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CHAPTER III RESEARCH METHOD

D. Data Analysis

4) Lesson 4: Fixing the report Learning goals:

a) Students are able to identify the properties of standard views of 3D objects.

b) Students are able to draw the standard views of an object based on its opposite standard view.

Mathematical activity and conjecture of students’ thinking:

Teachers begin the activity by instructing students to work in the same group as the previous lessons. The context in this meeting is about Reza who messed up the old report of a new temple last night. Some report lost its photos.

Therefore, students are asks to help him to rearrange the photos in the report or draw a new one. In the first problem, students are asked to guess how to put the photos of a report into the right position like how they were. Teachers give each group 5 photos and a layout. The photos and the layout are shown in Figure 4.7.

Conjectures of students’ answers, actions, and strategies:

a) Students firstly put the top view of the temple since the photo obviously belongs to the top view. The reason maybe because it has no ‘similar’

Figure 4.7 The layout and the photos for the first problem of lesson 4

picture like the others. However, some students may takes time to realize which photo the top view is. In this case, teachers take an example of students work from previous lesson and asks them to investigate it to find the pattern or how the photo relate to each other.

b) Students may do not have idea how to put the photo and saying that it can be anything. In this case, teachers can asks the students about their experience in the previous lesson. For instance, teacher can begin by assuming one photo is belong to certain position. Afterwards, teachers ask how it will look like from the opposite.

c) Students nicely choose ‘similar’ photo for the opposite position. However, they falsely put the photos with respect to the top view. In this case, teachers scaffold the students by imagining how many cube the students will see from the front or side based on the top view. For example:

d) Students correctly put the photos by relating the photos to its opposite and the top view. In this case, maybe the students will conclude that there are

Or

two possibilities of how the photos are arranged based on the top view. In this case, teachers can ask further question like what makes them different, and whether it influences the shape of the new temple.

After all the groups finish their work, teachers select one group to present their work in front of the class. Teachers lead the discussion by posing questions to the presenter like

a) How did you put those photos in the report? Can you show us?

b) Why did you put them this way? Please explain to us c) How did you figure out the photo from the top?

Why this photo is in the opposite of this one?

d) How about the other group? are there groups that have different arrangements?

If there are groups that have different answer, teacher can invite the group to discuss it. In the end of the lesson, teachers help the students to conclude what they have been done or learned.

Afterwards, teachers ask the students to move to the second problem (see the worksheet and the teacher guide in the appendix). In this second activity, teachers give each groups 3 layouts of different cases. Each layout contains 3 different standard drawings. In the first case, the photos are from the top, the

left, and the front. The photos in second case are from the top, from the right and from the left. The last one contains only two drawings from the top, and the back. The task is that students have to complete the standard views in the each report based on the remaining photos attached. Teachers must warn the students that maybe only some reports can be repaired. In this activity, teachers do not provide the students neither building blocks nor the camera. Students have to draw to completely fill the layout. The following Figure 4.8 presents the three different cases in this problem.

Conjectures of students’ answers, actions, and strategies:

a) To draw the photo from the opposite direction of the given photo, students may use the photo in the opposite as the reference. Based on the previous investigation, they may imitate the opposite views to draw the views in the layout.

b) Students understand that the shape will be ‘similar’ to its opposite, but they are wrongly draw the orientation. The following pictures show that possibilities.

Figure 4.8 Three different cases for the second problem of lesson 4

In this case, teachers make sure why the students did that because there is possibilities that what students imagine or students’ orientation is correct.

If the drawings stand then they are correct drawings. If students did it wrong (they do not have reason why they did that), teachers scaffold the students by making the photo stands and ask the students to imagine what they will see from the opposite. Teachers also can refer to the previous investigation of the two reports.

c) Some groups may claim that they cannot draw the empty photo for the 2nd and 3rd cases. In this case, teacher should ask more why they cannot draw it. Probably, students are aware that they need the opposite photos of the views.

d) Some groups may predict the empty photos in the 2nd and the 3rd cases this way:

In this case, teachers ask the students such as “How could you know/ figure it out?” “Why do you have three blocks there?”. Probably, students just imagine or assume that the temple will be like that. In this case, teacher can refer to the previous investigation. Teacher may use blocks to illustrate the possibilities of the temple.

After all the groups finish their work, teachers select one group to present their work in front of the class. Teachers lead the discussion by posing questions to the presenter like:

a) How many reports can you fix? Which one is that?

b) How did you fix it? Why did the view become like this?

c) How many reports left? Why did not you fix it?

d) How about the other group?

After discussing students’ answers, teachers can close the class by guiding students to conclude what they have done today.

5) Lesson 5: Building the Temples