Preschool Teachers’ Pedagogical Content Knowledge Regarding the Concept of Numbers

Year 2024, , 652 - 680, 29.08.2024

Nurcan Satan , Kübra Aksakal , Ayşe Bağdat , Mesture Kayhan Altay

https://doi.org/10.14812/cuefd.1326946

Abstract

The current study examines preschool teachers' pedagogical content knowledge of number concepts (counting principles) and relationships between numbers (part-whole relation and subitizing) from the perspectives of knowledge of student, knowledge of teaching, and knowledge of curriculum. The study makes use of qualitative research method, for which data were gathered through semi-structured interviews with nine preschool teachers with varying years of experience in the field. The data were analysed using a content analysis method, and the results were divided into three categories: student knowledge, pedagogical knowledge, and curriculum knowledge. The results showed that preschool teachers valued counting principles in mathematics classes and frequently incorporated game-integrated activities into their lessons to help students with counting. The most emphasized student errors by preschool teachers were one-to-one correspondence and the principle of cardinality. The results further suggested that teachers lacked pedagogical content knowledge of the part-whole relationship because they could only connect it to addition and skip counting. They interpreted the part-to-whole relationship of numbers as equal sharing, it was further discovered. It was worthy of note that the participants did not mention subitizing, or conceptual and perceptual subitizing, but managed to list the features of subitizing accurately while talking about the examples given. In order to improve teachers' pedagogical content knowledge, in-service seminars or trainings can be organized that emphasize the relationships between numbers (part-whole relationship, subitizing, etc.).

Keywords

Preschool Teacher, Pedagogical Content Knowledge, Counting Principles, Part-Whole Relation, Subitizing

Okul Öncesi Öğretmenlerinin Sayı Kavramına İlişkin Pedagojik Alan Bilgileri

Abstract

Bu çalışmanın amacı, okul öncesi öğretmenlerinin sayı kavramlarına (sayma ilkeleri) ve sayılar arasındaki ilişkilere (parça-bütün ilişkisi ve şipşak sayma) yönelik pedagojik alan bilgilerini öğrenci bilgisi, öğretim bilgisi ve öğretim programı bilgisi bileşenleri çerçevesinde incelemektir. Çalışmada nitel araştırma yöntemi benimsenmiştir. Veriler, farklı mesleki deneyim yıllarına sahip dokuz okul öncesi öğretmeniyle yapılan yarı yapılandırılmış görüşmeler aracılığıyla toplanmıştır. Verilerin analizinde içerik analiz yöntemi kullanılmıştır. Çalışmada elde edilen bulgular öğrenci bilgisi, öğretim bilgisi ve öğretim programı bilgisi olmak üzere üç başlık altında sınıflandırılmıştır. Çalışmanın sonuçları, okul öncesi öğretmenlerinin matematik sınıflarında sayma ilkelerini önemsedikleri ve derslerinde ağırlıklı olarak oyun içine entegreli sayma ilkelerini geliştirici etkinlikler kullandıklarını göstermektedir. Okul öncesi öğretmenlerinin en çok vurguladıkları öğrenci hataları bire bir eşleme ve kardinal değer ilkesi olmuştur. Çalışmada öğretmenlerin parça bütün ilişkisi ile ilgili pedagojik alan bilgisi eksiklerinin olduğu, parça bütün ilişkisini toplama işlemi ve ritmik sayma ile ilişkilendirebildikleri görülmüştür. Ayrıca sayıların parça-bütün ilişkisini eş paylaştırma olarak algıladıkları belirlenmiştir. Okul öncesi öğretmenlerinin şipşak sayma, kavramsal ve algısal şipşak sayma kavramlarını ifade etmedikleri fakat görüşme sorularında verilen örnek durumlarda kavramlarla ilgili özelliklerden doğru bir şekilde bahsettikleri görülmüştür. Öğretmenlerin pedagojik alan bilgilerini geliştirmek amacıyla sayılar arasındaki ilişkilere (parça-bütün ilişkisi, şipşak sayma gibi) vurgu yapan hizmet içi seminerler veya eğitimler düzenlenebilir.

