Primary school teachers' mathematical knowledge and instructional explanations of four operations

Year 2026, Issue: Erken Görünüm [Online First], 158 - 186

Fırat Karabağ , Gönül Güneş

https://doi.org/10.9779/pauefd.1449468

Abstract

This study, which aims to determine the level of primary school teachers' instructional knowledge of the four basic operations with natural numbers and to examine their instructional explanations, was conducted according to the sequential explanatory design, one of the mixed research methods. The mathematics teaching knowledge of primary school teachers was examined within the framework of content knowledge, student and content knowledge, instructional and content knowledge, and curricular knowledge components. In the quantitative part of the study, primary school teachers were administered a test on four operations with natural numbers, and in the qualitative part, clinical interviews were conducted with the identified teachers. The study was conducted with 70 primary school teachers with professional experience ranging from 1 to 30 years. The data were collected through an information form that included demographic information of the participants, a content knowledge test on teaching four operations with natural numbers, and clinical interviews. Data from the test were analyzed using the scoring rubric developed by the researchers. Data from the clinical interviews were subjected to descriptive content analysis. As a result of the research, primary school teachers showed the lowest performance in the instructional and content knowledge component and the most successful performance in the curriculum knowledge component. As a result of the findings, the deficiencies of primary school teachers regarding their pedagogical content and subject matter knowledge were identified and it was suggested that in order to overcome these deficiencies, learning environments should be provided for teachers to update and improve their theoretical and content teaching knowledge within the profession in cooperation with universities.

Keywords

Primary school teachers, Knowledge of mathematics teaching, Four operations with natural numbers, Instructional explanations

Sınıf Öğretmenlerinin Dört İşlem ile İlgili Matematiksel Bilgileri ve Öğretimsel Açıklamaları

Abstract

Sınıf öğretmenlerinin doğal sayılarla temel dört işleme ilişkin öğretme bilgilerinin seviyelerini belirlemeyi ve buna yönelik yaptıkları öğretimsel açıklamaları incelemeyi amaçlayan bu araştırma karma araştırma yöntemlerinden sıralı açıklayıcı desene göre yürütülmüştür. Sınıf öğretmenlerinin matematik öğretim bilgileri; konu alan bilgisi, öğrenci ve içerik bilgisi, öğretim ve içerik bilgisi ve müfredat bilgisi bileşenleri kapsamında incelenmiştir. Araştırmanın nicel kısmında sınıf öğretmenlerine doğal sayılarla dört işlem alanına ilişkin test uygulanmış, nitel kısmında ise belirlenen öğretmenlerle klinik mülakatlar yapılmıştır. Araştırma, mesleki deneyimleri 1 ila 30 yıl arası olan 70 sınıf öğretmeni ile gerçekleştirilmiştir. Araştırma verileri katılımcıların demografik bilgilerini içeren bilgi formu, doğal sayılarla dört işlem öğretimine ilişkin alan bilgisi testi ve klinik mülakatlar ile toplanmıştır. Testten elde edilen veriler araştırmacılar tarafından geliştirilen değerlendirme rubriği ile analiz edilmiştir. Klinik mülakat verileri ise betimsel içerik analizine tabi tutulmuştur. Araştırma sonucunda sınıf öğretmenleri en düşük performansı öğretim ve içerik bilgisi bileşeninde, en başarılı performansı ise müfredat bilgisi bileşeninde göstermişlerdir. Tespit edilen sonuçlar neticesinde sınıf öğretmenlerinin pedagojik alan ve konu alan bilgilerine ilişkin eksiklikleri belirlenmiş, bu eksikliklerin giderilmesi için üniversitelerle iş birliği yapılarak öğretmenlere, teorik ve alan öğretimi bilgilerini meslek içinde güncelleştirip geliştirebilecekleri öğrenme ortamlarının sağlanması gerektiği önerilmiştir.

