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High School Students’ Achievement Of Solving Quadratic Equations

Year 2017, Volume: 6 Issue: 2, 447 - 467, 30.06.2017
https://doi.org/10.14686/buefad.277494

Abstract

The purpose of the present study was to investigate tenth grade
students` achievement of solving quadratic equations, to examine their tendency
of using different solution ways which are completing the square, factorization
and quadratic formula and to determine the errors made by students. 50 tenth
grade students of a high school in northern part of Turkey constituted the
sample of the study. In data collection, 9 open-ended questions related to
quadratic equations was carried out all students in the sample. Data were
analyzed through content analysis and also descriptive statistics: percentage
and frequency were presented. Besides, the errors made by students were showed
by quoting from their answers. The findings showed that most of the students
have difficulty in solving quadratic equations and make various errors. The
students’ errors in solving quadratic equation were tend to be due to their
weaknesses in mastering topics such as algebra, fractions, negative numbers,
the rules of quadratic equations` solution methods, calculation and algebraic
simplification. In addition to this, the findings revealed that students were
usually in tendency to use factorization in order to solve quadratic equations.

References

  • Baki, A. & Kartal, T. (2004). The characterization of high school students’ algebra knowledge in terms of conceptual and operational knowledge. The journal of Turkish Educational Science, 2(1), 27-46.
  • Chazan, D. (1996). Algebra for all students? Journal of Mathematical Behavior, 15, 455-477.
  • Dede,Y.,Yalın, H. ve Argün, Z. (2002). The errors and misconceptions of 8th grade students in learning of the concept of variable. UFBMEK 16-18 Eylül, ODTÜ, Ankara.
  • Didiş, M. G., Baş, S., & Erbas, A. K. (2011). Stevens’ reasoning in quadratic equations with one unknown. The Seventh Congress of the European Society for Research in Mathematics Education (CERME-7). University of Rzeszów: Poland. http://www.cerme7.univ.rzeszow.pl/WG/3/CERME7_WG3_Gozde.pdf.
  • Erbaş K., Çetinkaya, A. & Yaşar E. (2009). Student difficulties and misconceptions in solving simple linear equations, Education and Science, 34(152):44-59.
  • Ersoy, Y. & Erbaş, A., (2000). Student difficulties in algebra teaching: The views of teachers, IV. Science Education Conference Proceedings. Hacettepe University Education Faculty. Ankara.
  • Hacısalihoğlu, H.H., Mirasyedioğlu, Ş. & Akpınar, A. (2004). Elementary ilköğretim 6-7-8. grades mathematics teaching (First Edition), Ankara: Asil Publishing.
  • Jinfa, C. (1998). Exploring students' conceptual understanding of the averaging algorithm. School Science and Mathematics, 98(2), 93-98.
  • Kaput, J.J. (1999). Teaching and learning a new algebra with understanding. In E. Fennema & T. Romberg (ed.) Mathematics classrooms that promote understanding (p.133-155). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Katz, J. V. (1997). Algebra and its teaching: An historical survey. Journal of Mathematical Behavior, 16(1), 25-38.
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
  • Lima, R. N. (2008). Procedural embodiment and quadratic equations. Retrieved from: http://tsg.icme11.org/document/get/701.
  • MacGregor, M. (2004). Goals and content of an algebra curriculum for the compulsory years of schooling. In K.
  • Makonye, J. & Nhlankla, S. (2014). Exploring ‘Non-Science’ Grade 11 Learners’ Errors in Solving Quadratic Equations. Mediterranean Journal of Social Sciences, 5(27), 634-644.
  • McCormick, R. (1997). Conceptual and procedural knowledge. International Journal of Technology and Design Education, 2: 141-159.
  • MoNE, TTKB (2005). Secondary education curriculum and workbook (9, 10, 11 ve 12. Grades), Ankara.
  • Norasiah, A. (2002). Diagnosis jenis kesilapan dalam hierarki Pembelajaran Serentak. [ Error type diagnosis in learning simultaneous equation]. Master of Education Research Project, Universiti Kebangsaan Malaysia.
  • Parish, C.R. & Ludwig, H.J. (1994). Language, intellectual structures and common mathematical errors: a call for research. School Science and Mathematics. 94(5), 235-239.
  • Roslina, R. (1997). Keupayaan algebra asas pelajar tingkatan empat sekolah menengah kerajaan Daerah Hulu Langat.[The ability of Form Four students in basic algebra]. Master of Education Research Project. Universiti Kebangsaan Malaysia.
  • Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 1-10.
  • Schoenfeld, A. H. (1985). Mathematical Problem Solving, Academic Press, Orlando.
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36.
  • Snell, K. S. (1958). The solution of quadratic equations. The Mathematical Gazette, 42 (340), 101-103.
  • Stake, R. E. (1994). Case studies. In N. K. Denzin, & Y.S Lincoln (Eds.), Handbook of qualitative research (pp. 236-247). Thousand Oaks, CA: Sage.
  • Usiskin, Z. (1988). Conceptions of school algerba and uses of variables. The Ideas of Algebra K-12, 8-19.
  • Vaiyavutjamai, P., & Clements, M. A. (2006). Effects of classroom instruction on students’ understanding of quadratic equations. Mathematics Education Research Journal, 18(1), 47-77.
  • Yıldırım, A. & Şimşek, H. (2004). Qualitative research methods in social science. Ankara: Seçkin Publishing.
  • Zakaria, E. & Maat, S., M. (2010). The analysis of students` error in learning of quadratic equations. International Education Studies, 3(3) 105-110.

