International Journal of Scientific & Technology Research

Home About Us Scope Editorial Board Blog/Latest News Contact Us
(Re-evaluation in-progress)

IJSTR >> Volume 9 - Issue 4, April 2020 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Flexibility In Mathematics: Case Of Open-Ended Graphing Task In College Algebra

[Full Text]



Faradillah Haryani



Flexibility, understanding, connection, conceptual understanding, college algebra, graphing task, analysis, discussion



This study aims to analyze the flexibility in Mathematics seen from the students work in working with graphing task in the College Algebra course. Flexibility is one of important aspects in problem solving which builds capability to connect the existing knowledge with the previous knowledge by extracting the information needed to be used in solving the problem. This connection will build the robust conceptual understanding. Researcher starts to routinize the flexibility in the teaching process by emphasizing the use of discussion, exploration, and analysis to train students see the specific information among concepts. Researcher also used flexible type questions to routinize the reversibility thought of students. After the teaching process, to assess the flexibility performance of students, researcher gives 4 open-ended graphing questions with different number of competences covered. Interview is also conducted for further investigation. The results showed that students are successfully developed their flexibility in Mathematics regardless their level of Mathematical ability. Their conceptual understanding is also improved, justified by the ability to give the reason of every answer they have made. However, the flexibility performance of students gets weaker when working with more linked competences in a question.



[1] T. P. Hiebert, J., & Carpenter, Learning and teaching with understanding. New York: Macmillan Publishing Company, 1992.
[2] Steven Todd Flanders, “Investigating Flexibility, Reversibility, and Multiple Representations in A Calculus Environment,” UNIVERSITY OF PITTSBURGH, 2014.
[3] V. . Krutetskii, The psychology of mathematical abilities in schoolchildren. University of Chicago press, 1976.
[4] B. Rittle-johnson and J. R. Star, “Does Comparing Solution Methods Facilitate Conceptual and Procedural Knowledge ? An Experimental Study on Learning to Solve Equations Does Comparing Solution Methods Facilitate Conceptual and Procedural Knowledge ? An Experimental Study on Learning to Solve Equations,” no. August 2007, 2014.
[5] Y. Yazgan, E. Faculty, and C. Arslan, “Common and flexible use of mathematical non routine problem solving strategies,” 12th Int. Congr. Math. Educ., no. January 2015, pp. 3044–3052, 2012.
[6] B. J. Dougherty, D. P. Bryant, B. R. Bryant, R. L. Darrough, and K. H. Pfannenstiel, “Developing Concepts and Generalizations to Build Algebraic Thinking: The Reversibility, Flexibility, and Generalization Approach,” Interv. Sch. Clin., vol. 50, no. 5, pp. 273–281, 2015.
[7] L. Xu, R. De Liu, J. R. Star, J. Wang, Y. Liu, and R. Zhen, “Measures of potential flexibility and practical flexibility in equation solving,” Front. Psychol., vol. 8, no. AUG, pp. 1–13, 2017.
[8] Ann M. Heirdsfield, “Flexible mental computation: What about accuracy?,” Proc. 26th Conf. Int. Gr. Psychol. Math. Educ., vol. 3, pp. 89–96, 2002.
[9] A. J. Baroody and A. Dowker, Eds., The development of arithmetic concepts and skills: Constructing adaptive expertise. Mahwah, NJ, US: Lawrence Erlbaum Associates Publishers, 2003.
[10] M. Schneider, B. Rittle-Johnson, and J. R. Star, “Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge.,” Dev. Psychol., vol. 47, no. 6, pp. 1525–1538, Nov. 2011.
[11] L. Verschaffel, J. Torbeyns, B. De Smedt, K. Luwel, and W. Van Dooren, “Strategy flexibility in children with low achievement in mathematics.,” Educational and Child Psychology, vol. 24, no. 2. British Psychological Society, Verschaffel, Lieven: Centre for Instructional Psychology and Technology, Katholieke Universiteit Leuven, Vesaliusstraat 2, Leuven, Belgium, 3000, lieven.verschaffel@ped.kuleuven.be, pp. 16–27, 2007.
[12] L. B. Warner, L. J. Alcock, J. Coppolo Joseph, and G. E. Davis, “How Does Flexible Mathematical Thinking Contribute To the Growth of Understanding?,” Proc. 27th Conf. Int. Gr. Psychol. nMathematics Educ. held jointly with 25th Conf. PME-NA, vol. 4, pp. 371–378, 2003.
[13] L. Akgün, T. Işleyen, E. Tatar, Y. Soylu, and A. Duru, “Comprehension test in calculus course,” Procedia - Soc. Behav. Sci., vol. 2, no. 2, pp. 1527–1531, 2010.
[14] J. Van De Walle , J., Karp, K., & Bay-Williams, Elementary and middle school mathematics: Teaching developmentally, 8th ed. Pearson, 2012.
[15] G. P. Wiggins and J. Mctighe, “The Understanding by Design Handbook,” no. May, pp. 36–42, 1999.