Keywords

Sınıf öğretmenleri, Matematik öğretme bilgisi, Doğal sayılarla dört işlem, Öğretimsel açıklamalar

Ethical Statement

Etik Kurul Onay Formu dosyalarda sunulmuştur.

References

• Aksu, Z. (2013). The development of pre-service primary school teachers' pedagogical content knowledge in fractions [Doctoral thesis, Atatürk University]. National Dissertation Center.
• Aksu, Z., & Konyalıoğlu, A. C. (2015). Pre-service primary school teachers’ pedagogical content knowledge in fractions. Kastamonu Education Journal, 23(2), 723-738.
• Akyıldız, P. (2019). An investigation of instructional explanations of pre-service mathematics teachers from mathematical belief perspective [Doctoral thesis, Gazi University]. National Dissertation Center.
• Akyıldız, S., & Altun, T. (2018). Examining technological pedagogical and content knowledge (TPACK) levels of primary pre-service teachers based on some variables. Trakya University Journal of Education Faculty, 8(2), 318-333. https://doi.org/10.24315/trkefd.322749
• An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7(2), 145-172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
• Arseven, A., Arseven, İ., & Tepehan, T. (2015). Examination of class teacher candidates’ mathematics teaching self-efficacy. Cumhuriyet International Journal of Education, 4(2), 29-40. https://doi.org/10.30703/cije.321367
• Baki, A. (2020). Mathematical knowledge for teaching. Ankara: Pegem Academy.
• Baki, M. (2012). Investigating development of prospective primary teachers' mathematical pedagogical content knowledge: Lesson study [Doctoral thesis, Karadeniz Technical University]. National Dissertation Center.
• Baki, M. (2013). Pre-service classroom teachers’ mathematical knowledge and instructional explanations associated with division. Education and Science, 38,167.
• Baki, M. (2017, 20-23 April). A study on classroom teacher candidates’ detection and interpretation of student errors in division operations [Conference presentation]. The 26th International Congress on Educational Sciences, Antalya, Türkiye.
• Balcı, D. (2004). Çağdaş yabancı dil öğretiminde öğrenmeyi öğretme. Teaching learning in contemporary foreign language teaching. http://www.ingilish.com/db2.htm
• Balcı, E. (2023). Investigating the preservice primary school teachers' mathematical knowledge in teaching of division operation. [Master's thesis, Middle East Technical University]. National Dissertation Center.
• Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education 59(5), 389-407. https://doi.org/10.1177/0022487108324554
• Başar, M., Ünal, M. & Yalçın, M. (2002). İlköğretim kademesiyle başlayan matematik korkusunun nedenleri. The causes of the fear of mathematics starting with primary education. The 5th National Science and Mathematics Education Congress, 16, 18.
• Canbazoğlu, S., Demirelli, H. & Kavak, N. (2010). İnvestigation of the relationship between pre-service science teachers' subject matter knowledge and pedagogical content knowledge regarding the particulate nature of matter. Elementary Education Online, 9(1).
• Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. Handbook of research design in mathematics and science education, 547-589.
• Çakmak, Z., Konyalıoğlu, A. C. & Işık, A. (2014). The investigation of pre-service elementary mathematics teachers’ content knowledge on three dimensional objects. Middle Eastern and African Journal of Research, 8(1), 28-44.
• Çelik, A. Ö., & Güzel, E. B. (2020). Comparing the clinical interviews conducted by the prospective mathematics teachers having different academic achievement. YYU Education Faculty of Journal, 17(1), 1-29. https Educational://doi.org/10.33711/yyuefd.671175
• Çıkrıkçı, F. H. (2015). An investigation of elementary school mathematics teacher candidates & apos; subject matter knowledge and pedagogical content knowledge regarding the algebra [Master's thesis, Dokuz Eylül University]. National Dissertation Center.