Keywords

Okul Öncesi Öğretmeni, Pedagojik Alan Bilgisi, Sayma İlkeleri, Parça-Bütün İlişkisi, Şipşak Sayma

References

• Aumann, L., Gasteiger, H., & Puca, R. M. (2024). Early childhood teachers' feedback in natural mathematical learning situations: Development and validation of a detailed category system. Acta Psychologica, 244. https://doi.org/10.1016/j.actpsy.2024.104175
• 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
• Baroody, A. J. (2016). Curricular approaches to connecting subtraction to addition and fostering fluency with basic differences in grade 1. PNA. Revista de Investigación en Didáctica de la Matemática, 10(3), 161–190. https://doi.org/10.30827/pna.v10i3.6087
• Björklund, C. (2014). Less is more–mathematical manipulatives in early childhood education. Early Child Development and Care, 184(3), 469–485. https://doi.org/10.1080/03004430.2013.799154
• Björklund, C., & Barendregt, W. (2016). Teachers’ pedagogical mathematical awareness in Swedish early childhood education. Scandinavian Journal of Educational Research, 60(3), 359–377. https://doi.org/10.1080/00313831.2015.1066426
• Björklund, C., Magnusson, M., & Palmér, H. (2020). Teachers’ involvement in children’s mathematizing–beyond dichotomization between play and teaching. In O. Thiel, & B. Perry (Eds.), Innovative approaches in early childhood mathematics (pp. 7–18). Routledge.
• Björklund, C., van den Heuvel-Panhuizen, M., & Kullberg, A. (2020). Research on early childhood mathematics teaching and learning. ZDM Mathematics Education, 52(4), 607–619. https://doi.org/10.1007/s11858-020-01177-3
• Blömeke, S., Jenßen, L., Dunekacke, S., Suhl, U., Grassmann, M., & Wedekind, H. (2015). Leistungstests zur Messung der professionellen Kompetenz frühpädagogischer Fachkräfte. Zeitschrift für pädagogische Psychologie, 29(3-4), 177-191. https://doi.org/10.1024/1010-0652/a000159
• Bobis, J. (2008). Early spatial thinking and the development of number sense. Australian Primary Mathematics Classroom, 13(3), 4–9.
• Clements, D. (1999). Subitizing. What is it? Why teach it? Teaching Children Mathematics, 5(7), 400–405. https://doi.org/10.5951/TCM.5.7.0400
• Clements, D. H., & Sarama, J. (2009). Learning trajectories in early mathematics sequences of acquisition and teaching. Encyclopedia of Language and Literacy Development, 7, 1-6.
• Clements, D. H. & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. https://doi.org/10.1126/science.1204537
• Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches. SAGE Publications.
• Dağlı, H., & Dağlıoğlu, H. (2021). Okul öncesi dönem çocuklarının duygu düzenleme becerileri ile problem çözme becerileri arasındaki ilişkinin çeşitli değişkenlere göre incelenmesi. Cumhuriyet International Journal Of Education. 10(3), 1020-1046. https://doi.org/10.30703/cije.799698
• Davydov, V. V. (1982). The psychological characteristics of the formation of elementary mathematical operations in children. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Red.), Addition and subtraction: A cognitive perspective (pp. 224–238). Lawrence Erlbaum Associates.
• Dursun, Ş. (2009). İlköğretim birinci sınıf öğrencilerinin matematiksel becerilerinin okul öncesi eğitimi alma ve almama durumuna göre karşılaştırılması. Kuram ve Uygulamada Eğitim Bilimleri, 9(4), 1691–1715.
• Ekdahl, A. L. (2021). Different learning possibilities from the same activity—Swedish preschool teachers’ enactment of a number relation activity. Scandinavian Journal of Educational Research, 65(4), 601–614. https://doi.org/10.1080/00313831.2020.1739131
