Araştırma Makalesi
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Pre-service Teachers' Mind Maps on Rational Numbers: Pirie-Kieren Theory

Yıl 2024, Cilt: 53 Sayı: 241, 133 - 164, 01.02.2024
https://doi.org/10.37669/milliegitim.1141497

Öz

The aim of this study is to examine the mathematical understanding levels of secondary school mathematics teacher candidates regarding the concept of rational numbers according to the Pirie-Kieren theory. The research was carried out with three pre-service teachers studying in a university in Istanbul's primary school mathematics teaching program. The pre-service teachers were selected from among volunteer pre-service teachers with a high and good level of academic achievement and high communication skills who took the courses "Basics of Mathematics", "Secondary School Mathematics Curriculum", and "Teaching Numbers". The research was designed according to the case study pattern. The data were collected through a rational numbers concept test consisting of four open-ended questions on the concept of rational numbers developed by the researchers and semi-structured interviews. The obtained data were analyzed according to the Pirie-Kieren comprehension layers. The study determined that pre-service teachers were mostly in the "image creation" layer. Considering the process together with the semi-structured interview results, it was determined that the pre-service teachers tried to construct their knowledge by folding back and forth between the layers of "having the image", "noticing the feature", and "abstraction". In addition, pre-service teachers' mind maps were created according to the Pirie-Kieren theoretical model, and the results were discussed. According to the results obtained, suggestions have been developed for researchers in this field.

