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| Abstract : Perpustakaan Tuanku Bainun |
| The purpose of this study was to assess a hierarchy of Malaysian pre-service secondary mathematics teachers_ algebraic thinking in using equation. The content domains incorporated in this framework were linear pattern (pictorial), direct variation, concept of function, arithmetic sequence and inverse variation. The SOLO model was used for coding the pre-service secondary mathematics teachers_ responses and the Rasch model (rating scale analysis) was used to clarify the construction of the hierarchy. The participants of this study consisted of 120 pre-service secondary mathematics teachers who were first year and second year students in a local university. They were given a pencil-and-paper test. The test comprised ten superitems. Results of the study revealed that seven different levels of algebraic thinking were identified, namely prestructural, unistructural, multistructural, lower relational, relational, upper relational and extended abstract. Results of the study also indicated that 57.5% of the pre-service secondary mathematics teachers performed at least at the lower relational level (algebraic thinking level), 42.5% of them performed at the multistructural level and below (pre-algebraic thinking level). The results provided evidence of the significance of the SOLO model in assessing algebraic thinking amongst the pre-service secondary mathematics teacher.
Keywords algebraic thinking, assessing, equation, Rasch Model, SOLO Model, preservice secondary mathematics teacher |
| References |
Adams, R. J., & Khoo, S. T. (1996). Quest: Interactive item analysis system. Version 2.1[computer software]. Melbourne, Australia: Australian Council for Educational Research.
Ahuja, O. P. (1998). Importance of algebraic thinking for pre-service primary teachers. The Mathematics Educators, 3(1), 72 ‒ 92.
Australian Education Council (1991). A national statement on mathematics for Australian school. Cariton, VIC: Curriculum.
Aoyama, K. (2007). Investigating a hierarchy of pre-service secondary mathematics teachers’ interpretation of graphs. International Electronic Journal of Mathematics Education, 2(3), 298 ‒ 318.
Blanton & Kaput (2003). Developing Elementary teachers’ algebra ‘Eyes and Ears’understanding characteristics of professional development that promote generative and self-sustaining change in teacher practice. Retrieved May 11 2009, from http://www.scps. k12.fl.us/scctm/TextFiles/pdf.
Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome). New York: Academic Press.
Biggs, J. B., & Collis, K.F. (1989). Towards a model of school-based curriculum development and assessment using the SOLO taxonomy. Australian Journal of Education, 33(2), 151 ‒ 163.
Bond, T. G., & Fox, C. M. (2001). Applying the Rasch model: Fundamental measurement in the human sciences. New Jersey: Lawrence Erlbaum Associates.
Bradley, K. D., Cunningham, J. D. & Gilman, R. (2006). Using the Rasch Rating Scale Model to test the fit and function of MSLSS scale across groups. Retrieved May 9 2009, from http://www.uky.edu/~kdbrad2/MSLSS-AeRA2006.pdf.
Bradley, K. D. & Sampson, S. O. (2005). Improving data collection through Raschmeasurement: A continuing study of teacher supply and demand. Retrieved May 9 2009, from www.uky. edu/~kbrad2/AERASupplyDemandHandout.pdf.
Burnett, P. C. (1999). Assessing the structure of learning outcome from counseling using the SOLO Taxonomy: An exploratory study. British Journal of Guidance & Counseling, 7(1), 567‒580.
Callingham, R. & Pegg, J. (2009). Using developmental frameworks to support curriculum outcomes. Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle: MERGA.
Chan,C. C., Tsui, M. S., & Chan, M. Y. C. (2002). Applying the Structure of the Observed Learning Outcomes (SOLO) Taxonomy on student’s learning outcomes: An empirical study. Assessment and Evaluation in Higher Education, 27(6), 511 ‒ 528.
Cheah, C. T., & Malone, J. A. (1996). Diagnosing misconceptions in elementary algebra. Journal of Science and Mathematics Education in South East Asia, 14(1), 61 ‒ 68.
Chick, H. L. (1988). Student responses to polynomial problem in the light of the SOLO taxonomy. Australian Senior Mathematics Journal, 2(2), 91 ‒ 110.
Chick, H. L. (1998). Cognition in the formal modes: Research mathematics and the SOLO Taxonomy. Mathematics Education Research Journal, 10(2), 4 ‒ 26.
