EXAMINATION OF THE PEDAGOGICAL CONTENT KNOWLEDGE OF MATHEMATICS TEACHERS

Authors

  • Burçin GÖKKURT ÖZDEMİR Bartın University, Bartın, Turkey
  • Yasin SOYLU Atatürk University, Erzurum, Turkey

Abstract

Mathematics education consists of numerous factors, and a vital factor is teachers. Therefore, well-trained teachers play a crucial role in the education system. In this context, the pedagogical content knowledge of teachers forms a vital foundation for effective mathematics teaching. The study aimed to examine the pedagogical content knowledge of mathematics teachers. Forty-one mathematics teachers took part in this study. The qualitative research method was applied and eight open-ended questions were asked for data gathering purposes. The content and descriptive analysis methods were used for data analysis. The study showed that the instructional explanations of teachers were typically at their strumental level (content-level). Accordingly, it can be conferred that teachers lack the sufficient level of conceptual knowledge required for the effective mathematics teaching that is the aim of  the curriculum. Therefore, it was suggested that teachers develop their pedagogical content knowledge through in-service courses in line with curriculum targets.

Keywords: Instructional explanations, mathematics teaching, pedagogical content knowledge

REFERENCES

Aksu, M, Demir,  C.& Sümer,Z.(1998, Ekim). Matematik öğretmenlerinin ve öğrencilerinin matematik hakkındaki inançları. III. Ulusal Fen Bilimleri Sempozyumu. Trabzon:Karadeniz Teknik Üniversitesi.

An,S, Kulm,G.,& Wu,Z.(2004). Thepedagogicalcontentknowledge of middleschool, mathematicsteachers in China and the U.S. Journal of MathematicsTeacherEducation, 7(2),145–172.

Azim, D. S.(1995). Preservice elementary teachers’ understanding of multiplication with fractions.(Unpublished doctoral dissertation). Washington StateUniversity.

Baki,A.(2006). The mathematical understandings that prospective teachers bring to teacher educationKuramdan uygulamaya matematik eğitimi(3.baskı).Trabzon: Derya Kitapevi.

Ball,D.L.(1990a). Themathematicalunderstandingsthatprospectiveteachersbringtoteachereducation. TheElementary School Journal, 90(4), 449-466.

Ball,D.L.(1990b). Prospectiveelementary and secondaryteachers understanding of division. JournalforResearch in MathematicsEducation, 21(2), 132-144.

Baskan, G. A.(2001). Öğretmenlik mesleği ve öğretmen yetiştirmede yeniden yapılanma.  Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 20,16–25.

Baştürk, S.& Dönmez, G.(2011). Examiningpre-service teachers’ pedagogicalcontentknowledgewithregardtocurriculumknowledge. International Online Journal of EducationalSciences, 3(2), 743-775.

Batura, A.&Nason,R.(1996). Studentteachers’subjectmatterknowledgewithinthe domain of areameasurement. EducationalStudies in Mathematics, 31(3), 235-268.

Bolat, M.& Sözen, M.(2009). Knowledge levels of prospectivescience and physicsteachers on basicconcepts on sound (sample of Samsun city). Procedia Social andBehavioral Science, 1,1231–1238.

Borko, H., Eisenhart, M., Brown, C. A., Underhill,R. G., Jones,D.,&Agard,P. C.(1992). Learning toteach hard mathematics: do noviceteachers and theirinstructorsgiveuptooeasily? JournalforResearch in MathematicsEducation, 23(3), 194-222.

Bukova-Güzel, E., Cantürk-Günhan, B., Kula, S., Özgür, Z.,&Elçi, A. N.(2013). Scaledevelopmentforpre-service mathematics teachers’ perceptionsrelatedtotheirpedagogicalcontentknowledge. South AfricanJournal of Education, 33(2), 1-21.

Canbazoğlu,S.(2008).Fen bilgisi öğretmen adaylarının maddenin tanecikli yapısı

ünitesine ilişkin pedagojik alan bilgilerinin değerlendirilmesi.(Yayımlanmamış yüksek lisans tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.

Cluff,J. J. (2005). Fractionmultiplication and divisionimagechange in pre-service elementaryteachers. Master of Arts:BrighamYoungUniversity.

Dani,D.(2004).Theimpact of content and pedagogycourses on scienceteachers’

Pedagogicalcontentknowledge. Unpublisheddoctoraldissertation. USA :TheUniversity of Cincinnati.

Even,R.(1993).Subject-matterknowledge and pedagogicalcontentknowledge: prospectivesecondaryteachers and thefunctionconcept. JournalforResearch in MathematicsEducation, 24(2), 94-116.