Kaynakça

  • Alajmi, A., and Reys, R. (2007). Reasonable and reasonableness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65(5), 77-94. https://doi.org/10.1007/s10649-006-9042-4
  • Behr, M., Lesh, R., Post, T., and Silver E. (1983). Rational number concepts. In R. Lesh and M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91-125). Academic Press.
  • Borgen, K. L., and Manu, S. S. (2002). What do students really understand?. The Journal of Mathematical Behavior, 21(2), 151-165. https://doi.org/10.1016/S0732-3123(02)00115-3
  • Brownell, W. A. (1947). The place of meaning in the teaching of arithmetic. Elementary School Journal, 47(5), 256-265. https://doi.org/10.1086/462322
  • Coe, R., and Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20, 41-53. https://doi.org/10.1080/0141192940200105
  • Çelik, B. (2006). Temel matematik. Nobel.
  • Düzenli-Gökalp, N., and Bulut, S. (2018). A new form of understanding maps: Multiple representations with Pirie and Kieren model of understanding. International Journal of Innovation in Science and Mathematics Education, 26(6), 1-21.
  • Düzenli-Gökalp, N., and Sharma, M. D. (2010). A study on addition and subtraction of fractions: The use of Pirie and Kieren model and hands-on activities. Procedia-Social and Behavioral Sciences, 2(2), 5168-5171. https://doi.org/10.1016/j.sbspro.2010.03.840
  • Ellerbruch, L. W., and Payne, J. N. (1978). A teaching sequence for initial fraction concepts through the addition of unlike fractions. In M. Suydam (Eds.), Developing computational skills. National Council of Teachers of Mathematics.
  • Glaser, R. (1991). The maturing of the relationship between the science of learning and cognition and educational practice. Learning and Instruction, 1(2), 129-144. https://doi.org/10.1016/0959-4752(91)90023-2
  • Gülkılık, H., Uğurlu, H. H., and Yürük, N. (2015). Examining students’ mathematical understanding of geometric transformations using the Pirie-Kieren model. Educational Sciences: Theory & Practice, 15(6), 1531-1548.
  • Hakim, F., and Murtafiah, M. (2022, 8 December). Undergraduate students’ levels of understanding in solving mathematical proof problem: The use of Pirie-Kieren theory. In AIP Conference Proceedings (Vol. 2575, No. 1). AIP Publishing. https://doi.org/10.1063/5.0108699
  • Healy, L., and Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428. https://doi.org/10.2307/749651
  • Kamii, C., and Clark, F. B. (1995). Equivalent fractions: Their difficulty and educational implications. The Journal of Mathematical Behavior, 14(4), 365-378. https://doi.org/10.1016/0732-3123(95)90035-7
  • Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Eds.), Number and measurement: Papers from a research workshop, (pp. 101-144). ERIC/SMEAC.
  • Kieren, T. E. (1981). Five faces of mathematical knowledge building. Department of Secondary Education, University of Alberta.
  • Kilpatrick, J., Swafford, J. O., and Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
  • Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959
  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for Research. In F. K. Lester (Eds.), Second handbook of research on mathematics teaching and learning (pp. 629-667). National Council of Teachers of Mathematics.
  • Lamon, S. J. (2020). Teaching fractions and ratios for understanding: Essential content knowledge and ınstructional strategies for teachers (4. Ed.). Newgen Publishing UK.
  • Lawan, A. (2011, 11-15 Jully). Growth of students’understanding of part-whole sub-construct of rational number on the layers of Pirie-Kieren theory [Long Papers]. 17. National Congress of the Association for Mathematics Education of South Africa (AMESA) (pp. 69-80), University of the Witwatersrand, Johannesburg.
  • López-Martín, M. D. M., Aguayo-Arriagada, C. G., and García López, M. D. M. (2022). Preservice elementary teachers’ mathematical knowledge on fractions as operator in word problems. Mathematics, 10(3), 423. https://doi.org/10.3390/math10030423
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understandings of fundamental mathematics in China and the United States. Lawrence Erlbaum.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for research in mathematics education, 26(5), 422-441. https://doi.org/10.2307/749431
  • Martin, L. C. (2008). Folding back and the dynamical growth of mathematical understanding: Elaborating the Pirie-Kieren Theory. The Journal of Mathematical Behavior, 27(1), 64-85. https://doi.org/10.1016/j.jmathb.2008.04.001
  • Martin, W. G., and Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41-51. https://doi.org/10.2307/749097
  • Martinie, S. L. (2007). Middle school rational number knowledge [Unpublished doctoral dissertation]. Kansas State University.
  • Miles, M. B., and Huberman, A. M. (1994). Qualitative data analysis. Sage.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı ve kılavuzu. MEB Basımevi.
  • Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. https://doi.org/10.3102/0002831208320851
  • Niven, I. (1961). Numbers: Rational and irrational. Mathematical Association of America.