• Fischer, F. E. (1990). A part–part–whole curriculum for teaching number in the kindergarten. Journal for Research in Mathematics Education, 21(3), 207–215. https://doi.org/10.2307/749374
• Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.) McGraw-Hill.
• Gasteiger, H., & Benz, C. (2018). Enhancing and analyzing kindergarten teachers’ professional knowledge for early mathematics education. The Journal of Mathematical Behavior, 51, 109–117. https://doi.org/10.1016/j.jmathb.2018.01.002
• Gelman, R., & Gallistel, C. R. (1986). The child's understanding of number. Harvard University.
• Ginsburg, H. P. (2016). Helping early childhood educators to understand and assess young children’s mathematical minds. ZDM Mathematics Education, 48, 941–946. https://doi.org/10.1007/s11858-016-0807-7
• Güven, Y. (2005). Erken çocuklukta matematiksel düşünme ve matematiği öğrenme. Küçük Adımlar Eğitim Yayınları.
• Hachey, A. C. (2013). The early childhood mathematics education revolution. Early Education & Development, 24(4), 419–430. https://doi.org/10.1080/10409289.2012.756223
• Hunting, R. P. (2003). Part-whole number knowledge in preschool children. The Journal of Mathematical Behavior, 22(3), 217-235. https://doi.org/10.1016/S0732-3123(03)00021-X
• Kutluca, A. Y. (2021). Exploring preschool teachers' pedagogical content knowledge: The effect of professional experience. Journal of Science Learning, 4(2), 160–172. https://doi.org/10.17509/jsl.v4i2.31599
• Klahr, D., & Wallace, J. G. (1976). Cognitive development: An information-processing view. Routledge.
• Lee, J. (2010). Exploring kindergarten teachers’ pedagogical content knowledge of mathematics. International Journal of Early Childhood, 42, 27–41. https://doi.org/10.1007/s13158-010-0003-9
• Lee, J. E. (2017). Preschool teachers’ pedagogical content knowledge in mathematics. International Journal of Early Childhood, 49, 229–243. https://doi.org/10.1007/s13158-017-0189-1
• Li, X. (2021) Investigating U. S. preschool teachers’ math teaching knowledge in counting and numbers. Early Education and Development, 32(4), 589–607. https://doi.org/10.1080/10409289.2020.1785226
• MacDonald, B. L. (2013). Subitizing activity: Item orientation with regard to number abstraction [Unpublished doctoral dissertation]. Virginia Tech University.
• MacDonald, B. L. (2015). Ben’s perception of space and subitizing activity: A constructivist teaching experiment. Mathematics Education Research Journal, 27(4), 563–584. https://doi.org/10.1007/s13394-015-0152-0
• MacDonald, B. L., & Shumway, J. F. (2016). Subitizing games: Assessing preschoolers' number understanding. Teaching Children Mathematics, 22(6), 340–348. https://doi.org/10.5951/teacchilmath.22.6.0340
• McCray, J. S., & Chen, J. Q. (2012). Pedagogical content knowledge for preschool mathematics: Construct validity of a new teacher interview. Journal of Research in Childhood Education, 26(3), 291–307. https://doi.org/10.1080/02568543.2012.685123
• MEB. (2013). Okul öncesi eğitim programı. T.C. Millî Eğitim Bakanlığı, Temel Eğitim Genel Müdürlüğü.
• Neuman, D. (1987). The origin of arithmetic skills: A phenomenographic approach. [Unpublished doctoral dissertation]. Acta Universitatis Gothoburgensis.
• Olkun, S., Çelik, E., Tural Sönmez, M., & Can, D. (2014). İlköğretim birinci sınıf Türk öğrencilerinde sayma ilkelerinin gelişimi. Başkent University Journal of Education, 1(2), 115–125. http://buje.baskent.edu.tr/index.php/buje/article/view/50/35
