### PRE-SERVICE SECONDARY MATHEMATICS TEACHERS’ UNDERSTANDING OF ABSOLUTE VALUE

**Tian Abdul Aziz**, Universitas Muhammadiyah Prof. DR. HAMKA, Indonesia

**Supiat Supiat**, Universitas Muhammadiyah Prof. DR. HAMKA

**Yohanes Soenarto**, Universitas Muhammadiyah Prof. DR. HAMKA

#### Abstract

This study aims to give a comprehensive account of pre-service secondary mathematics teachers’ understanding of absolute value. Thirty two-item absolute value understanding test was developed and administered to thirty-eight students attending mathematics education department at one private university in Jakarta City, Indonesia. Five of them were selected purposively and interviewed to gain deep information and confirm their written responses in the test. We find that most participants struggled with the absolute value task. There are inconsistencies of the definition of absolute value expressed by them. Besides, typical mistakes made are: (a) removal of absolute value bars; (b) focus heavily on rules; (c) conversion of absolute value bars to parentheses; (d) exclusion of number inside absolute value bars; (e) poor algebraic manipulation; and (f) inability to draw absolute value graph. Based on the findings, the most common cause of mistakes made by the participants is didactical contract in mathematics teaching and learning. Limitation and implications of the study are presented.

#### Keywords

#### Full Text:

PDF#### References

Almog, N., & Ilany, B. S. (2012). Absolute value inequalities: High school students’ solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364. doi: 10.1007/s10649-012-9404-z.

Aziz, T. A., & Kurniasih, M. D. (2019). External representation flexibility of domain and range of function. Journal on Mathematics Education, 10(1), 143–156. doi: 10.22342/jme.10.1.5257.143-156.

Aziz, T. A., Pramudiani, P., & Purnomo, Y. W. (2017). How do college students solve logarithm questions? International Journal on Emerging Mathematics Education, 1(1), 25–40. doi: 10.12928/ijeme.v1i1.5736.

Aziz, T. A., Pramudiani, P., & Purnomo, Y. W. (2018). Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views. Journal of Physics: Conference Series, 948(1), 12043. doi: 10.1088/1742-6596/948/1/012043.

Brousseau, G., Sarrazy, B., & Novotná, J. (2014). Didactic contract in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 153–159). Dordrecht: Springer Netherlands.

Çi̇ltaş, A., & Tatar, E. (2011). Diagnosing learning difficulties related to the equation and inequality that contain terms with absolute value. International Online Journal of Educational Sciences, 3(2), 461-473.

Elia, I., Özel, S., Gagatsis, A., Panaoura, A., & Özel, Z. E. Y. (2016). Students’ mathematical work on absolute value: focusing on conceptions, errors and obstacles. ZDM - Mathematics Education, 48(6), 895–907. doi: 10.1007/s11858-016-0780-1.

Ellis, M. W., & Bryson, J. L. (2011). A conceptual approach to absolute value equations and inequalities. Mathematics Teacher, 104(8), 592–598.

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. doi: 10.1080/0020739x.2013.790510.

Horak, V. M. (1994). Investigating absolute-value equations with the graphing calculator. Mathematics Teacher, 87(1), 9–11.

Konyalioglu, A. C., Aksu, Z., & Senel, E. O. (2012). The preference of visualization in teaching and learning absolute value. International Journal of Mathematical Education in Science and Technology, 43(5), 613–626. doi: 10.1080/0020739X.2011.633627.

Ponce, G. A. (2008). Using, seeing, feeling, and doing absolute value for deeper understanding. Mathematics Teaching in the Middle School, 14(4), 234–240.

Schneider, M. (2014). Epistemological obstacles in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 214–217). Dordrecht: Springer Netherlands.

Stupel, M., & Ben-Chaim, D. (2014). Absolute value equations – what can we learn from their graphical representation? International Journal of Mathematical Education in Science and Technology, 45(6), 923–928. doi: 10.1080/0020739X.2014.884646.

Taylor, S. E., & Mittag, K. C. (2015). Easy absolute values? Absolutely. Mathematics Teaching in the Middle School, 21(1), 49–52. doi: 10.5951/mathteacmiddscho.21.1.0049.

Wade, A. (2012). Teaching absolute value meaningfully. The Mathematics Teacher, 106(3), 192–198. doi: 10.5951/mathteacher.106.3.0192.

Wagster, L. W. (1986). Using number lines to solve difficult absolute-value problems. The Mathematics Teacher, 79(4), 260–263.

DOI: https://doi.org/10.21831/cp.v38i1.21945

### Refbacks

- There are currently no refbacks.

**Social Media:**

Jurnal Cakrawala Pendidikan by Lembaga Pengembangan dan Penjaminan Mutu Pendidikan UNY is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Based on a work at http://journal.uny.ac.id/index.php/cp/index.