  • Nopa, J. R., Suryadi, D., and Hasanah, A. (2019, February). The 9th grade students’ mathematical understanding in problem solving based on Pirie-Kieren theory. In Journal of Physics: Conference Series (Vol. 1157, No. 4), IOP Publishing. https://doi.org/10.1088/1742-6596/1157/4/042122
  • Peñaloza, J. A., and Vásquez, F. M. R. (2022). Understanding ratio through the Pirie-Kieren model. Acta Scientiae, 24(4), 24-56. https://doi.org/10.17648/acta.scientiae.6826
  • Pinto, M., and Tall, D. (1996). Student teachers' conceptions of the rational numbers. In Published in Proceedings of PME 20 (Vol. 4, pp. 139-146), Valencia.
  • Pirie, S., and T. Kieren (1991). A dynamic theory of mathematical understanding: Some features and implications. Paper presented at the Annual Meeting of the American Educational Research Association.
  • Pirie, S., and Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it?. Educational Studies in Mathematics, 26(2/3), 165-190. https://doi.org/10.1007/BF01273662
  • Pouta, M., Lehtinen, E., and Palonen, T. (2021). Student teachers’ and experienced teachers’ professional vision of students’ understanding of the rational number concept. Educational Psychology Review, 33, 109-128. https://doi.org/10.1007/s10648-020-09536-y
  • Reys, R. E., Reys, B. J., McIntosh, A., Emanuelsson, G., Johansson, B., and Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan and the United States. School Science and Mathematics, 99(2), 61-70. https://doi.org/10.1111/j.1949-8594.1999.tb17449.x
  • Schoenfeld, A. H. (2013). Reflections on problem solving theory and practice. The Mathematics Enthusiast, 10(1), 9-34. https://doi.org/10.54870/1551-3440.1258
  • Simon, M. A. (2002). Focusing on key developmental understandings in mathematics. Learning, 24, 990.
  • Simon, M. A. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical Thinking & Learning, 8(4), 359-371. https://doi.org/10.1207/s15327833mtl0804_1
  • Stafylidou, S., and Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015
  • Star, J. R., and Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169-181. https://doi.org/10.1080/14926156.2013.784828
  • Syafiqoh, N., Amin, S. M., and Siswono, T. Y. E. (2018, November). Analysis of student’s understanding of exponential concept: a perspective of Pirie-Kieren theory. In Journal of Physics: Conference Series (Vol. 1108, No. 1, p. 012022), IOP Publishing. https://doi.org/10.1088/1742-6596/1108/1/012022
  • Şengül, S., and Argat, A. (2015). The analysis of understanding factorial concept processes of 7th grade students who have low academic achievements with Pirie Kieren theory. Procedia-Social and Behavioral Sciences, 197, 1263-1270. https://doi.org/10.1016/j.sbspro.2015.07.398
  • Şengül, S., and Göktepe Yıldız, S. (2016). An examination of the domain of multivariable functions using the Pirie-Kieren model. Universal Journal of Educational Research, 4(7), 1533-1544. https://doi.org/10.13189/ujer.2016.040706
  • Şengül, S., Kaba, Y., and Argat, A. (2016, 13-15 July). The analyis of understanding factorial concept processes of 7th grade students who have high academic achievements with Pirie-Kieren theory [Tam metin bildiri]. International Conference on New Horizons in Education (INTE 2016) (pp. 730-737).
  • Towers, J. M. (1998). Teachers' interventions and the growth of students' mathematical understanding [Unpublished PhD thesis]. The University of British Columbia.
  • Trance, N. J. C. (2017). Evaluating preservice teacher cognition over student mathematics misconception. The Science and Technology Research Journal, 12(1), 97-108.
  • Valcarce, M. C., Martín, M. L. D., Astudillo, M. T. G., and Pérez, M. C. M. (2013). Comprensión del concepto de serie numérica a través del modelo de Pirie y Kieren. Enseñanza de Las Ciencias. Revista de İnvestigación y Experiencias Didácticas, 31(3), 135-154. https://doi.org/10.5565/rev/ec/v31n3.963
  • Vula, E., and Kingji-Kastrati, J. (2018). Pre-service teacher procedural and conceptual knowledge of fractions. In G. J. Stylianides and K. Hino (Eds.), Research advances in the mathematical education of pre-service elementary teachers, (pp. 111-123). Springer.
  • Warner, L. B. (2008). How do students’ behaviors relate to the growth of their mathematical ideas?. The Journal of Mathematical Behavior, 27(3), 206-227. https://doi.org/10.1016/j.jmathb.2008.07.002
  • Wearne, D., and Hiebert, J. (1988). Constructing and using meaning for mathematical symbols: The case of decimal fractions. In J. Hiebert and M. Behr (Eds.), Number concepts and operations in the middle grades, (pp. 220-235). NCTM, and Lawrence Erlbaum Associates.
  • Yao, X. (2020). Characterizing learners’ growth of geometric understanding in dynamic geometry environments: A perspective of the Pirie–Kieren theory. Digital Experiences in Mathematics Education, 6, 293-319. https://doi.org/10.1007/s40751-020-00069-1
  • Yetim, S., ve Alkan, R. (2010). İlköğretim 7. sınıf öğrencilerinin rasyonel sayılar ve bu sayıların sayı doğrusundaki gösterimleri konusundaki yaygın yanlışları ve kavram yanılgıları. Fen Bilimleri Dergisi, 11, 87-109.
  • Yin, R. K. (2009). Case study research: Design and methods (5. Ed.). Sage.

