P4C Practices in Mathematics Education: The Case of Math Stories

Year 2023, Volume: 22 Issue: 3, 515 - 558, 20.10.2023

İbrahim Çetin , Hatice Çetin

https://doi.org/10.20981/kaygi.1338302

Abstract

This study aims to examine the questions that middle school students formulated during "Philosophy for Children (P4C)" activities. The research is a case study from qualitative research designs. The participants of the study were 7th grade middle school students from a public school. Within the scope of the research, five math story videos were shown to the students as stimuli, and then the students were asked to form questions about these videos and then discuss them. Within the scope of the research, 97 valid questions were generated. These questions were analyzed using an indicator developed by the researchers that included four different categories. These categories are "Basic Knowledge and Recall", "Cause and Effect Analysis", "Critical Thinking and Evaluation" and "Empathizing and Expressing Thoughts". The categories emerged as the questions were analyzed during the research. According to the findings, the questions in the first category are questions related to students' ability to understand and remember basic information, such as who, what, where, when, and how. Questions in the second category were more related to students' ability to understand cause and effect relationships and required students to think more deeply and analytically. In the third category of the study, it was found that students questioned the topics with a critical perspective and discussed different possible scenarios. Finally, in the fourth category, students generated questions related to their ability to express their own thoughts and to understand and accept different perspectives. When the students started the activities, they produced questions mostly in the knowledge and recall category, but as the activities progressed, it was observed that they used different thinking skills such as empathizing and critical thinking to produce questions in this direction and that these skills improved over time. In conclusion, the study provides an important perspective to understand middle school students' question generation skills and thought processes during P4C activities.

Keywords

Philosophy for Children, History of Mathematics, Questions, Critical Thinking, Empathy

Matematik Eğitiminde P4C Uygulamaları: Matematik Hikayeleri Örneği

Abstract

Bu araştırma, ortaokul öğrencilerinin "Çocuklar için Felsefe (P4C)" etkinlikleri sırasında oluşturdukları soruları incelemeyi amaçlamaktadır. Araştırma nitel araştırma desenlerinden durum çalışmasıdır. Araştırmanın katılımcıları bir devlet okulunda öğrenim göre ortaokul 7. sınıf öğrencileridir. Araştırma kapsamında, beş adet matematik hikayesi videosu öğrencilere uyaran olarak izletilmiş daha sonrasında öğrencilerden izledikleri bu videolara yönelik sorular oluşturmalarını ve akabinde tartışmaları istenmiştir. Araştırma kapsamında 97 adet geçerli soru üretilmiştir. Öğrencilerin oluşturdukları bu sorular, araştırmacılar tarafından geliştirilen dört farklı kategori içeren bir gösterge analiz edilmiştir. Bu kategoriler; "Temel Bilgi ve Hatırlama”, “Neden-Sonuç Analizi” Eleştirel Düşünme ve Değerlendirme” ve “Empati Kurma ve Düşüncelerini İfade Etme” dir. Kategoriler araştırma süresince soruları analiz ettikçe ortaya çıkmıştır. Bulgulara göre, ilk kategorideki sorular öğrencilerin temel bilgileri anlama ve hatırlama yeteneklerine yönelik; kim, ne, nerede, ne zaman ve nasıl gibi sorulardır. İkinci kategorideki sorular daha çok neden-sonuç ilişkilerini anlama becerileri ile ilgili olup, öğrencilerin daha derinlikli ve analitik düşünmelerini gerektirmiştir. Araştırmanın üçüncü kategorisinde, öğrencilerin eleştirel bir bakış açısı ile konuları sorguladığı ve olabilecek farklı senaryoları ele aldığı tespit edilmiştir. Son olarak, dördüncü kategoride öğrencilerin kendi düşüncelerini ifade etme ve farklı bakış açılarını anlama ve kabul etme yetenekleri ile ilgili sorular ürettikleri tespit edilmiştir. Öğrenciler etkinliklere başladığında daha çok bilgi ve hatırlama kategorisinde sorular üretirken etkinlikler ilerledikçe empati kurma, eleştirel düşünme gibi farklı düşünce becerilerini kullanarak bu yönde sorular ürettikleri ve bu becerilerinin zamanla geliştiği gözlemlenmiştir. Sonuç olarak, araştırma ortaokul öğrencilerinin P4C etkinlikleri sırasında soru üretme becerilerini ve düşünce süreçlerini anlamak için önemli bir perspektif sunmaktadır.

