Penggunaan blok algebra dalam membantu pembelajaran teknik penyempurnaan kuasa dua pelajar: Sebuah kertas konsep
List of Authors
  • Chiu Yiew Kian , Muhammad Sofwan Mahmud

Keyword
  • Penyempurnaan kuasa dua, konsep abstrak, persamaan kuadratik, blok algebra

Abstract
  • Penyempurnaan kuasa dua merupakan satu kaedah pemfaktoran yang penting dalam proses penyelesaian persamaan kuadratik. Kaedah ini dapat membantu pelajar memahami penyelesaian masalah berkaitan persamaan kuadratik dengan menggunakan kaedah pemfaktoran. Justeru, para guru memainkan peranan bagi memastikan pelajar dapat menguasai sepenuhnya teknik penyempurnaan kuasa dua dengan menggunakan bahan dan kaedah yang bersesuaian dengan kebolehan pelajar. Kertas ini akan mengupas tinjauan literatur berkaitan masalah yang dihadapi oleh pelajar semasa menggunakan teknik penyempurnaan kuasa dua. Selain itu, kertas ini juga turut mengenal pasti apakah persepsi pelajar terhadap pembelajaran teknik penyempurnaan kuasa dua. Justeru pengkaji telah merumuskan bahawa terdapat 2 perkara yang tidak diberi perhatian iaitu; (1) Apakah jenis miskonsepsi yang dialami oleh pelajar semasa menggunakan teknik penyempurnaan kuasa dua? (2) Apakah bahan yang boleh digunakan oleh guru semasa menerangkan konsep abstrak penyempurnaan kuasa dua? Miskonsepsi yang dialami oleh pelajar dalam penyempurnaan kuasa dua menyebabkan pelajar tidak dapat menukar persamaan kuadratik kepada bentuk am penyempurnaan kuasa dua serta tidak dapat membuat keputusan dalam menggunakan kaedah yang betul dalam menyelesaikan persamaan kuadratik.

Reference
  • 1. Ahmed, A., Clark-jeavons, A., & Oldknow, A. (2016). How can teaching aids improve the quality of mathematics education. Educational Studies in Mathematics, 56(2), 313–328. Retrieved from https://doi.org/10.1023/B:EDUC.0000040412.39121.e0

    2. Alhassan, M. N., & Agyei, D. D. (2020). Examining Colleges of Education Mathematics Tutors’ Conceptions in Teaching Completing the Square in Ghana. International Journal of Scientific and Research Publications (IJSRP), 10(3), 253–261. Retrieved from https://doi.org/10.29322/ijsrp.10.03.2020.p9927

    3. Ali, M., Mutawah, A., Thomas, R., Mahmoud, E. Y., & Fateel, M. (2019). Conceptual understanding , procedural knowledge and problem-solving skills in mathematics : High school graduates work analysis and standpoints. International Journal of Education and Practice, 7(3), 258–273. Retrieved from https://doi.org/10.18488/journal.61.2019.73.258.273

    4. Borji, V., Radmehr, F., & Font, V. (2019). The impact of procedural and conceptual teaching on students’ mathematical performance over time. International Journal of Mathematical Education in Science and Technology, 52(3), 404–426. Retrieved from https://doi.org/10.1080/0020739X.2019.1688404

    5. Canobi, K. H. (2009). Procedure interactions in children ’ s addition and subtraction. Journal of Experimental Child Psychology, 102(2), 131–149. Retrieved from https://doi.org/10.1016/j.jecp.2008.07.008

    6. Didis, M. G., & Erbas, A. K. (2015). Performance and difficulties of students in formulating and solving quadratic equations with one unknown. Educational Sciences: Theory & Practice, 15(4), 1137–1150. Retrieved from https://doi.org/10.12738/estp.2015.4.2743

    7. Fachrudin, A. D., Putri, R. I. I., & Darmawijoyo. (2014). Building students’ understanding of quadratic equation concept using naïve geometry. Journal on Mathematics Education, 5(2), 192–202. Retrieved from https://doi.org/10.22342/jme.5.2.1502.191-202

    8. Hagan, J. E., Amoaddai, S., & Lawer, V. T. (2020). Students ’ Perception towards Mathematics and Its Effects on Academic Performance. Asian Journal of Education and Social Studies, 8(1), 8–14. Retrieved from https://doi.org/10.9734/AJESS/2020/v8i130210

    9. Johnson, A. R., Baroody, A. J., Baroody, J., & Feil, Y. (2012). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38(2), 115–131. Retrieved from https://doi.org/10.2307/30034952

    10. Kabar, M. G. D. (2018). Secondary School Students’ Conception of Quadratic Equations with One Unknown. International Journal for Mathematics Teaching and Learning, 19(1), 112–129. Retrieved from https://eric.ed.gov/?q=factoring&id=EJ1189630

    11. Katz, V. (2001). Using History to teach Mathematics An International Perspective. ZDM - International Journal on Mathematics Education, 33(5), 137–138.