Öğretmen Adaylarının Rasyonel Sayılara İlişkin Zihin Haritaları: Pirie-Kieren Teorisi

Yıl 2024, Cilt: 53 Sayı: 241, 133 - 164, 01.02.2024
https://doi.org/10.37669/milliegitim.1141497

Öz

Bu araştırmanın amacı, ortaokul matematik öğretmeni adaylarının, rasyonel sayılar kavramına ilişkin matematiksel anlama düzeylerinin Pirie-Kieren teorisine göre incelenmesidir. Araştırma, İstanbul ilindeki bir üniversitenin ilköğretim matematik öğretmenliği programında öğrenim görmekte olan üç öğretmen adayı ile yürütülmüştür. Öğretmen adayları “Matematiğin Temelleri”, “Ortaokul Matematik Öğretim Programları” ve “Sayıların Öğretimi” derslerini almış, akademik başarıları yüksek ve iyi düzeyde olan iletişim becerileri yüksek, gönüllü öğretmen adayları arasından seçilmiştir. Araştırma, durum çalışması desenine göre tasarlanmıştır. Veriler, araştırmacılar tarafından geliştirilmiş rasyonel sayılar kavramına ilişkin dört açık uçlu sorudan oluşan rasyonel sayılar kavram testi ve yarı-yapılandırılmış görüşmelerle toplanmıştır. Elde edilen veriler, Pirie-Kieren anlama katmanlarına göre analiz edilmiştir. Araştırmada öğretmen adaylarının ağırlıklı olarak “görüntü oluşturma” katmanında bulundukları belirlenmiştir. Yarı-yapılandırılmış görüşme sonuçları ile beraber süreç göz önüne alındığında ise öğretmen adaylarının “görüntüye sahip olma”, “özelliği fark etme” ve “soyutlama” katmanları arasında ileri geri katlamalar yaparak bilgilerini yapılandırma çabası gösterdikleri tespit edilmiştir. Ayrıca, öğretmen adaylarının Pirie-Kieren teorik modeline göre zihin haritaları oluşturularak sonuçlar tartışılmıştır. Elde edilen sonuçlara göre bu alandaki araştırmacılar için öneriler geliştirilmiştir.