Collis, K. F., Romberg, T. A., & Jurdak, M. E. (1986). A technique for assessing mathematical problem-solving ability. Journal for Research in Mathematics Education, 17(3), 206 ‒ 221.
Fernandez, M. L., & Anhalt, C. O. (2001). Transition toward algebra. Mathematics Teaching in the Middle School, 7(4), 236 ‒ 242.
Kuchemann, D. (1981). Algebra. In K. Hart (Ed.), Children’s understanding of mathematic: 11 ‒ 16 (pp 102 ‒119). London: Murray.
Lake, D. (1999). Helping students to go SOLO: Teaching critical numeracy in the biological science, Journal of Biological Education, 33(4), 191‒199.
Lam, P., & Foong, Y. Y. (1998). Assessment of mathematics structure of learning outcome proficiency attainment level using hierarchical items in testlets. Educational Research Quarterly, 27(2), 3 ‒ 15.
Levins, L. (1997). Assessment of students’ outcome using a theoretical framework. Australian Science Teachers’ Journal, 43(1), 56-60.
Lim, H. L. (2007). Penggunaan Model SOLO dalam penilaian kebolehan penyelesaianpersamaan linear pelajar Tingkatan Empat. Unpublished PhD Thesis. University of Malaya .
Ministry of Education. (2000). Kurikulum Bersepadu Sekolah Menengah: Huraian Sukatan Matematik Tingkatan Empat. Kuala Lumpur: Pusat Perkembangan Kurikulum.
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston VA: Author.
Orton, A., & Orton, J. (1994). Pre-service secondary mathematics teachers’ perception and use of pattern and generalization. Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education, Lisbon: University of Lisbon (pp. 404‒414).
Panizzon, D., Callingham, R., Wright, T. & Pegg, J. (2007). Shifting sands: Using SOLO to promote assessment for learning with secondary mathematics and science teachers. In P. Jeffery (Ed.), Proceedings of the AARE annual conference, Fremantle. Retrieved from http://www.aare.edu.au/07pap/pan07110.pdf
Pegg, J. (2001). Fundamental cycles in learning algebra. Center for Cognition Research inLearning and Teaching, University of New England Research Retrieved September 7, 2003, from http://www.edfac.unimelb.edu.au.
Reading, C. (1999). Understanding data tabulation and representation. Centre for Cognition Research in Learning and Teaching, University of New England. Retrieved October 1, 2003, from http://fehps.une.edu.au./f/s/curric/cReading/
Stephens, A. C. (2006). Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Education, 9, 249‒278.
Swafford, J. O., & Langrall, C. W. (2000). Grade 6 pre-service secondary mathematics teachers’ preinstructional use of equation to describe the represent problem, Journal for Research in Mathematics Education, 31(1), 89‒112.
Teng, S. L. (2002). Konsepsi alternatif dalam persamaan linear di kalangan pelajar Tingkatan Empat. (Unpublished master’s dissertation). Universiti Sains Malaysia.
Vallecillos, A., & Moreno, A. (2002). Framework for instruction and assessment on elementary inferential statistics thinking. Proceedings of the Second International Conference on the Teaching of Mathematics, Greece (pp. 1‒9).
Watson, J., Chick, H., & Collis, K. (1988). Applying the SOLO taxonomy to error on area problems. Proceedings of the 12th Biennial Conference of the Australian Association of Mathematics Teachers, Newcastle (pp. 260-281).
Wilson, L.D., & Chavarria, S. (1993). Superitem test as a classroom assessment tool. In N.L. Webb & F. A. Arthur (Eds.), Assessment in the mathematics classroom (pp. 135 ‒ 142). Virginia: NCTM.
Wilson, M., & Iventosch, L. (1988). Using the partial credit model to investigate responses to tructured subtest. Applied Measurement in Education, 1(4), 319 ‒ 334.
Wongyai, P., & Kamol, N. (2004). A framework in characterizing lower secondary school pre-service secondary mathematics teachers’ algebraic thinking. Retrieved December 23, 2004, from http://www.icme- organisers.dk/tsg09/PiyavadeeWongyai.pdf
Wright, B. D., & Masters, G. N. (1982). Rating scale analysis. Chicago: MESA Press.
Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379 ‒ 402. |
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