International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Assessing Algebraic Solving Ability Of Form Four Students
APA
In-text citation: (Lian & Idris, 2006)
Reference: Lian, L. H., & Idris, N. (2006). Assessing Algebraic Solving Ability Of Form Four Students. International Electronic Journal of Mathematics Education, 1(1), 55-76. https://doi.org/10.29333/iejme/171
AMA
In-text citation: (1), (2), (3), etc.
Reference: Lian LH, Idris N. Assessing Algebraic Solving Ability Of Form Four Students. INT ELECT J MATH ED. 2006;1(1), 55-76. https://doi.org/10.29333/iejme/171
Chicago
In-text citation: (Lian and Idris, 2006)
Reference: Lian, Lim Hooi, and Noraini Idris. "Assessing Algebraic Solving Ability Of Form Four Students". International Electronic Journal of Mathematics Education 2006 1 no. 1 (2006): 55-76. https://doi.org/10.29333/iejme/171
Harvard
In-text citation: (Lian and Idris, 2006)
Reference: Lian, L. H., and Idris, N. (2006). Assessing Algebraic Solving Ability Of Form Four Students. International Electronic Journal of Mathematics Education, 1(1), pp. 55-76. https://doi.org/10.29333/iejme/171
MLA
In-text citation: (Lian and Idris, 2006)
Reference: Lian, Lim Hooi et al. "Assessing Algebraic Solving Ability Of Form Four Students". International Electronic Journal of Mathematics Education, vol. 1, no. 1, 2006, pp. 55-76. https://doi.org/10.29333/iejme/171
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Lian LH, Idris N. Assessing Algebraic Solving Ability Of Form Four Students. INT ELECT J MATH ED. 2006;1(1):55-76. https://doi.org/10.29333/iejme/171

Abstract

Mathematics researchers generally agree that algebra is a tool for problem solving, a method of expressing relationship, analyzing and representing patterns, and exploring mathematical properties in a variety of problem situations. Thus, several mathematics researchers and educators have focused on investigating the introduction and the development of algebraic solving abilities. However research works on assessing students' algebraic solving ability is sparse in literature. The purpose of this study was to use the SOLO model as a theoretical framework for assessing Form Four students' algebraic solving abilities in using linear equation. The content domains incorporated in this framework were linear pattern (pictorial), direct variations, concepts of function and arithmetic sequence. This study was divided into two phases. In the first phase, students were given a pencil-and-paper test. The test comprised of eight superitems of four items each. Results were analyzed using a Partial Credit model. In the second phase, clinical interviews were conducted to seek the clarification of the students' algebraic solving processes. Results of the study indicated that 62% of the students have less than 50% probability of success at relational level. The majority of the students in this study could be classified into unistructural and multistructural. Generally, most of the students encountered difficulties in generalizing their arithmetic thinking through the use of algebraic symbols. The qualitative data analysis found that the high ability students seemed to be more able to seek the recurring linear pattern and identify the linear relationship between variables. They were able to coordinate all the information given in the question to form the algebraic expression and linear equations. Whereas, the low ability students showed an ability more on drawing and counting method. They lacked understanding of algebraic concepts to express the relationship between the variables. The results of this study provided evidence on the significance of SOLO model in assessing algebraic solving ability in the upper secondary school level.