Lise Öğrencilerinin İkinci Dereceden Denklemleri Çözme Başarıları

Year 2017, Volume: 6 Issue: 2, 447 - 467, 30.06.2017
https://doi.org/10.14686/buefad.277494

Abstract

Bu çalışmanın amacı onuncu sınıf öğrencilerinin ikinci dereceden
denklemleri çözme başarılarını incelemek, tam kareye tamamlama, çarpanlara
ayırma, ikinci dereceden denklem formülü olmak üzere farklı çözüm yollarını
kullanma eğilimlerini araştırmak ve öğrenciler tarafından yapılan hataları
belirlemektir. Çalışmanın örneklemini Türkiye’nin kuzeyinde yer alan bir lisede
öğrenim gören 50 onuncu sınıf öğrencisi oluşturmaktadır. Veriler ikinci
dereceden denklemlere yönelik 9 sorunun örneklemdeki bütün öğrencilere
uygulanmasıyla elde edilmiştir. İçerik analizi yapılarak veriler analiz
edilmiş, yüzde ve frekans değerleri verilerek tanımlayıcı istatistiksel bilgi
sunulmuştur. Bunun yanı sıra, öğrencilerin cevaplarından alıntılar yapılarak
hata türleri gösterilmiştir. Bulgular, öğrencilerin ikinci dereceden
denklemleri çözmekte zorlandıklarını ve çözerken çeşitli hatalar yaptıklarını
göstermektedir. Öğrencilerin ikinci dereceden denklemleri çözerken yaptıkları
hatalar cebirsel ifadeler, kesirler, negatif sayılar, ikinci dereceden denklem
çözme kuralları, hesaplama ve cebirsel sadeleştirme gibi konuları tam
öğrenememesine dayalı zayıflığından kaynaklanmaktadır. Ayrıca, öğrencilerin
genellikle ikinci dereceden denklemleri çarpanlara ayırma yöntemiyle çözme
eğiliminde oldukları sonucuna ulaşılmıştır.

