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5 September 2013


(Part 2)

Composed by : Ratih Ayu Apsari

The content is summarized from seven articles of National Conference of Mathematics XIV (2008), Sriwijaya University.

[3] D.N. Handayani: Butterfly-Wing Context to Support The Earlier Development of Number Sense.

One of mathematical phenomenology that deal with the early number sense, specially in first grade students of primary school is the cardinality. In the formal mathematics, cardinality of a set is a measure of the number of element of the set. The problem is, the beginner students often not realize the aim of counting. For instance, when they aregiven five candies and asked to count how many candies is it, they might start counting as “one, two, three, four, five”. However, even though they stop at “five”, the teacher should investigate it carefully: are they allready understand that 5 means five objects or they think that the fifth object is 5.

To help the students reach the basic understanding in number sense, the butterfly-wing context had been choosen in this research, because it has pattern which similar in the left and right side. The students were asked to observed the pattern in the butterfly wings and guided to recognize the pattern. At the end of lesson, the students are expected to count “how many” in sets of objects using various structures.

[4] Meiliasari: The Context of Structured Candy on Earlier Addition and Substraction Up to 20.

At the earlier phase of learning, children generally use many kind of counting strategies, such as count all objects one by one and count from larger addend, which usually use their fingers to keep the track. When deal with larger number, some students might realize that the counting method seems to be no longer effective. The children will develop new strategies, such as doubling (i.e., 6+8 = 6+6+2)  and splitting (i.e., 6+8 = 6+4+4=10+4). The development of this process may take quite long time.

In order to help te students working in addition in easier and quicker way – and less possibility to do computational error, this study was conducted using the context of candies, which is very familiar in student’s daily live. It is had been tested that the question such as; Dinda as 4 candies and then her mother give another 3 candies. How many candies does Dinda has?  Is more acceptable in low class students rather than directly use the abstract symbol as 3+4 = …?

The lesson activity is organize as follow. At the first time, teacher told students to count a number of candies. They can manually count it (unstructured way) or they can arrange it first, suc as by making two rows of candies which has some number for each row, and then count it (structured way). The purpose of this activity is to make students realized that structure helps them to counting faster.


Picture 4: Illustratation of Unstructured and Structured Candies (Picture Modified)

The next activity is purpose to guide the students to recognize the double structure. Before enroll the worksheet phase, the students are invited to sing the “double song” (satu ditambah satu sama dengan dua, dua ditamba dua sama dengan empat, etc.) which is populer in Indonesia. This song is purpose to stimulate the students’ understanding in double sum. In this stage, the worksheet still use the context of candies which are arranged in one or two packs of two rows of five.


Picture 5: Illustration of Question in Worksheet 2

The third activity is illustrated on the following picture.


Picture 6: Illustration of 5+2=7

The task is about a candy box which just fullfil by 7 canies (the white circles is means the place is not covered by candy). At first, the students expected can tell that it all 7 candies on the box. Second, they can explain that since there are 5 candies in first row and 2 candies in second rows, te total is 7. In mathematical sentence, they can write the mathematical sentence 5 + 2 = 7.

 To help the students construct their understanding in subtraction, the researcher embeded the concept on the subtraction as the invers of addition, rather than using counting strategies, such as counting up (such as (5 – 3 = 4,5 so 5-3=2) or counting backward (5 – 3 = 5,4 so 5 – 3 = 2). That’s why, the students will make the correlation between addition and subtraction. For intance, 6 + 4 = 10, so that 10 – 6 = 4 and 10 – 4 = 6.

[5] Neni Mariana : School Building Context to Develop Spatial Ability.

Spatial ability is the skill to mentally manipulate, understand, reorganize, or interpret relationships of shapes and space. This comprehension is related to matematics, specially geometry achievement for the students (Casey, 2008; Melancon, 1994; Tartre, 1990; Tracy, 1987).

The researcher actually designed for nine activities for learning, but for this chance, the disscussion will just about five of it. The activities are set as the following step.

Activity 1 : My School Building

The goal of this activity is the children are able to localize for main buildings of the school on a grid paper. This activity use several cube with same size.

Activity 2 : Where Our Classroom Is

The goal of this is activity is the children are able to localize their alssroom position on a grid paper. Through this activity, children are expected to gradually emerge 2-dimension scale model. The previous activity is just use the same-size cube. This condition not match with real situation, because in the school some building have different weight, height, and even the shape. By starting tis activity, a conflict will appear about the shape of the school. Consequently, the pupils will come up with a conclusion that not all buildings can be represented by one cube since some of them higher, wider, etc.

Activity 3 : Removable Buildings

The purpose of this activity is to make sure that children are able to: (a) localize all rooms by making a map of the basements on a grid paper, and (b) connect between 3D constructions and 2D shapes of their basements.

Activity 4 : Make a Route to an Important Place in the School

The goal for this activity is the students are able to spatially explain routes to some important places using directions, such as to the left, straight ahead, to the right, and so forth.

Activity 5 : A Mini Lesson – Where Do You Have to Stand?

The aim for this activity is to help the students to denote one-to-one correspondence between a certain point of standing viewer and a certain point of a part of the school buildings.

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