• Deringöl, Y. (2018). An examination of the mathematics teaching efficacy and the mathematics teaching anxiety of classroom teacher candidates. Journal of Theoretical Educational Science, 11(2), 261-278. https://doi.org/10.30831/akukeg.364483
• Doğruel, A. B. (2019). An examination of elementary school mathematics teachers’ pedagogical content knowledge on ratio and proportion [Master's thesis, Afyon Kocatepe University]. National Dissertation Center.
• Doğruel, A. B., & Karakuş, F. (2022). An examination of middle school mathematics teachers’ content knowledge on ratio and proportion. Afyon Kocatepe University Journal of Social Sciences, 24(3), 885-904. https://doi.org/10.32709/akusosbil.938560
• Durak, E. (2021). Examination of classroom teachers' problem-solving processes and instructional explanations [Master's thesis, Karadeniz Technical University]. National Dissertation Center.
• Ekiz, D. (2020). Scientific research method. Ani Publishing.
• Eroğlu, D. (2012). Examining prospective elementary mathematics teachers ‘knowledge about students’ mistakes related to fractions [Master's thesis, Middle East Technical University]. National Dissertation Center.
• Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In: D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.147-164). Macmillan Publishing.
• Gökkurt, B. (2014). An examination of secondary school mathematics teachers & apos; pedagogical content knowledge on geometric shapes [Doctoral thesis, Atatürk University]. National Dissertation Center.
• Gökkurt, B., Şahin, Ö., Soylu, Y., & Doğan, Y. (2015). Pre-service teachers’ pedagogical content knowledge regarding student mistakes on the subject of geometric shapes. İlköğretim Online, 14(1), 55-71.
• Grossman, P.L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press.
• Hacıömeroğlu, G. (2013a). Elementary preservice teachers’ mathematical knowledge for teaching: analysis of students’ solution to addition and subtraction operations. Education and Science, 38, 168.
• Hacıömeroğlu, G. (2013b). Elementary preservice teachers’ efficacy beliefs regarding mathematics teaching and their beliefs about classroom management. Uludağ University Journal of Education Faculty, 26(1), 1-18.
• Işık, A., Çiltaş, A., & Baş, F. (2010). Teacher training and teaching profession. Atatürk University Social Sciences Institute Journal, 14(1), 53-62.
• Karataş, İ. & Güven, B. (2003). Methods used to evaluate problem solving behaviours: Potential of clinical interview. İlköğretim Online, 2(2), 2-9.
• Keleş, F. (2019). An investigation of the knowledge of mathematics teachers of primary school teachers [Master's thesis, Karadeniz Technical University]. National Dissertation Center.
• Keleş, F., & Güneş, G. (2022). An investigation of the knowledge of teaching mathematics of novice primary school teachers. Kastamonu Education Journal, 30(1),60-77. https://doi.org/10.24106/kefdergi.774584
• Kinach, B. M. (2002a). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51-71. https://doi.org/10.1016/S0742-051X(01)00050-6
• Kinach, B. M. (2002b). Understanding and Learning-to-explain by Representing Mathematics: Epistemological dilemmas facing teacher educators in the secondary mathematics ‘methods’ course. Journal of Mathematics Teacher Education, 5(2), 153-186.
• Kutlu, D. (2018). Examination of the pedagogical content knowledge levels of novice secondary school mathematics teachers [Master's thesis, Karadeniz Technical University]. National Dissertation Center.
• Kwong, C. W., Joseph, Y. K. K., Eric, C. Cm., & Khoh, L. T. S. (2007). Development of mathematics pedagogical content knowledge in student teachers. The Mathematics Educator, 10(2), 27-54.
• Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3-11. https://doi.org/10.1177/002248719004100302
