Solving high school algebra problems using the bar method
Keywords:
algebra; mathematics education; mathematical instructionAbstract
The study focuses on the relevance of mathematical representations for solving algebra problems in secondary school, especially during the transition to abstract mathematics. The role of visual and algebraic representations in understanding and solving algebraic problems is examined. The methodology used included teaching with variation and the bar method, strategies that explore mathematical patterns. Some students had difficulty with the bar method due to resistance to drawing and representing quantity relationships. However, for others, this method was useful, providing a visual framework for understanding equality and recognizing relationships between quantities in the problem. The study underscores the importance of mathematical representations and the value of pedagogical strategies that encourage variation and the use of visual techniques in mathematics instruction.
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References
Baldor, A. (2019). Álgebra. Patria.
Baysal, E., y Sevinc, S. (2022). The role of the Singapore bar model in reducing students’ errors on algebra word problems. International Journal of Mathematical Education in Science and Technology, 53(2), 289–310. https://doi.org/10.1080/0020739X.2021.1944683
Gu, E., Huang, R. y Gu, L. (2017). Theory And Development Of Teaching Through Variation in Mathematics in China. En R. Huang y Y. Li (Eds.). Mathematics Teaching and Learning, (V 2, pp. 13–41). Springer. https://doi.org/10.1007/978-94-6300-782-5_2
Hiebert, J. y Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425. https://doi.org/10.3102/00028312030002393.
Hoven, J. y Garelick, B. (2007). Singapore math: Simple or Complex? Educational Leadership, 65(3), 28–31. https://www.researchgate.net/publication/228376108_Singapore_Math_Simple_or_Complex.
Jiang, C., Hwang, S. y Cai, J. (2014). Chinese and Singaporean sixth-grade students’ strategies for solving problems about speed. Educational Studies in Mathematics, 87, 27–50. https://link.springer.com/article/10.1007/s10649-014-9559-x.
Kaput, J. (1989). Linking representations in the symbol system of algebra. En S. Wagner y C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167-194). Routledge.
Kieran, C. (2022). The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions. ZDM Mathematics Education 54, 1131–1150. https://link.springer.com/article/10.1007/s11858-022-01435-6.
Marton, F. (2015). Necessary conditions of learning. Routledge.
Ng, S.F. y Lee, K.(2009). The Model Method: Singapore Children’s Tool for Representing and Solving Algebraic Word Problems. Journal for Research in Mathematics Education, 40(3), 282–313. https://doi.org/10.5951/jresematheduc.40.3.0282
Pérez Ariza, K. (2020). Una tipología de ejercicios para el tratamiento de la comprensión de problemas aritméticos verbales. LUZ, 19(3), 66–80. https://luz.uho.edu.cu/index.php/luz/article/view/1053.
Schifter, D., y Jo Russell, S. (2022). The centrality of student-generated representation in investigating generalizations about the operations. ZDM. Mathematics education,54, 1289–1288. https://doi.org/10.1007/s11858-022-01379-x.
Sevinc, S. y Lizano, C. (2022). Bar model method as a problem-solving heuristic: an investigation of two preservice teachers’ solution paths in problems involving ratio and percentage. Mathematics Education Research Journal, 36, 71-95. https://link.springer.com/article/10.1007/s13394-022-00427-9.
Thirunavukkarasu M. y Senthilnathan, S. (2017). Effectiveness of bar model in teaching algebra at secondary level. International Journal of Teacher Educational Research, 6(10-12), 34–43. https://www.researchgate.net/publication/322202385_Effectiveness_of_Bar_Model_in_Teaching_Algebra_at_Secondary_Level_EFFECTIVENESS_OF_BAR_MODEL_IN_TEACHING_ALGEBRA_AT_SECONDARY_LEVEL.
Tiangtrong, P. (2020). Using Bar Model Method to Solve Algebraic Problems: Word Problems, Linear Equations of One Variable and System of Linear Equations of Two Variables. Mathematics Journal, 65(700), 22–44. https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/207663.
Van Manen, M. (1990). Researching Lived Experience: Human Science for an Action Sensitive Pedagogy. State University of New York Press.
Watson, A. y Mason, J. (2009). Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making. Mathematical Thinking and Learning, 8(2), 91–111. https://doi.org/10.1207/s15327833mtl0802_1
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