    12. Kementerian Pendidikan Malaysia. (2019). Buku Teks Matematik Tambahan Tingkatan 4 KSSM.

    13. Krantz, S. G. (2006). An episodic history of mathematics: Mathematical culture through problem solving. United States: The Mathematical Association of America.

    14. Maciejewski, W., & Star, J. R. (2019). Justifications for choices made in procedures. Educational Studies in Mathematics, 101(3), 325–340. Retrieved from https://doi.org/10.1007/s10649-019-09886-7

    15. MacLellan, E. (2005). Conceptual learning: The priority for higher education. British Journal of Educational Studies, 53(2), 129–147. Retrieved from https://doi.org/10.1111/j.1467-8527.2005.00287.x

    16. Makgakga, S. (2014). Errors and misconceptions in solving quadratic. Retrieved from http://www.amesa.org.za/AMESA2014/Proceedings/papers/Short Paper/4. Sello Makgakga -AMESAPAPER2014final.pdf

    17. Makonye, J. P., & Matuku, O. (2017). Exploring learner errors in solving quadratic equations. International Journal of Educational Sciences, 12(1), 7–15. Retrieved from https://doi.org/10.1080/09751122.2016.11890407

    18. Nur Fadhilah, Amir & M.Yusran, Z. (2019). Mistake analysis of class x students in Handayani Sungguminasa high school in completing the problems of equation and equality equation square. Journal of Mathematics Education, 4(1), 33–42. Retrieved from https://doi.org/10.31327/jomedu.v4i1.877

    19. Putri, R. I. I., Kohar, A. W., Widadah, S., & Fachrudin, A. D. (2018). Developing a Local Instruction Theory for Learning the Concept of Solving Quadratic Equation Using Babylonian Approach. Journal of Physics: Conference Series, 11(8), 1–6. Retrieved from https://doi.org/10.1088/1742-6596/1108/1/012069

    20. Radmehr, F., & Drake, M. (2017). Exploring students’ mathematical performance, metacognitive experiences and skills in relation to fundamental theorem of calculus. International Journal of Mathematical Education in Science and Technology, 52(3), 404–426. Retrieved from https://doi.org/10.1080/0020739X.2017.1305129

    21. Reid O’connor, B., & Norton, S. (2019). Investigating students’ mathematical difficulties with quadratic equations. Proceedings of the 39th Annual Conference of the Mathematics Education Research Group of Australasia, 552–559.

    22. Rillero, P. (2016). Deep conceptual learning in science and mathematics: Perspectives of teachers and administrators. Electronic Journal of Science Education, 20(2), 14–31.

    23. Schneider, M., & Rittle-johnson, B. (2015). Developing conceptual and procedural Knowledge of mathematics. In R. C. Kadosh & A. Dowker (Eds.), Oxford library of psychology (pp. 1–23). New York: Oxford University Press. Retrieved from https://doi.org/10.1093/oxfordhb/9780199642342.013.014

    24. Skemp, R. R. (1987). The physcology of learning mathematics (Expanded A). Hillsdale, New Jersey: Lawrence Erlbaum Associates.

    25. Smith, M., & Bill, V. (2018). Promoting a conceptual understanding of mathematics. MAthematics Teaching In The Middle School, 24(1), 36–43.

    26. Star, J. R. (2015). Procedural knowledge reconceptualizing. Journal for Research in Matematics Education, 36(5), 404–411. Retrieved from https://doi.org/10.2307/30034943

    27. Zeeuw, A. De, Craig, T., & You, H. S. (2013). Assessing Conceptual Understanding in Mathematics. In Frontiers in Education Conference (pp. 10–13). Retrieved from https://doi.org/10.1109/FIE.2013.6685135