Acciones para la dimensionamiento de gestión

The students took a 20-minute posttest after went into the entire lesson sequence. The posttest items were designed to assess students‟ current knowledge about angle and its magnitude. The following table summarizes the gained scores of those 6 students:

Table 5.1. Small group‟s pre and posttest scores

No Name Pretest

Score

Posttest Score

1 Abell Ricardo. O (Abell) 4.38 8.75

2 Ajeng Ayu Puspita Sari (Ajeng) 3.44 9.4

3 M. Alif Zhafar. G (Alif) 6.25 9.06

4 M. Hilal Naufal (Hilal) 3.12 8.44

5 M. Muqsith Giga Saputra (Giga) 4.4 8.75

6 Rafli Dwiyanda (Rafli) 2.5 7.18

M (SD) 4.01 (1.2) 8.59 (.69)

If we compare the gained scores from both pre and posttests (table 5.1), we can clearly see a significant increase in students test scores. However, our main intention is to use the pre and posttest results as a resource for clarification of students‟ development throughout the lessons sequence. Due to the limitation in evaluating students‟ gained scores for describing their development, we conducted a further analysis on the students‟ written work. The analysis revealed which knowledge that students acquired and in what aspect of students understanding toward the concept has changed after following the lessons sequence.

Based on the analysis on students‟ written work and video registrations of the interview, we noted several important remarks as follow:

a. Angle definitions that students embraced

In the end of the learning process, the students perceived the angle was not just as the space in between two lines in the plane which meet in a point. They also perceived the angle as the difference of direction between two lines. The clarifications of this claim can be found in students‟ written work and their verbal justifications. For example, in one of the test items, we presented a set of angle

figures, in which of the magnitudes of the angles are different and the lengths of the arms are varied in size. All of the students encountered no difficulty when we asked them to compare the sizes of those angles; even when we displayed a bigger angle with the shortest arms. Their verbal explanations clearly indicated that they perceived the angle as the difference of direction between two lines. In addition to that, we also presented a set of right-angle figures that varied in orientation and also varied in the length of their arms. The students were able to recognize the angles as the right-angle figures and this justified our claim about angle definitions that students embraced.

We argue the development of students‟ inventory of angle definitions is a cumulative result of the activities in the lessons sequence. For instance, in the first lesson, we asked the students to explain how an angle was formed. Mainly the students came up with the explanation that used the difference of direction between two line segments in order to explain about angle formation. The activity in the second lesson strengthens students‟ comprehension of the angle as the difference of direction between two lines. A particular activity that promotes students understanding about angle as the difference of direction between two lines is when the students constructed the upper case letters using matchsticks. In the activity, the students realized that the angle also could be defined using the direction of the lines.

b. Students’ comprehension about angle magnitude

The students have developed their understanding about angle magnitude. Ordering the angle magnitude on the real-world objects and to reason with the angle magnitudes on the tiled floor models proved to be the fruitful ways to promote students‟ development. In the posttest, we presented a problem that asked the students to reordering the given angle figures into an ascending order. Due to their adequate understanding about angle magnitude, all of the students had no difficulty in performing this task.

The understanding about angles similarity had developed as well. The activities that had impact to this development are the activities of angles on the letters from the matchsticks and letters on the tiled floor models. From those particular activities, the students understand that the corresponding angles on

letters like F, X, and Z are similar. Some problems in the posttest required the students to have the comprehension of the concept of angles similarity. For instance, in the test we presented an X like figure and asked the students to write down what they knew about the magnitude of the angles on it. Almost all of the students could recognize the angles had the same magnitude. They explained that the X shape figure represented a vertical angles situation.

c. Students’ capability to apply the concepts to solve the problems

From the lesson sequence, we observed that the students acquired the knowledge about vertical angles, straight angle, full-angle, and corresponding angles in the parallel-transversal situation. Two problems in the posttest put these understanding into a test. The first problem on this context asked the students to determine an unknown angle magnitude from a known angle magnitude in a straight angle situation. Only one student that made a mistake by assuming the straight angle is 360 . However, from the interview with this student, he reconsidered his answer and figured out that he had made a mistake. He said that he overlooked the problem and as a result he thought that the figure was circular instead of straight.

The second problem asked the students to find out the unknown angles magnitudes in parallel-transversal situation. We provided a numerical value of an angle, and asked the students to deduce the values of the other angles. From their written work and their verbal explanations during the interview session, revealed that the students had good understanding about the concept of corresponding angles. As a result the students could solve the problem without any significant difficulty.