Kaynakça

  • Alajmi, A., and Reys, R. (2007). Reasonable and reasonableness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65(5), 77-94. https://doi.org/10.1007/s10649-006-9042-4
  • Behr, M., Lesh, R., Post, T., and Silver E. (1983). Rational number concepts. In R. Lesh and M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91-125). Academic Press.
  • Borgen, K. L., and Manu, S. S. (2002). What do students really understand?. The Journal of Mathematical Behavior, 21(2), 151-165. https://doi.org/10.1016/S0732-3123(02)00115-3
  • Brownell, W. A. (1947). The place of meaning in the teaching of arithmetic. Elementary School Journal, 47(5), 256-265. https://doi.org/10.1086/462322
  • Coe, R., and Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20, 41-53. https://doi.org/10.1080/0141192940200105
  • Çelik, B. (2006). Temel matematik. Nobel.
  • Düzenli-Gökalp, N., and Bulut, S. (2018). A new form of understanding maps: Multiple representations with Pirie and Kieren model of understanding. International Journal of Innovation in Science and Mathematics Education, 26(6), 1-21.
  • Düzenli-Gökalp, N., and Sharma, M. D. (2010). A study on addition and subtraction of fractions: The use of Pirie and Kieren model and hands-on activities. Procedia-Social and Behavioral Sciences, 2(2), 5168-5171. https://doi.org/10.1016/j.sbspro.2010.03.840
  • Ellerbruch, L. W., and Payne, J. N. (1978). A teaching sequence for initial fraction concepts through the addition of unlike fractions. In M. Suydam (Eds.), Developing computational skills. National Council of Teachers of Mathematics.
  • Glaser, R. (1991). The maturing of the relationship between the science of learning and cognition and educational practice. Learning and Instruction, 1(2), 129-144. https://doi.org/10.1016/0959-4752(91)90023-2
  • Gülkılık, H., Uğurlu, H. H., and Yürük, N. (2015). Examining students’ mathematical understanding of geometric transformations using the Pirie-Kieren model. Educational Sciences: Theory & Practice, 15(6), 1531-1548.
  • Hakim, F., and Murtafiah, M. (2022, 8 December). Undergraduate students’ levels of understanding in solving mathematical proof problem: The use of Pirie-Kieren theory. In AIP Conference Proceedings (Vol. 2575, No. 1). AIP Publishing. https://doi.org/10.1063/5.0108699
  • Healy, L., and Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428. https://doi.org/10.2307/749651
  • Kamii, C., and Clark, F. B. (1995). Equivalent fractions: Their difficulty and educational implications. The Journal of Mathematical Behavior, 14(4), 365-378. https://doi.org/10.1016/0732-3123(95)90035-7
  • Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Eds.), Number and measurement: Papers from a research workshop, (pp. 101-144). ERIC/SMEAC.
  • Kieren, T. E. (1981). Five faces of mathematical knowledge building. Department of Secondary Education, University of Alberta.
  • Kilpatrick, J., Swafford, J. O., and Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
  • Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959
  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for Research. In F. K. Lester (Eds.), Second handbook of research on mathematics teaching and learning (pp. 629-667). National Council of Teachers of Mathematics.
  • Lamon, S. J. (2020). Teaching fractions and ratios for understanding: Essential content knowledge and ınstructional strategies for teachers (4. Ed.). Newgen Publishing UK.
  • Lawan, A. (2011, 11-15 Jully). Growth of students’understanding of part-whole sub-construct of rational number on the layers of Pirie-Kieren theory [Long Papers]. 17. National Congress of the Association for Mathematics Education of South Africa (AMESA) (pp. 69-80), University of the Witwatersrand, Johannesburg.
  • López-Martín, M. D. M., Aguayo-Arriagada, C. G., and García López, M. D. M. (2022). Preservice elementary teachers’ mathematical knowledge on fractions as operator in word problems. Mathematics, 10(3), 423. https://doi.org/10.3390/math10030423
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understandings of fundamental mathematics in China and the United States. Lawrence Erlbaum.
  • Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for research in mathematics education, 26(5), 422-441. https://doi.org/10.2307/749431
  • Martin, L. C. (2008). Folding back and the dynamical growth of mathematical understanding: Elaborating the Pirie-Kieren Theory. The Journal of Mathematical Behavior, 27(1), 64-85. https://doi.org/10.1016/j.jmathb.2008.04.001
  • Martin, W. G., and Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41-51. https://doi.org/10.2307/749097
  • Martinie, S. L. (2007). Middle school rational number knowledge [Unpublished doctoral dissertation]. Kansas State University.
  • Miles, M. B., and Huberman, A. M. (1994). Qualitative data analysis. Sage.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı ve kılavuzu. MEB Basımevi.
  • Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. https://doi.org/10.3102/0002831208320851
  • Niven, I. (1961). Numbers: Rational and irrational. Mathematical Association of America.
  • Nopa, J. R., Suryadi, D., and Hasanah, A. (2019, February). The 9th grade students’ mathematical understanding in problem solving based on Pirie-Kieren theory. In Journal of Physics: Conference Series (Vol. 1157, No. 4), IOP Publishing. https://doi.org/10.1088/1742-6596/1157/4/042122