References

  • Baki, A. & Kartal, T. (2004). The characterization of high school students’ algebra knowledge in terms of conceptual and operational knowledge. The journal of Turkish Educational Science, 2(1), 27-46.
  • Chazan, D. (1996). Algebra for all students? Journal of Mathematical Behavior, 15, 455-477.
  • Dede,Y.,Yalın, H. ve Argün, Z. (2002). The errors and misconceptions of 8th grade students in learning of the concept of variable. UFBMEK 16-18 Eylül, ODTÜ, Ankara.
  • Didiş, M. G., Baş, S., & Erbas, A. K. (2011). Stevens’ reasoning in quadratic equations with one unknown. The Seventh Congress of the European Society for Research in Mathematics Education (CERME-7). University of Rzeszów: Poland. http://www.cerme7.univ.rzeszow.pl/WG/3/CERME7_WG3_Gozde.pdf.
  • Erbaş K., Çetinkaya, A. & Yaşar E. (2009). Student difficulties and misconceptions in solving simple linear equations, Education and Science, 34(152):44-59.
  • Ersoy, Y. & Erbaş, A., (2000). Student difficulties in algebra teaching: The views of teachers, IV. Science Education Conference Proceedings. Hacettepe University Education Faculty. Ankara.
  • Hacısalihoğlu, H.H., Mirasyedioğlu, Ş. & Akpınar, A. (2004). Elementary ilköğretim 6-7-8. grades mathematics teaching (First Edition), Ankara: Asil Publishing.
  • Jinfa, C. (1998). Exploring students' conceptual understanding of the averaging algorithm. School Science and Mathematics, 98(2), 93-98.
  • Kaput, J.J. (1999). Teaching and learning a new algebra with understanding. In E. Fennema & T. Romberg (ed.) Mathematics classrooms that promote understanding (p.133-155). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Katz, J. V. (1997). Algebra and its teaching: An historical survey. Journal of Mathematical Behavior, 16(1), 25-38.
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
  • Lima, R. N. (2008). Procedural embodiment and quadratic equations. Retrieved from: http://tsg.icme11.org/document/get/701.
  • MacGregor, M. (2004). Goals and content of an algebra curriculum for the compulsory years of schooling. In K.
  • Makonye, J. & Nhlankla, S. (2014). Exploring ‘Non-Science’ Grade 11 Learners’ Errors in Solving Quadratic Equations. Mediterranean Journal of Social Sciences, 5(27), 634-644.
  • McCormick, R. (1997). Conceptual and procedural knowledge. International Journal of Technology and Design Education, 2: 141-159.
  • MoNE, TTKB (2005). Secondary education curriculum and workbook (9, 10, 11 ve 12. Grades), Ankara.
  • Norasiah, A. (2002). Diagnosis jenis kesilapan dalam hierarki Pembelajaran Serentak. [ Error type diagnosis in learning simultaneous equation]. Master of Education Research Project, Universiti Kebangsaan Malaysia.
  • Parish, C.R. & Ludwig, H.J. (1994). Language, intellectual structures and common mathematical errors: a call for research. School Science and Mathematics. 94(5), 235-239.
  • Roslina, R. (1997). Keupayaan algebra asas pelajar tingkatan empat sekolah menengah kerajaan Daerah Hulu Langat.[The ability of Form Four students in basic algebra]. Master of Education Research Project. Universiti Kebangsaan Malaysia.
  • Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 1-10.
  • Schoenfeld, A. H. (1985). Mathematical Problem Solving, Academic Press, Orlando.
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36.
  • Snell, K. S. (1958). The solution of quadratic equations. The Mathematical Gazette, 42 (340), 101-103.
  • Stake, R. E. (1994). Case studies. In N. K. Denzin, & Y.S Lincoln (Eds.), Handbook of qualitative research (pp. 236-247). Thousand Oaks, CA: Sage.
  • Usiskin, Z. (1988). Conceptions of school algerba and uses of variables. The Ideas of Algebra K-12, 8-19.
  • Vaiyavutjamai, P., & Clements, M. A. (2006). Effects of classroom instruction on students’ understanding of quadratic equations. Mathematics Education Research Journal, 18(1), 47-77.
  • Yıldırım, A. & Şimşek, H. (2004). Qualitative research methods in social science. Ankara: Seçkin Publishing.
  • Zakaria, E. & Maat, S., M. (2010). The analysis of students` error in learning of quadratic equations. International Education Studies, 3(3) 105-110.
There are 28 citations in total.

Details

Journal Section Articles
Authors

Pınar Güner

Publication Date June 30, 2017
Published in Issue Year 2017 Volume: 6 Issue: 2

Cite

APA Güner, P. (2017). High School Students’ Achievement Of Solving Quadratic Equations. Bartın University Journal of Faculty of Education, 6(2), 447-467. https://doi.org/10.14686/buefad.277494

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