Feiman-Nemser, S.&Parker,M. B.(1990). Makingsubjectmatterpart of theconversationorhelpingbeginningteacherslearntoteach.Journal of TeacherEducation, 41(3), 32-43.

Gökbulut, Y. (2010). Sınıf öğretmeni adaylarının geometrik cisimler konusundaki pedagojik alan bilgileri.(Yayımlanmamış doktora tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.

Gökkurt, B. (2014). Ortaokul matematik öğretmenlerinin geometrik cisimler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi. (Yayımlanmamış doktora tezi). Atatürk Üniversitesi Eğitim Bilimleri Enstitüsü, Erzurum.

Gökkurt, B. & Soylu, Y. (2016a). Ortaokul matematik öğretmenlerinin pedagojik alan bilgilerinin bazı bileşenler açısından incelenmesi: koni örneği. İlköğretim Online, 15(3), 946-973.

Gökkurt, B. & Soylu, Y. (2016b). Matematik öğretmenlerinin matematiksel alan bilgilerinin incelenmesi: prizma örneği.  Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi,16(2), 451-482.

Grouws, D.&Schultz,K.(1996). Mathematicsteachereducation. In J. Sikula (Ed).Handbook of research on teacher education,(2nd edition), Macmillan.

Halim, L.&Meerah, S.(2002). Sciencetraineeteachers’ pedagogicalcontent

knowledge and itsinfluence on physics teaching. Research in Scienceand

TechnologicalEducation,20(2), 215-225.

Henningsen, M &Stein,M. K.(1997). Mathematical tasks and studentcognition: classroom-basedfactorsthatsupport and inhibithigh-levelmathematicalthinking and reasoning. JournalforResearch in MathematicsEducation, 28(5), 524–549.

Işıksal, M.(2006). A study on pre-service elementarymathematics’ subjectmatterknowledge and pedagogicalcontentknowledgeregardingthemultiplication and division of fractions.(Unpublisheddoctoraldissertation). Ankara: Middle East Technical University

Kaptan, F.&Kuşakçı,F.(2002, Eylül). Fen öğretiminde beyin fırtınası tekniğinin öğrenci yaratıcılığına etkisi. V. Ulusal Fen Bilimleri ve Matematik Eğitimi KongresiBildirileri içinde (s. 197-202). Ankara: ODTÜ.

Karal-Eyüboğlu, I.S. (2011). Fizik öğretmenlerinin pedagojik alan bilgi gelişimi. (Yayımlanmamış doktora tezi).  Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü, Trabzon.

Kazima, M., Pillay,  V.,&  Adler, J.(2008).  Mathematicsfor teaching: observationsfromtwocasestudies. South AfricanJournal of Education, 28, 283-299.

Kılcan-Arslan, S.(2006). İlköğretim matematik öğretmenlerinin kesirlerle bölmeye ilişkin kavramsal bilgi düzeyleri.(Yayımlanmamış yüksek lisans tezi). Abant İzzet Baysal Üniversitesi, Sosyal Bilimler Enstitüsü, Bolu.

Kinach,B. M.(2002a). Understanding and learning-to-explainbyrepresentingmathematics: epistemologicaldilemmasfacingteachereducators in thesecondarymathematicsmethodscourse. Journal of  Mathematics Teacher Education, 5(2), 153-186.

Kinach, B. M.(2002b). A cognitivestrategyfordevelopingpedagogicalcontentknowledge in thesecondarymathematicsmethodscourse: toward a model of effectivepractice. Teaching and TeacherEducation, 18(1), 51-71.

Lee, E.&Luft, J. A. (2008).Experiencedsecondaryscienceteachers’ representation of

pedagogicalcontentknowledge. International Journal of ScienceEducation, 30(10),1343–1363.

Lesniak, K. M. (2003).  Fromexpertlearnertonoviceteacher: growth in knowledge learning toteachscience.(Unpublisheddoctoralthesis). USA: Faculty of theGraduate School of theStateUniversity of Newyork,

Lubinski, C. A., Fox, T.& Thomason,R. (1998). Learning tomake sense of division of fractions: one K-8 pre-service teacher’sperspective.School Science and Mathematics, 98(5), 247-253.

Ma, L.(1999). Knowing and teaching elementarymathematics: teachers’ understanding offundamentalmathematics in China and the United States. Mahwah, NJ: Erlbaum.

McDiarmid, G. W., Ball, D. L.,& Anderson,C.(1989). Why staying one chapter ahead doesn't really work: subject-specific pedagogy. In MC Reynolds (ed). Knowledge base forthebeginningteacher. Elmsford, NY: PergamonPress.

Mcmillan H. J. &Schumacher,S. (2010). Research in education. Boston, USA: PearsonEducation.

