Comparation of two numbers

Classroom Observation in SD Muhammadiyah 1 Palembang (Third Report)

INTRODUCTION

This is a report of classroom observation in SD Muhammadiyah I Palembang for grade three students. For students in this level, they still had difficulty to understand how to compare two numbers. Based on this fact, this observation was performed to help the students understand concept of comparing two numbers.  Using a context in a classroom during teaching Mathematics might will help the students to get better understanding about Mathematics concept that they learn. Right context will make them easier to figure out what matter they face. When they have been able to do this, they will have ability to analyze the problem using their own understanding from knowledge or experiences that they ever got. Then, finally they can be easier to make a conclusion about the matter.

GOAL

The goal of this observation was to know what context that can be used to help the students understand concept of comparing two numbers.

OBSERVATION QUESTION

By using a context through some questions given to the students, whether those questions can help them to understand concept of comparing two numbers?

DATA DESCRIPTION AND ANALYSIS

In this observation the students were given some questions as contexts to help them understand concept of comparing two numbers. One of questions is like below:

The price of 3 candies is Rp 1000 (image A), and the price of 4 candies is Rp 900 (image B). From the two groups, if we want to buy a candy, which candy that has lower price? How do you know that it will have lower price?


Here are the answers of two students (Faurel and Bangir) as examples how the students answer a question about comparison of two numbers using context related to their daily life.

Faurel’s answer:

The first time Faurel answered this question, she said that a candy in group B had lower price, because its price was 210 and the price of a candy in group A was 325. From this answer she seemed had made a calculation to determine the price of a candy in each group. However she didn’t explain how she got 210 and 325.

Therefore, she was asked to explain how she got those numbers. This is her explanation:

From that answer, she had divided 1000 by 3 which gave result 325. She also divided 900 by 4 which gave result 210. She was asked again how her way to get those results. She got a little difficulty to write it, but she could explain how she got her answers. Her explanation can be written like below:

Candy A                                                                     Candy B

1000 = 900 + 100                                                900 = 800 + 100

900 : 3 = 300                                                          800 : 4 = 200

100 : 3 = 25                                                              100 : 4 = 10

300 + 25 = 325                                                       200 + 10 = 210

From Faurel’s answer, it can be known that she had thought how to determine the price of a candy in each group. Then, she compared which one had lower price. When she answered it, she used concept of addition and division. To solve this question she also applied concept of whole number. She tried to divide 1000 by 3 and 900 by 4 to get the price of a candy in each group. However, because the result was not whole number, she tried to write 1000 = 900 + 10 and 900 = 800 + 100. Her idea about this was 900 divided by 3 and 800 divided by 4 could give result in whole number. How to divide 100 by 3 was still difficult for her. Then, for the result of 100 divided by 4 was 10, her explained was like below:

100 = 10 + 10 + 10 + 10

In that time she thought again and realized that it was wrong. She finally could find the exact result was 100 = 25 + 25 + 25 + 25. So, she got the price of a candy in group B was 225.

Although she could not find what the result of 100 divided by 3, she said that she had known which candy having lower price. It was done by comparing 300 and 200. She had known that 200 was smaller than 300, so she could make conclusion that a candy in group B had lower price than a candy in group A.

What Faurel did to solve this question is using of unite method about division. This was a result of what she ever got from her learning. When she was asked more how she got her answer, she can explained and used other method in Mathematics such as addition and approaches to whole number. She could find the solution of this question using her own understanding supported by questions that made her thought more about the question and the answer she got.

Bagir’s answer:


When Bagir was asked how he got 350 for a candy in group A and 200 for a candy in group B, his explanation is like below:

In group A, the price of three candies was 1000, so the price of a candy maybe was 325 or 350. He explained that:

325 + 325 + 325 = 975

350 + 350 + 350 = 1050

He chose 325 and 350 because according to what he knew, the values of money in rupiah from the smallest one were Rp 25, Rp 50, Rp100, etc. So, he could obtain 325 from three 100 and one 25. He also could obtain 350 from three 100 and one 50.

325 = 100 + 100 + 100 + 25

350 = 100 + 100 + 100 + 50

Furthermore, he compared the result 975 and 1050. The difference between 975 and 1000 was 25, and the difference between 1000 and 1050 was 50. From this result he knew that 975 closer to 1000 than 1050 to 1000. So, at the first time he guessed that the price of a candy in group B was 325.

However, finally he chose 350 as the best result for the price of a candy in group A. He gave reason why he didn’t choose 325. This was because he thought that in fact it couldn’t or very rarely to get money in Rp 25. So, he chose 350 because in fact Rp 50 still can be found.

To find the price of a candy in group B, he used same way as in group A. Then, he chose Rp 200 as the price of each candy in group B.

From Bagir’s answer, it can be known that he involved his mathematical ideas with his knowledge related to money. He also used his mind to think about the numbers that close to 1000. He didn’t choose 300 + 300 + 300 = 900; 400 + 400 + 400 = 1200; or other choices because he thought that the results of 325 or 350 were better than others. He knew which was closer to 1000 by counting difference between those numbers using subtraction of the lower number from the higher number.

In this question he also can be easier to know which is smaller number and which is higher number because he has known that in real Rp 25 is lower than Rp 50 and Rp 50 is lower than Rp100, etc. So, in this question, using of money help him to understand more about comparison between two numbers and he also can give reasons toward his answers.

From Faurel’s answers and Bagir’s, it can be known that both of them tried to solve the question by counting price of a candy in each candy. Both of them use approaches of whole number. Either Faurel or Bangir didn’t write some their calculation in paper. When they were asked about it, they said that they made calculation in their mind that mean they figure out it.  A difference between Faurel’s answer and Bagir’s was Faurel used division and explore her answer by adding some numbers. Bagir didn’t use division, but used approach to the closest number by counting the difference between two numbers. Beside it, he involved his mathematical idea with the real matter.

CONCLUSION

Using a context in teaching of Mathematics can help students get better understanding about concept of Mathematics that they learn. They can analyze the problem and create Mathematical ideas by their own understanding. They also can involve knowledge and experiences that they ever got. Their knowledge related to facts will make them easier to figure out and explore more about the problem and solutions for it. Therefore, it will give various solutions according to their knowledge and experience. In addition they can know more about the use of Mathematics in the real life.

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