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Pre-service Teachers’ Absolute Value Equations and Inequalities Solving Strategies and Errors

Year 2018, Volume: 10 , 163 - 167, 12.09.2018

Abstract

Many students in different grade levels face
difficulties while solving absolute value equations and inequalities. These
difficulties may be attributed to the strategies that the math teacher used in
solving absolute value equations and inequalities.
This study
investigated the strategies that pre-service teachers used and the errors they
made while solving absolute value equations and inequalities. Fifty-one
pre-service teachers enrolled in an introductory mathematics course
participated in this study.  Data were collected from a test that
consisted of four absolute value equations and inequalities. Participants were
asked to solve these absolute value equations and inequalities and show their
work. Participants’ errors while solving each absolute value equations and
inequalities were recorded. The results of the study indicated that many
pre-service teachers made few errors when solving absolute value equations and
inequalities. 

References

  • Almog, N., & Ilany, B.S. (2012). Absolute value inequalities: high school students’ solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364. Retrieved from https://link.springer.com/article/10.1007/s10649-012-9404-z#citeas Capraro, M. M., & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols?. Reading Psychology, 27(2–3), 147–164. Curtis, M. A. (2016). Solving Absolute Value Equations and Inequalities on a Number Line. Electronic Theses, Projects, and Dissertations. 411. Retrieved from http://scholarworks.lib.csusb.edu/etd/411 Dreyfus, T., & Hoch, M. (2004). Equations – a structural approach. Proceedings of the 28th Conference of the International Group of Psychology of Mathematics Education, Bergen, Norway, 1, 152-155. El-Shara, I, & Al-Abed, A. (2010). Errors Analysis of Solving Inequalities Among Mathematics Majors at the University of Jordan. Jordan Journal of Educational Science, 6(2), p 93-108. Gagatsis, A., & Panaoura, A. (2014). A Multidimensional Approach to Explore the Understanding of the Notion of Absolute Value. International Journal of Mathematical Education in Science and Technology, 45(2),159-173. Retrieved from https://www.learntechlib.org/p/168141/. Kieran, C. (2004). The equation / inequality connection in constructing meaning for inequality situations. Proceedings of the 28th Conference of the International Group of Psychology of Mathematics Education. Bergen, Norway, 1,143-147. Knuth, E., Stephens, A., McNeil, N., & Alibali, M. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37 (4), 297-312. Retrieved from http://www.region11mathandscience.org/archives/files/equality/Trainers/EqualSignJRMEKnuth.pdf Rittle-Johnson, B. & Alibali, M. 1999. Conceptual and procedural knowledge of mathematics: Does one lead to the other?. Journal of Educational Psychology, 91(1), 175–189. Serhan, D. (2015). Pre-service Teachers Linear Equation Solving Strategies & Errors. Global Journal of Mathematics, 2, 79-82. Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In J. Kilpatrick, W. B. Martin, and D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 219–233). Reston, VA: National Council of Teachers of Mathematics. Retrieved from http://www.psy.cmu.edu/~siegler/NCTM.pdf Star, J. R. (2005). Research Commentary: Reconceptualizing Procedural Knowledge. Journal for Research in Mathematics Education, 36 (5), 404-411. Thomaidis, Y., & Tzanakis, C. (2007). The notion of historical ‘parallelism’ revisited: Historical evolution and students’ conception of the order relation on the number line. Educational Studies in Mathematics, 66, 165–183. Tsamir, P., & Bazzini, L. (2004). Consistencies and inconsistencies in student’s solution to algebraic ‘single value’ inequalities. Mathematics Education Science Technology, 35(6), 793-812. Vaiyavutjamai, P., & Clements, M. A. (2006). Effects of classroom instruction on student performance on and understanding of, linear equation and linear inequalities. Mathematical Thinking and Learning, 8(2), 113-147. Wilhelmi, M. R., Godino, J. D., & Lacasta, E. (2007). Didactic effectiveness of mathematical definitions: The case of the absolute value. International Electronic Journal of Mathematics Education, 2 (2), 72-90.
Year 2018, Volume: 10 , 163 - 167, 12.09.2018

Abstract

References

  • Almog, N., & Ilany, B.S. (2012). Absolute value inequalities: high school students’ solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364. Retrieved from https://link.springer.com/article/10.1007/s10649-012-9404-z#citeas Capraro, M. M., & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols?. Reading Psychology, 27(2–3), 147–164. Curtis, M. A. (2016). Solving Absolute Value Equations and Inequalities on a Number Line. Electronic Theses, Projects, and Dissertations. 411. Retrieved from http://scholarworks.lib.csusb.edu/etd/411 Dreyfus, T., & Hoch, M. (2004). Equations – a structural approach. Proceedings of the 28th Conference of the International Group of Psychology of Mathematics Education, Bergen, Norway, 1, 152-155. El-Shara, I, & Al-Abed, A. (2010). Errors Analysis of Solving Inequalities Among Mathematics Majors at the University of Jordan. Jordan Journal of Educational Science, 6(2), p 93-108. Gagatsis, A., & Panaoura, A. (2014). A Multidimensional Approach to Explore the Understanding of the Notion of Absolute Value. International Journal of Mathematical Education in Science and Technology, 45(2),159-173. Retrieved from https://www.learntechlib.org/p/168141/. Kieran, C. (2004). The equation / inequality connection in constructing meaning for inequality situations. Proceedings of the 28th Conference of the International Group of Psychology of Mathematics Education. Bergen, Norway, 1,143-147. Knuth, E., Stephens, A., McNeil, N., & Alibali, M. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37 (4), 297-312. Retrieved from http://www.region11mathandscience.org/archives/files/equality/Trainers/EqualSignJRMEKnuth.pdf Rittle-Johnson, B. & Alibali, M. 1999. Conceptual and procedural knowledge of mathematics: Does one lead to the other?. Journal of Educational Psychology, 91(1), 175–189. Serhan, D. (2015). Pre-service Teachers Linear Equation Solving Strategies & Errors. Global Journal of Mathematics, 2, 79-82. Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In J. Kilpatrick, W. B. Martin, and D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 219–233). Reston, VA: National Council of Teachers of Mathematics. Retrieved from http://www.psy.cmu.edu/~siegler/NCTM.pdf Star, J. R. (2005). Research Commentary: Reconceptualizing Procedural Knowledge. Journal for Research in Mathematics Education, 36 (5), 404-411. Thomaidis, Y., & Tzanakis, C. (2007). The notion of historical ‘parallelism’ revisited: Historical evolution and students’ conception of the order relation on the number line. Educational Studies in Mathematics, 66, 165–183. Tsamir, P., & Bazzini, L. (2004). Consistencies and inconsistencies in student’s solution to algebraic ‘single value’ inequalities. Mathematics Education Science Technology, 35(6), 793-812. Vaiyavutjamai, P., & Clements, M. A. (2006). Effects of classroom instruction on student performance on and understanding of, linear equation and linear inequalities. Mathematical Thinking and Learning, 8(2), 113-147. Wilhelmi, M. R., Godino, J. D., & Lacasta, E. (2007). Didactic effectiveness of mathematical definitions: The case of the absolute value. International Electronic Journal of Mathematics Education, 2 (2), 72-90.
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Details

Primary Language English
Journal Section Articles
Authors

Derar Serhan This is me

Farouq Almeqdadı This is me

Publication Date September 12, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Serhan, D., & Almeqdadı, F. (2018). Pre-service Teachers’ Absolute Value Equations and Inequalities Solving Strategies and Errors. The Eurasia Proceedings of Educational and Social Sciences, 10, 163-167.