References

  • 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., & Teller, R. (1987). The process of learning (2nd. Ed.). Hobart, USA: Academic Press.
  • Bishop, J. W., Otto, A. D. & Lubinski, C. A. (2001). Promoting algebraic reasoning using students' thinking. Mathematics Teaching in the Middle School, 6(9), 508-514.
  • Bond, T. G. & Fox, C. M. (2001). Applying the Rasch model: Fundamental measurement in the human sciences. New Jersey: Lawrence Erlbaum Associates.
  • Carey, D. A. (1992). Research into practice: Students' use of symbols'. Arithmetic Teacher, 40, 184-186.
  • 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.
  • Clements, M. A. (1999). The teaching and learning of algebra. Proceedings of The First Brunei Mathematics Teacher Conference, Negara Brunei, 31-46.
  • Collis, K. & Romberg, T. A. (1991). Assessment of mathematical performance: An analysis of open-ended test items. In W. C. Merlin and B. L. Eva (Eds.), Testing and Cognition (pp. 82-115). New Jersey: Prentice Hall.
  • 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.
  • Ferrucci, Beverly, J., Yeap, B. H., Carter, Jack, A. (2003). A modeling approach for enhancing problem solving in the middle grades. Mathematics Teaching in the Middle School, 8(9), 470-476.
  • Friedlander, A. & Hershkowitz, R. (1997). Reasoning with algebra. The Mathematics Teacher, 90(6), 442-447.
  • Heng, A. B. & Norbisham, H. (2002). Memperbaiki kemahiran menyelesaikan Persamaan linear satu anu di kalangan pelajar tingkatan empat. Prosiding Persidangan Kebangsaan Pendidikan Matematik, Universiti Pendidikan Sultan Idris, 95-102.
  • Herbert, K., & Brown, R. H. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3(6), 340-345.
  • 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.
  • Lee, L. (1996). An initiation into algebraic culture through generalization activities. In N. Bednarz, C. Kieran and L. Lee (Eds.), Approached to algebra: Perspective for research and teaching (pp. 87-106). Dordrecht: Kluwer.
  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran and L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Dordrecht: Kluwer.
  • Murphy, T. (1999). Changing assessment practices in an algebra class, or 'Will this be on the test?' Mathematics Teacher, 92(3), 247-249.
  • Ong, S. H. (2000). Understanding of algebraic notation and its relationship with cognitive development among Form Four students. Unpublished Master Dissertation. University of Malaya.
  • Orton, A. and Orton, J. (1994). Students' 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, 404-414.
  • Pegg, J. (2001). Fundmental cycles in learning algebra. Retrieved September 7, 2003, from University of New England, Center for Cognition research in Learning and Research Web site: http://www.edfac.unimelb.edu.au
  • Reading, C. (1998). Reactions to data: Students' understanding of data interpretation. Retrieved February 7, 2003, from http://cybers/c/M%20Documents/solo%20and%2020rash.htm.
  • Reading, C. (1999). Understanding data tabulation and representation. Retrieved October 1, 2003, from University of New England, Armidale, Centre for Cognition research in Learning and research Web site: http://fehps.une.edu.au./f/s/curric/c Reading/.
  • Romberg, T. A., Zarinnia, E. A. & Collis, K. F. (1990). A new world view of assessment in mathematics. In G. Kulm (Ed.), Assessing higher order thinking in mathematics (pp. 21-38). Washington: America Association for the Advancement of Science.
  • Stacey, K. & MacGregor, M. (1999a). Implications for mathematics education policy of research on algebra learning. Australian Journal of Education, 43(1), 58-71.
  • Stacey, K. ,& MacGregor, M. (1999b). Taking the algebraic thinking out of algebra. Mathematics Education Research Journal, 11(1), 25-38.
  • Swafford, J. O., & Langrall, C. W. ( 2000). Grade 6 students' preinstructional use of equation to describe the represent problem. Journal for Research in Mathematics Education, 31(1), 89-112.
  • Tall, D. & Razali, M. H. (1993). Diagnosing students' difficulties in learning mathematics. International Journal Mathematics Education Science, 24(2), 209-222.
  • Teng, S. L. (2002). Konsepsi alternatif dalam persamaan linear di kalangan pelajar Tingkatan Empat. Unpublished Master Dissertation. University Science of Malaysia.
  • Thornton, S. J. (2001). New approach to algebra. Mathematics Teaching in the Middle School, 6(7), 388-391.
  • 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, 1-9.
  • Watson, J., Chick, H., & Collis, K. (1988). Applying the SOLO taxonomy to error on area problems. Proceeding of the 12th Biennial Conference of the Australian Assossiation of Mathematics Teachers, Newcastle, 260-281.
  • Wilson, M., & Iventosch, L. (1988). Using the partial credit model to investigate responses to structured subtest. Applied Measurement in Education, 1(4), 319-334.
  • Wright, B. D. & Masters, G. N. (1982). Rating scale analysis. Chicago: MESA Press.

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