• Olkun, S., & Özdem, Ş. (2015). Kavramsal şipşak sayılama uygulamalarının hesaplama performansına etkisi. Başkent University Journal of Education, 2(1), 1–9. http://buje.baskent.edu.tr/index.php/buje/a
• Patton, M. Q. (2005). Qualitative research. In B. S. Everitt & D. C. Howell (Eds.), Encyclopedia of Statistics in Behavioral Science (1 st ed.). Wiley. https://doi.org/10.1002/0470013192.bsa514
• Polignano, J. C. (2014). Number sense development during the preschool years: Relations within and between key skill indicators [Unpublished doctoral dissertation]. Lehigh University.
• Sarnecka, B. W., & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108(3), 662–674. https://doi.org/10.1016/j.cognition.2008.05.007
• Sarnecka, B. W., & Wright, C. E. (2013). The idea of an exact number: Children's understanding of cardinality and equinumerosity. Cognitive Science, 37(8), 1493–1506. https://doi.org/10.1111/cogs.12043
• Schaeffer, B., Eggleston, V. H., & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6(3), 357–379. https://doi.org/10.1016/0010-0285(74)90017-6
• Schmittau, J. (2004). Vygotskian theory and mathematics education: Resolving the conceptual-procedural dichotomy. European Journal of Psychology of Education, 19(1), 19–43. https: //doi.org/ 10.1007/ BF03173235
• Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 414. https://doi.org/10.3102/0013189X015002004
• Sinnakaudan, S., Kuldas, S., Hashim, S., & Ghazali, M. (2016). Enabling pupils to conceive part-whole relations of numbers and develop number sense: Year one of primary schools in Malaysia. International Journal for Mathematics Teaching and Learning, 17(3), 1–20. http://dx.doi.org/10.4256/ijmtl.v17i3.25
• Smith, K. H. (2000). Early childhood teachers’ pedagogical knowledge in mathematics: A quantitative study [Unpublished doctoral dissertation]. Georgia State University.
• Sophian, C., & McCorgray, P. (1994). Part-whole knowledge and early arithmetic problem solving. Cognition and Instruction, 12(1), 3–33. https://doi.org/10.1207/s1532690xci1201_1
• Sperry-Smith, S. (2016). Erken çocuklukta matematik. (S. Erdoğan, Çev.). Eğiten Kitap.
• Şapul, Y. (2019). Türkiye ve Singapur okul öncesi eğitim programlarının temel prensiplerinin ve matematiksel içeriklerinin karşılaştırılması [Unpublished master's thesis]. Gaziantep Üniversitesi.
• Tian, F., & Huang, J. (2019). Early childhood teachers' pedagogical content knowledge in mathematics: A research report from China. Universal Journal of Educational Research, 7(11), 2258–2261. http://dx.doi.org/10.13189/ujer.2019.071102
• Torbeyns, J., Op’t Eynde, E., Depaepe, F., & Verschaffel, L. (2024). Preschool teachers’ mathematical questions during shared picture book reading. ZDM–Mathematics Education, 38(1), 1–15. https://doi.org/10.1007/s11858-023-01544-w
• Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri (11. Bs.). Seçkin Yayınevi.
• Yükseköğretim Kurulu (YÖK), (2018). Öğretmen yetiştirme lisans programları, programların güncelleme gerekçeleri, getirdiği yenilikler ve uygulama esasları. https://www. yok. gov. tr/kurumsal/idari-birimler/egitim-ogretim-dairesi/yeni-ogretmen-yetistirme-lisans-programlari. Erişim: 02.08.2023.
• Zhang, Y. (2015). Pedagogical content knowledge in early mathematics: What teachers know and how it associates with teaching and learning [Unpublished doctoral dissertation]. Loyola University.