Development of the math teaching unit about locus (for the unit plan, refer to Appendix F)

Based on the analysis of the unit in students‟ textbook, the researcher developed

an instructional unit for teaching Locus. The unit covers the objectives of grade 9 related to “Locus”. It emphasizes on: a) real life situations where students have to model

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exploration of the locus of a point, c) the use of technology namely DGS that is Geometer‟s Sketchpad.

3.2.6.1 Time-line

The unit is developed based on seven sessions (same number of sessions, for the same unit, as the year before). In three of the sessions, DGS is used. The researcher provided the teacher with the lesson plans and activities that were discussed and agreed upon.

3.2.6.2 Context

The class teacher (same grade-9 teacher as the previous year) taught the class during the implementation of the unit based on the lesson plans that were provided by the researcher. The researcher attended the sessions to guarantee that the lesson plans were correctly implemented and to collect data. Three out of the seven sessions took place in a computer lab in which students had access to computers with Geometer‟s Sketchpad installed. The other sessions were conducted in a regular classroom with a chalk board and an overhead projector.

3.2.6.3 Material

The activities to be conducted in the computer lab were prepared by the researcher. These activities allow the students to come up with the different cases of locus of a point. The same homework exercises that were given to the non-DGS grade-9 students in the first year were given to the DGS grade-9 students of the second year.

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3.2.6.4 Lab sessions

Three sessions took place in the computer lab. These sessions were videotaped in order to compare students‟ interaction with the teacher in the first-year and the second-

year classes (without vs. with the use of DGS).

3.2.6.5 The general objectives of the instructional unit

The general objectives of the unit are:

At the end of this unit, students should be able to:

- Identify the geometric loci of points satisfying given properties (listed in Appendix F)

- Solve open geometric locus problems requiring conjecturing and proving.

The distribution of the instructional unit is according to Table 1 below that provides an outline of the sessions that were covered. For more detailed information about the procedure of each session refer to Appendix F.

Table 1

Instructional unit sessions in glance

Session number Procedure

Session 1 Students solve two questions prepared by the researcher with an objective to distinguish between fixed and variable elements.

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Teacher introduces two cases of locus of a point through problem situations. Together, the teacher and the students, will model the problem situations.

Using a computer and an overhead projector, the teacher will model the two cases of locus of a point mathematically.

Session 2 Correction of H.W. + Teacher introduces

three cases of locus of a point using a computer and an overhead projector + C.W. two exercises from students‟ book

Session 3 Correction of H.W. + Teacher introduces the

last two cases of locus of a point through problem situations. Together, the teacher and the students, will model the problem

situations.

Using a computer and an overhead projector, the teacher will model the two cases of locus of a point mathematically

C.W. one exercise from students‟ book

Session 4 Correction of H.W. + Students solve activities 1 and 2 in the computer lab

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3.2.6.6 Lab settings

First, students were prepared for the use of Geometer‟s Sketchpad. Due to time limitation, the researcher asked the computer teacher to train all the 18 students on Geometer‟s Sketchpad in the computer sessions by asking them simple constructions, two weeks before starting the unit implementation. Second, students with similar levels of achievement were paired. Class teacher explained to the students the activity

procedures and the researcher interviewed one pair of students at a time, according to the clinical interview technique (Ginsburg, 1981), to investigate their thinking processes.

3.2.6.7 Clinical interviews

During each of the three DGS-based sessions, clinical interviews with students were conducted. Two pairs of low achievers and two pairs of middle achievers were interviewed. In the first lab session two pairs of low achievers were interviewed. In the second lab session one pair of middle achievers was interviewed. In the third lab session one pair of middle achievers was interviewed. One of the low achievers‟ pair was chosen

to be interviewed based on their request; however, the other pairs were chosen in the computer lab

Session 6 Correction of H.W. + Students solve activity 4 in the computer lab

Session 7 Students solve two high level problems

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randomly. Students were asked questions about their way of thinking while solving the problem and were free to answer the way they want. The pair was asked questions that reveal students‟ way of thinking but did not affect their thinking. Examples of questions are: “Can you tell me how you reached the solution?” “Why did you choose to do this?” “Why are you moving this point?” .. etc.

The interviews were audio taped and the students‟ computer files were saved and kept for analysis. (Note: the interviewed students were asked to save their work every 5 minutes under different files‟ names in order to follow their work and compare the audio

taping results with their sequences of figure manipulation).