  • Peñaloza, J. A., and Vásquez, F. M. R. (2022). Understanding ratio through the Pirie-Kieren model. Acta Scientiae, 24(4), 24-56. https://doi.org/10.17648/acta.scientiae.6826
  • Pinto, M., and Tall, D. (1996). Student teachers' conceptions of the rational numbers. In Published in Proceedings of PME 20 (Vol. 4, pp. 139-146), Valencia.
  • Pirie, S., and T. Kieren (1991). A dynamic theory of mathematical understanding: Some features and implications. Paper presented at the Annual Meeting of the American Educational Research Association.
  • Pirie, S., and Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it?. Educational Studies in Mathematics, 26(2/3), 165-190. https://doi.org/10.1007/BF01273662
  • Pouta, M., Lehtinen, E., and Palonen, T. (2021). Student teachers’ and experienced teachers’ professional vision of students’ understanding of the rational number concept. Educational Psychology Review, 33, 109-128. https://doi.org/10.1007/s10648-020-09536-y
  • Reys, R. E., Reys, B. J., McIntosh, A., Emanuelsson, G., Johansson, B., and Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan and the United States. School Science and Mathematics, 99(2), 61-70. https://doi.org/10.1111/j.1949-8594.1999.tb17449.x
  • Schoenfeld, A. H. (2013). Reflections on problem solving theory and practice. The Mathematics Enthusiast, 10(1), 9-34. https://doi.org/10.54870/1551-3440.1258
  • Simon, M. A. (2002). Focusing on key developmental understandings in mathematics. Learning, 24, 990.
  • Simon, M. A. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical Thinking & Learning, 8(4), 359-371. https://doi.org/10.1207/s15327833mtl0804_1
  • Stafylidou, S., and Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015
  • Star, J. R., and Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169-181. https://doi.org/10.1080/14926156.2013.784828
  • Syafiqoh, N., Amin, S. M., and Siswono, T. Y. E. (2018, November). Analysis of student’s understanding of exponential concept: a perspective of Pirie-Kieren theory. In Journal of Physics: Conference Series (Vol. 1108, No. 1, p. 012022), IOP Publishing. https://doi.org/10.1088/1742-6596/1108/1/012022
  • Şengül, S., and Argat, A. (2015). The analysis of understanding factorial concept processes of 7th grade students who have low academic achievements with Pirie Kieren theory. Procedia-Social and Behavioral Sciences, 197, 1263-1270. https://doi.org/10.1016/j.sbspro.2015.07.398
  • Şengül, S., and Göktepe Yıldız, S. (2016). An examination of the domain of multivariable functions using the Pirie-Kieren model. Universal Journal of Educational Research, 4(7), 1533-1544. https://doi.org/10.13189/ujer.2016.040706
  • Şengül, S., Kaba, Y., and Argat, A. (2016, 13-15 July). The analyis of understanding factorial concept processes of 7th grade students who have high academic achievements with Pirie-Kieren theory [Tam metin bildiri]. International Conference on New Horizons in Education (INTE 2016) (pp. 730-737).
  • Towers, J. M. (1998). Teachers' interventions and the growth of students' mathematical understanding [Unpublished PhD thesis]. The University of British Columbia.
  • Trance, N. J. C. (2017). Evaluating preservice teacher cognition over student mathematics misconception. The Science and Technology Research Journal, 12(1), 97-108.
  • Valcarce, M. C., Martín, M. L. D., Astudillo, M. T. G., and Pérez, M. C. M. (2013). Comprensión del concepto de serie numérica a través del modelo de Pirie y Kieren. Enseñanza de Las Ciencias. Revista de İnvestigación y Experiencias Didácticas, 31(3), 135-154. https://doi.org/10.5565/rev/ec/v31n3.963
  • Vula, E., and Kingji-Kastrati, J. (2018). Pre-service teacher procedural and conceptual knowledge of fractions. In G. J. Stylianides and K. Hino (Eds.), Research advances in the mathematical education of pre-service elementary teachers, (pp. 111-123). Springer.
  • Warner, L. B. (2008). How do students’ behaviors relate to the growth of their mathematical ideas?. The Journal of Mathematical Behavior, 27(3), 206-227. https://doi.org/10.1016/j.jmathb.2008.07.002
  • Wearne, D., and Hiebert, J. (1988). Constructing and using meaning for mathematical symbols: The case of decimal fractions. In J. Hiebert and M. Behr (Eds.), Number concepts and operations in the middle grades, (pp. 220-235). NCTM, and Lawrence Erlbaum Associates.
  • Yao, X. (2020). Characterizing learners’ growth of geometric understanding in dynamic geometry environments: A perspective of the Pirie–Kieren theory. Digital Experiences in Mathematics Education, 6, 293-319. https://doi.org/10.1007/s40751-020-00069-1
  • Yetim, S., ve Alkan, R. (2010). İlköğretim 7. sınıf öğrencilerinin rasyonel sayılar ve bu sayıların sayı doğrusundaki gösterimleri konusundaki yaygın yanlışları ve kavram yanılgıları. Fen Bilimleri Dergisi, 11, 87-109.
  • Yin, R. K. (2009). Case study research: Design and methods (5. Ed.). Sage.
Toplam 56 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik Eğitimi
Bölüm Araştırma Makalesi
Yazarlar

Sare Şengül 0000-0002-1069-9084

Büşra Kıral Demir 0000-0001-5816-6183

Yayımlanma Tarihi 1 Şubat 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 53 Sayı: 241

Kaynak Göster

APA Şengül, S., & Kıral Demir, B. (2024). Öğretmen Adaylarının Rasyonel Sayılara İlişkin Zihin Haritaları: Pirie-Kieren Teorisi. Milli Eğitim Dergisi, 53(241), 133-164. https://doi.org/10.37669/milliegitim.1141497