Vol. 1(2) SEP 2011 - SAVAP International

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Academic Research International ISSN: 2223-9553 Volume 1, Issue 2, September 2011 course was offered to B.Sc.Ed. program students who intended to major or minor in mathematics. The researchers had selected four B.Sc.Ed. program students who majored in mathematics, and four B.Sc.Ed. program students who minored in mathematics for the purpose of this study. Each PSSMT was given a pseudonym, namely Beng, Liana, Mazlan, Patrick, Roslina, Suhana, Tan, and Usha, in order to protect the anonymity of all interviewees. The brief background information about the subjects is shown in Table 1. Table 1. Subjects’ Ethnicity, Gender, Age, Major, Minor, and CGPA Subject Ethnicity Gender Age Major Minor CGPA Usha Indian Female (21, 9) Mathematics Biology 2.92 Mazlan Malay Male (21, 8) Mathematics Chemistry 2.70 Patrick Bidayuh Male (21, 7) Mathematics Chemistry 3.04 Beng Chinese Female (22, 9) Mathematics Physics 3.82 Roslina Malay Female (21, 8) Biology Mathematics 3.15 Liana Malay Female (21, 5) Chemistry Mathematics 2.77 Tan Chinese Male (22, 7) Chemistry Mathematics 3.69 Suhana Malay Female (20, 10) Physics Mathematics 2.52 Instrumentation Eight types of interview tasks were devised for this study. This paper reports only the responses of the subjects on Task 6.1 (see Appendix A). In Task 6.1, subjects were required to help his or her student to calculate the perimeter and area of the given diagram (Diagram 1) that involved composite figure, namely rectangle and parallelogram/triangle. The objective of this task was to determine the subjects' procedural knowledge for calculating perimeter and area for the composite figure. Task 6.1 was used to determine the subjects’ linguistic knowledge of standard units of perimeter and area measurement by determining whether the subject use the correct standard units of measurement for perimeter (cm) and area (cm 2 ) when they write the answers for these measurements. Task 6.1 was also used to determine the subjects’ strategic knowledge for checking the correctness of their answers for perimeter as well as area. Task 6.1 was used to determine the subjects’ ethical knowledge by ascertaining whether the subjects write units of measurement upon completing a task. This task was also used to ascertain whether the subjects check the correctness of their answers. Data Collection Data for this study was collected using clinical interview technique. In the present study, materials collected for analysis consisted of audiotapes and videotapes of clinical interviews, subject's notes and drawings, and researcher’s notes during the interviews. The audiotapes and videotapes were verbatim transcribed into written form and the transcriptions were the raw data for this study. The transcriptions include verbal and nonverbal interaction between researcher and subject. Data Analysis The data analysis process encompassed four levels. At level one, the audio and video recording of the clinical interview were verbatim transcribed into written form. The transcription included the interaction between the researcher and the subject during the interviews as well as the subject's Copyright © 2011 SAVAP International www.savap.org.pk www.journals.savap.org.pk 278
Academic Research International ISSN: 2223-9553 Volume 1, Issue 2, September 2011 nonverbal behaviors. At level two, raw data in the forms of transcription were coded, categorized, and analyzed according to specific themes to produce protocol related to the description of subjects’ subject matter knowledge of calculating perimeter and area for the composite figure. At level three, case study for each subject was constructed based on information from the written protocol. At this level, analysis was carried out to describe each subject's behaviors in solving the task. At level four, cross-case analysis was conducted. The analysis aimed to identify pattern of responses of subject matter knowledge of calculating perimeter and area for the composite figure held by the subjects. Based on this pattern of responses, preservice teachers' subject matter knowledge of calculating perimeter and area for the composite figure were summarized. FINDINGS OF THE STUDY Procedural Knowledge Finding of the study suggests that seven of the PSSMTs, namely Beng, Liana, Mazlan, Patrick, Roslina, Suhana, and Usha, have successfully calculated the perimeter of Diagram 1 as 104 cm. Table 2 reveals PSSMTs who have successfully and unsuccessfully calculated the perimeter of Diagram 1. Table 2. PSSMTs who Have Successfully and Unsuccessfully Calculated the Perimeter of Diagram 1 Calculating the perimeter of Diagram 1 Successful Unsuccessful PSSMTs Beng, Liana, Mazlan, Patrick, Roslina, Suhana, Usha Tan Of the seven PSSMTs who have successfully calculated the perimeter of Diagram 1, five of them, namely Beng, Mazlan, Patrick, Roslina and Usha, used the list all-and-sum algorithm to calculate the perimeter of the diagram. They listed all the length of sides that surrounded the diagram and then summed them up to get the perimeter of the diagram as 104 cm. Table 3 exhibits the algorithms used by PSSMTs to calculate the perimeter of Diagram 1. The other two PSSMTs, namely Liana and Suhana, used the doubling-and-sum algorithm to calculate the perimeter of the diagram. They doubled the length of sides UP, PQ, and QR and then summed them up to get the perimeter of the diagram as 104 cm. Table 3. The Algorithms Used by PSSMTs to Calculate the Perimeter of Diagram 1 Algorithms used to calculate the perimeter of Diagram 1 List all-and-sum Doubling-and-sum PSSMTs Beng, Mazlan, Patrick, Roslina, Tan, Usha Liana, Suhana Only one PSSMT, namely Tan, have unsuccessfully calculated the perimeter of Diagram 1. Tan mentally cut the triangle TRS of Diagram 1 and pasted it next to the triangle TQR of Diagram 1 so that it formed a rectangle (“TQSR”) with the dimension of 15 cm by 8 cm. He used the list all-andsum algorithm to calculate the perimeter of the diagram, He listed all the length of sides that surrounded the “long” rectangle and then summed them up to get the perimeter of the diagram as 86 cm (the correct answer should be 104 cm). Tan did not know that the “cut and paste” transformation does not conserve the perimeter of a diagram. Thus, he incorrectly calculated the perimeter of the diagram as 86 cm based on the length of sides that surrounded the “long” rectangle formed (20 + 8 + 15 + 20 + 8 + 15) and not based on the length of sides that surrounded Diagram 1 (20 + 17 + 15 + 20 + 17 + 15 = 104). Finding of the study suggests that six of the PSSMTs, namely Beng, Liana, Patrick, Roslina, Suhana, and Tan, have successfully calculated the area of Diagram 1 as 420 cm 2 . Table 4 shows PSSMTs who have successfully and unsuccessfully calculated the area of Diagram 1. Copyright © 2011 SAVAP International www.savap.org.pk www.journals.savap.org.pk 279
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