Vivencias significativas – Comprensión del pasado

In this part of the chapter, we describe four data collection phases that we use in this study. The aim is to give an overview about what and how the data are

collected. The participants of this study are the teacher and the students in grade seven.

3.2.1 Preparation phase

In the preparation phase, we collect several different data and use different methods to collect them. The table 3.3 describes about what and how the data are collected in this phase:

Table 3.3. Data and Method

Data Method

Semi-structured Interview

Lesson Observation Written Work Teaching method with the teacher before

and after the study

the teacher in the classroom before the teaching experiment

-

Classroom management

with the teacher before and after the study

in the classroom before the teaching experiment

-

Socio-mathematical norms

with the teacher before the study - - Teacher’s knowledge about Indonesian realistic mathematics education (PMRI)

with the teacher before the study

- -

Students’ prior knowledge about angle

with the teacher and the focus group before

the teaching experiment - on pretest before the teaching experiment

Those data are analyzed and the results are used to make necessary calibrations in the planned teaching and learning activity and the teacher‟s guide.

3.2.2 First teaching experiment (first cycle)

It is appropriate to test the designed materials in advance with a small group of students (6 students) to get an insight into students‟ reaction to the designed tasks. The researcher acts as the teacher in the first cycle. The data that we collect from this sub-phase are students‟ definitions of an angle that are derived from the

everyday life objects, students‟ strategies to solve the tasks, students‟ knowledge about parallel lines, students‟ knowledge about the magnitude of angles, and students‟ reasoning about the magnitude of angles on a straight line that falling across two parallel lines. In order to collect these data we make a video recording, and collect field notes, and students‟ written work. These data are analyzed and the results are used to test the initial HLT, improving the predictive power of the initial HLT, and to make necessary adjustments to the designed learning activities.

3.2.3 Second teaching experiment (second cycle)

In this sub-phase, the improved version of HLT is applied in the classroom environment by the teacher. We collect crucial data that similar with the data in the first cycle, such as; students‟ definitions of an angle that are derived from the everyday life objects, students‟ strategies to solve the given tasks, students‟ knowledge about parallel lines, students‟ knowledge about angles magnitude (0 , 90 , [180 , 360 ], and [360 , )), and students‟ reasoning about the magnitude of angles on a straight line that falling across two parallel lines. We collect data using video recordings, field notes on teacher‟s and students‟ crucial actions, and the students‟ written work. Then, those data are prepared to be analyzed in retrospective analysis.

3.2.4 Third teaching experiment (third cycle)

The re-improved version of the HLT is tested to a small group of students in order to try some crucial elements of the refined materials. In this sub-phase, our main attentions are to get explanations, justifications and clarifications about students thinking, and to understand how the design helps the students to acquire the intended knowledge. The data that we collect in this sub-phase are similar with the data that we collect in the first and the second cycles. Either the method to collect the data is also similar.

3.2.5 Pretest and posttest

Pretest and posttest are conducted to assess the students‟ acquisition of knowledge and to provide the „quantitative‟ description of students‟ understanding about the topic. This quantitative description can be acquired from students‟ answers on items test (pretest and posttest). However, we are also interested in the qualitative description of students‟ understanding about the topic. Therefore, we designed the test items in such a way that we can observe how students solve the problems. Generally, in the pretest and the posttest we will find multiple choices, numerical problems, exploration questions and diagrammatic problems. The pretest in this study is conducted in the preparation phase. The aim is to inquire students‟ prior knowledge about angles (what students know and don‟t know). At the end of the teaching experiment, the posttest is conducted as a follow-up action from the pretest on the preliminary phase. The aim of the posttest is to assess the students‟ development of understanding about the concept of angle and its magnitude.

The pretest and the posttest are similar but not the same. In order to allow us to compare the results from both tests, we retain a proportion of items in the pretest and blend the retained items with new items which examine the equivalent expected learning outcomes in the posttest, or use different types of questions for an equal item in the pretest and the posttest. Beside the students‟ written work on the pretest and the posttest, we collect data from the interview as well. Considering the scale of this study, we perform the interview only with the focus group in the second teaching experiment (second cycle). The aims of conducting the interview are to inquire students‟ understanding on the topic and make an inventory of students‟ solution procedure to the given problems.

3.2.6 Validity and reliability

Bakker and Eerde (2013) explained about validity and reliability in design research that validity was concerned with whether we really measured what we intended to measure. Reliability was about the independence of the researcher. Since we want to evaluate students‟ comprehension about the concept of angle, in this study we collect several data, such as students‟ written works, interview tapes

from both the teacher and students, field notes, and video registrations. The use of different types of methods allows us to conduct triangulation that can contribute to the internal validity of the study. Moreover, we employ electronic devices (cameras and tape recorders) to increase the objectivity and the internal reliability of the data collection in this study.