Meriç G. & Tezcan R 2005. Fen bilgisi öğretmeni yetiştirme programlarının örnek ülkeler kapsamında değerlendirilmesi (Türkiye, Japonya, Amerika ve İngiltere Örnekleri). Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 7, 62-82.

Moats, L. C.&Foorman, B. R. (2003).  Measuringteachers’ contentknowledge of language and reading. Annals of Dyslexia, 53(1), 23-45

Monte-Sano, C.(2011). Learning to open up history for students: preservice teachers' emerging pedagogical content knowledge. Journal of Teacher Education, 62(3), 260-272. doi: Doi 10.1177/0022487110397842.

Nagle, L. Mç& McCoy, L. P.(1999). Division of fractions: proceduralversusconceptualknowledge. In McCoy, LP (ed). Studies in teaching:1999 researchdigest. Researchprojectspresented at annualResearch Forum (Winston-Salem, NC), PP.81-85. ERIC DocumentReproduction Service No:.ED 443 814.

National Council of Teachers of Mathematics [NCTM](2000).  Principles and standarts for school mathematics. Roston, Virginia.

Özel, M. (2012). Farklı öğretim deneyimine sahip fen ve teknoloji öğretmenlerinin kimyasal tepkimeler konusundaki pedagojik alan bilgilerinin incelenmesi. (Yayımlanmamış doktora tezi).  Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.

Perkins, D. N.& Simmons,R.(1988). Patterns of misunderstanding: An integrative modelfor science, math, and programming. Review of Educational Research , 58(3),303–326.

Pesen,C.(2006). Eğitim fakülteleri ve sınıf öğretmenleri için yapılandırmacı öğrenme yaklaşımına göre matematik öğretimi (3. Baskı). Ankara: Öncü basımevi.

Shulman L. (1986). Paradigms and research programs in the study of teaching: a contemporary perspective. In M, Wittrock (Ed.), Handbook of Research on Teaching. NY: Macmillian Publishing Company.

Shulman, L.S. (1987). Knowledge and teaching: Foundation of the new reform. Harvard Educational Review, 57(1), 1-21.

Simon, M. A. & Blume, G. W.(1994). Building and understanding  multiplicative relationships: a study of prospective elementary teachers. JournalforResearch in MathematicsEducation, 25(5),472-494.

Stengel, B. S. & Tom,  A. R. (1996). Changes and choices in teaching methods. InB Murray Frank (Ed.), The teacher educator’s handbook: building a knowledge bas e for the preparation of teachers (pp. 593-619). San Francisco: Jossey Bass.

Şahin, Ö., Gökkurt, B., Başıbüyük, K., Erdem, E., Nergiz, T. ve Soylu, Y. (2013). Matematik ve sınıf öğretmeni adaylarının pedagojik alan bilgilerinin karşılaştırılması. The Journal of Academic Social Science Studies, 6(4,) 693-713.

Tirosh, D.(2000). Enhancingprospectiveteachers‟  knowledge of children’s conceptions: thecase of division of fractions. JournalforResearch in MathematicsEducation, 31(1),

5–25.

 Toluk-Uçar, Z.(2009). Developingpre-service teachers understanding of fractionsthrough problem posing. Teaching and TeacherEducation, 25(1), 166–175.

Toluk-Uçar Z, Pişkin, M.,  Akdoğan, E. N., & Taşçı, D.(2010). İlköğretim öğrencilerinin matematik, matematik öğretmenleri ve matematikçiler hakkındaki inançları.Eğitim ve Bilim, 35(155), 131-144.

Toluk-Uçar, Z.(2011). Öğretmen adaylarının pedagojik içerik bilgisi: öğretimsel açıklamalar. Turkish Journal of Computer and Mathematics Education, 2(2), 87-102.

Türnüklü, E. & Yeşildere, S. (2007). The pedagogical content knowledge in mathematics: pre-service primary mathematics teachers’ perspectives in Turkey. Issues in the Undergraduate Mathematics preparation of School Teachers: The Journal, 1, 1-13.

Uşak, M. (2005). Fen bilgisi öğretmen adaylarının çiçekli bitkiler konusundaki pedagojik alan bilgileri. (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.

Van derSandt,  S. & Nieuwoudt,  H. D. (2003). Grade 7  teachers’ and prospective teachers’ content knowledge of geometry. South AfricanJournal of Education,23, 199-205.

Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9. Baskı). Ankara: Seçkin Yayıncılık.

Yüksel, G. (2008). Farklı içerik bilgisi seviyelerindeki lise matematik öğretmen adaylarının ders planlarında gözlenen pedagojik içerik bilgilerinin incelenmesi.(Yayımlanmamış yüksek lisans tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü.

Downloads

Published

2017-06-30

Issue

Section

Research Article