 packs, because 100 have one more zero, Eli said. From this statement, it seems that he has already got the conclusion in his mind about this problem, how to solve it. Jodi wrote the simple table on the whiteboard and filled it based on their discussion. It was intended to attract children’s attention what the result of Isa and Eli’s thinking.

        Isa figured out that the first number should be how many packs and the other one should be how many loose. She wrote on the whiteboard, circled the number and gave explanation of her thinking. Jodi gave some questions and made Isa gave more interpretation of what she did. Isa has already understood the concept by giving statement “you could do it with any single number”. She is sure of what she did. She reflects her mathematical development by stating there are two ways of counting, easy way and hard way, easy by using the number and hard way by counting it. Then Jodi repeated again Isa’s explanation intended to whole class discussion. She showed by counting the packs using her fingers in front of the children. She did it again and again until the children gave the correct response. Here, students tried to figure out what Jodi said about packs from the number given.

        4. Conclusion

          Grouping strategy done by Isa and Eli reflected children can construct their thinking of understanding in unitizing. They refined the learning object from grouping strategy with counting one by one in pack of ten. With an intervention done by Jodi, gradually they have already understood the meaning of counting objects in tens. They understand about unitizing so that they understand the meaning of any single number they work with, whether it is as tens or as ones.


          Anisa Fatwa Sari

          Ekasatya Aldila Afriansyah

          Yenny Anggreini Sarumaha


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