• Milli Eğitim Bakanlığı [MEB]. (2017). Öğretmenlik mesleği genel yeterlikleri. https://oygm.meb.gov.tr/www/ogretmenlik-meslegi-genel-yeterlikleri/icerik/486
• Milli Eğitim Bakanlığı [MEB]. (2018). İlkokul 1-8.sınıflar matematik dersi öğretim programı. Ankara: Milli Eğitim Müdürlüğü Basımı.
• Önal, H. (2017). İlkokul 1. ve 2. sınıf öğrencilerinin matematik dersinde dört işlem ile ilgili yaptıkları hatalar ve çözüm önerileri [Doctoral thesis, Marmara University]. National Dissertation Center.
• Özdemir, B. G., Bayraktar, R. & Yılmaz, M. (2017). Explanations of primary and middle school mathematics teachers on misconceptions. Trakya University Journal of Education Faculty, 7(2), 284-305.
• Reid, M. & Reid, S. (2017). Learning to be a math teacher: What knowledge is essential? International Electronic Journal of Elementary Education, 9(4), 851-872.
• Shulman, L. S. (1986). Those who understand; Knowledge growth on teaching, Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
• Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform, Harvard Educational Review, 57(1), 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
• Sıvacı, S. Y. (2003). The, subject-matter knowledge in mathematics, competencies of professional knowledge and their attitudes towards mathematics of the last grade students of classroom teaching programmers [Doctoral thesis, Hacettepe University]. National Dissertation Center.
• Şimşek, N. & Boz N. (2015). Investigating of pedagogical content knowledge of pre-service primary teachers related to the length measurement in the context students’ understanding. Cumhuriyet International Journal of Education, 4(3), 10-30.
• Tanışlı, D. (2013 Preservice primary school mathematics teachers’ questioning skills and knowledge of students in terms of pedagogical content knowledge. Education and Science, 38(169), 81-95.
• Tarım, K., Özsezer, M. S. B. & Canbazoğlu, H. B. (2017). Pre-service classroom teachers; perceptions of related with mathematics and teaching mathematics. Journal of Ahi Evran University Kırşehir Education Faculty, 18(3), 1032-1052.
• Tashakkori, A. & Creswell, J.W. (2007). The new era of mixed methods. Journal of Mixed Methods, 1(1), 2-8. https://doi.org/10.1177/2345678906293042
• Toluk-Uçar, Z. (2010). Preservice elementary teachers’ mathematics knoıwledge and instructional explanations. Education Sciences, 5(3), 911-920.
• Vural, D. Ö. & Çankaya, E. A. (2020). Knowledge, belief, and teaching: a study on subtraction in fractions and multiplication. Cumhuriyet International Journal of Education, 9(1), 1-27.
• Yıldırım, K. (2013). An Investigation of primary school teachers’ level of mathematics anxiety [Master's thesis, Adıyaman University]. National Dissertation Center.
• Yıldırım, A. & Şimşek, H. (2018). Social information qualitative research methods. Seçkin Publishing.
• Yıldızlı, H. & Sarı, M. H. (2017). The Investigation of primary teachers’ content knowledge on geometric objects. Uludağ University Journal of Education Faculty, 30(2), 601-636. https://doi.org/10.19171/uefad.368975
• Yurtbakan, E., Aydoğdu-İskenderoğlu, T. & Sesli, E. (2016). Öğrencilerin matematik dersindeki başarılarını arttırma yolları konusunda sınıf öğretmenlerinin görüşleri. Primary school teachers' views on ways to increase students' achievement in mathematics. Ondokuz Mayıs University Journal of Education, 35(29), 101-119.
• Yurtyapan, M. İ. & Karataş, İ. (2020). An Investigation of pedagogical content knowledge of secondary school mathematics teachers in relation with triangle and quadrilateral concepts. Turkish Journal of Computer and Mathematics Education, 11(1), 53-90.
• Zaslavsky, O. (2010). The explanatory power of examples in mathematics: Challenges for teaching. In Instructional explanations in the disciplines (pp. 107-128). Springer. https://doi.org/10.1007/978-1-4419-0594-9_8