Vol. 1(2) SEP 2011 - SAVAP International

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Academic Research International ISSN: 2223-9553 Volume 1, Issue 2, September 2011 area formula of a rectangle where its length and width is 28 cm and 15 cm respectively. Tan got the area of the diagram as 420 cm 2 . Tan checked the answer for area using the partition-and-sum algorithm to calculate the area of the diagram. He partitioned Diagram 1 into rectangle PQTU and parallelogram QRST. Tan calculated the area of the rectangle using the area formula of a rectangle as 300 cm 2 . He calculated the area of the parallelogram using the area formula of a parallelogram as 120 cm 2 . Tan then summed them up to get the area of the diagram as 420 cm 2 . Tan explained that both methods gave the same answer, namely 420 cm 2 . Ethical Knowledge All the PSSMTs, namely Beng, Liana, Mazlan, Patrick, Roslina, Suhana, Tan, and Usha, wrote the measurement unit (without being probed), namely cm, for the answer of the perimeter of Diagram 1 that they have calculated. Likewise, all the PSSMTs, namely Beng, Liana, Mazlan, Patrick, Roslina, Suhana, Tan, and Usha, also wrote the measurement unit (without probed), namely cm 2 , for the answer of the area of Diagram 1 that they have calculated. All the PSSMTs have successfully calculated the perimeter of Diagram 1, except Tan. Neverthelsss, none of the PSSMTs checked the correctness of the answer for the perimeter. Tan might has spotted his mistake should he checked the answer for the perimeter of Diagram 1. When probed to check answer, then only all the PSSMTs suggested the strategies that they would use to check the answer for perimeter. All the PSSMTs have successfully calculated the area of Diagram 1, except Mazlan and Usha. Neverthelsss, none of the PSSMTs checked the correctness of the answer for the area. Mazlan and Usha might have spotted their mistake should they checked the answer for the area of Diagram 1. When probed to check answer, then only all the PSSMTs suggested the strategies that they would use to check the answer for area. CONCLUSION AND DISCUSSION Most of the PSSMTs in this study had adequate procedural knowledge of calculating perimeter and area of composite figure. For instance, all but one PSSMT had successfully calculated the perimeter of Diagram 1 in Task 6.1 as 104 cm. Similarly, six out of eight PSSMTs had successfully calculated the area of Diagram 1 in Task 6.1 as 420 cm 2 . Mazlan and Usha confused with the slanted side and the height of the parallelogram in Diagram 1 that they used the slanted side QR as the height (TR = 8 cm) of the parallelogram. Thus, Mazlan and Usha incorrectly calculated the area of the diagram as 555 cm 2 . This finding is concurs with Cavanagh (2008) and van de Walle (2007) who found that students tend to confuse with the slanted side (slanted height) and the height (perpendicular height) of a parallelogram. However, the finding of this study is in contrast with the findings of Baturo and Nason (1996). Baturo and Nason (1996) revealed that preservice primary school teachers in their study had inadequate procedural knowledge of calculating area of the given shapes. All the PSSMTs in this study understand the general measurement convention that perimeter and area is measured by linear units (such as mm, cm, m, km) and square units (such as mm 2 , cm 2 , m 2 , km 2 ) respectively. These findings are in contrast with the findings of previous studies (Baturo & Nason, 1996; Cavanagh, 2008; Tierney, Boyd, & Davis, 1990). Tierney, Boyd, and Davis (1990) noticed that many prospective primary school teachers from a teachers college in their study labelled the area measurements in linear units. Likewise, Baturo and Nason (1996) found that several preservice primary school teachers in their study wrote the calculated area measurement in linear unit such as 128 cm. Similarly, Cavanagh (2008) revealed that high school students in his study inappropriately labeled the length of sides in cm 2 or areas in cm on the written test. They did not understand the general measurement convention that length is measured in linear units while area is measured in square units. Copyright © 2011 SAVAP International www.savap.org.pk www.journals.savap.org.pk 282
Academic Research International ISSN: 2223-9553 Volume 1, Issue 2, September 2011 None of the PSSMTs in this study check the correctness of the answers for the perimeter and area of Diagram 1. Once getting an answer, they seemed to satisfy that the task was finished. When probed to check answer, then only they suggested the strategies that they would use to check the answers. This finding is in agreement with the finding of previous study (Baturo & Nason, 1996) which found that majority of the preservice primary school teachers in their study had to be prodded towards checking their answers. The PSSMTs in this study employed two types of strategies to verify their answers for calculating perimeter and area of composite figure in Tasks 6.1, namely recalculating strategy and alternative method. Recalculating strategy refers to strategy using the same method and calculates again while alternative method refers to method that was different from the original method. This finding is slightly contrast with the finding of previous study (Baturo & Nason, 1996) which found that most preservice primary school teachers in their study who attempted to verify their answers did so by recalculating strategy or using the inverse operation. They never think of using an alternative method to verify their answers. REFERENCES Aida Suraya, M. Y. (1996). Skim nombor perpuluhan bagi murid tahun lima sekolah rendah [Decimal numbers schemes of year five primary school pupils]. Unpublished doctoral thesis, University of Malaya, Kuala Lumpur. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special Journal of Teacher Education, 59 (5), 389-407. Baturo, A. & Nason, R. (1996). Students teachers' subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235-268. Cavanagh, M. (2008). Area measurement in year 7. Reflections, 33(1), 55-58. Retrieved September 27, 2008, from http://www.curriculum.support.education.nsw.gov.au/secondary/mathematics/assets/pdf/s4_teach_ide as/area/area_meas.pdf Chew, C. M. (2007). Form one students’ learning of solid geometry in a phase-based instructional environment using the Geometer’s Sketchpad. Unpublished doctoral thesis, University of Malaya, Kuala Lumpur. Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impacts. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan. Lim, H. L. (2007). Penggunaan model SOLO dalam penilaian kebolehan penyelesaian persamaan linear pelajar tingkatan empat [Assessing form four students’ linear equation solving ability by using SOLO model]. Unpublished doctoral thesis, University of Malaya, Kuala Lumpur. Merriam, S. B. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass. Ministry of Education Malaysia (2003). Integrated Curriculum for Secondary School: Curriculum Specification Mathematics Form 1. Kuala Lumpur: Curriculum Development Centre. Mosenthal, J. H., & Ball, D. L. (1992). Constructing new forms of teaching: Subject matter knowledge in inservice teacher education. Journal of Teacher Education, 43(5), 347-356. Nik Azis, N. P. (1996). Penghayatan matematik KBSR dan KBSM: Perkembangan professional [Appreciation of the integrated curriculum of primary and secondary school mathematics: Professional development]. Kuala Lumpur: Dewan Bahasa dan Pustaka. Copyright © 2011 SAVAP International www.savap.org.pk www.journals.savap.org.pk 283
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