Keywords

Çocuklar için Felsefe, Matematik Tarihi, Soru Sorma, Eleştirel Düşünme, Empati

References

• Akkocaoğlu Çayır, N., ve Akkoyunlu, B. (2016). Çocuklar için felsefe eğitimi üzerine nitel bir araştırma. Turkish Online Journal of Qualitative Inquiry. 7(2), 97. https://doi.org/10.17569/tojqi.91449
• Alexander, M. E., Commander, N., Greenberg, D., & Ward, T. (2010). Using the four-questions technique to enhance critical thinking in online discussions. Journal of Online Learning and Teaching, 6(2), 409-415. https://jolt.merlot.org/vol6no2/alexander_0610.pdf
• Anderson, R. C., & Pearson, P. D. (1984). A schema-theoretic view of basic processes in reading comprehension. In P. D. Pearson, R. Barr, M. L. Kâmil ve P. Mosenthal (Eds.), Handbook of reading research, 255–291. New York: Longman. https://files.eric.ed.gov/fulltext/ED239236.pdf
• Barnett, J. E., & Francis, A. L. (2012). Using higher order thinking questions to foster critical thinking: A classroom study. Educational Psychology, 32(2), 201-211. https://doi.org/10.1080/01443410.2011.638619
• Barrow, W. (2010). Dialogic, participation and the potential for philosophy for children. Thinking Skills and Creativity, 5(2), 61–69. https://doi.org/10.1016/j.tsc.2010.01.002
• Bogdan, R., & Biklen, S. (1998). Introduction to qualitative research in education. England: Pearson.
• Braund, M. (2009). Talk in primary science: A method to promote productive and contextualised group discourse. Education 3-13, 37(4), 385–397. https://doi.org/10.1080/03004270903099876
• Brown, A.L., & Campione, J. C. (1994). Guided discovery in a community of learners, in K. McGilly (ed.), Classroom Lessons: Integrating Cognitive Theory and Classroom Practice, MIT Press, Cambridge, MA, 229–270.
• Brune, M., & Brune-Cohrs, U. (2006). Theory of mind—evolution, ontogeny, brain mechanisms and psychopathology. Neuroscience & Biobehavioral Reviews, 30(4), 437-455. https://doi.org/10.1016/j.neubiorev.2005.08.001
• Chang, Y. Y., & Chiou, W. (2015). Means yield to ends in weight loss: focusingon ‘how’ versus ‘why’ aspects of losing weight can lead to poorer regulation ofdietary practices. J. Acad. Nutr. Dietetics 115, 1387–1391. https://doi.org/10.1016/j.jand.2015.02.032
• Chin, C., Brown, D. E., & Bruce, B. C. (2002). Student-generated questions: A meaningful aspect of learning in science. Journal of Research in Science Teaching, 24(5), 521–549. https://doi.org/10.1080/09500690110095249
• Chiou, W., Wu, W., & Chang, M. (2013). Think abstractly, smoke less: abrief construal-level intervention can promote self-control, leading to reducedcigarette consumption among current smokers. Addiction 108, 985–992. https://doi.org/10.1111/add.12100
• Cleary, J. P. (2011). The Role of philosophy for children's community of philosophical ınquiry in critical media literacy (Unpublished Doctoral Dissertation), Montclair State University, New Jersey. Erişim Tarihi: 14.07.2023 (https://digitalcommons.montclair.edu/etd/262/).
• Cunningham, R., & Smith, J. (2012). P4C in mathematics. Philosophy for children through the secondary curriculum, Ed: Lewis L; Chandley N Pages: 68-91.
• Daniel, M. (2011). Philosophy, Critical Thinking and Philosophy for Children. Educational Philosophy and Theory, 5(43), 415-435. https://doi.org/10.1111/j.1469-5812.2008.00483.x
• Daniel, M. F., Gagnon, M., & Auriac-Slusarczyk, E. (2016). Dialogical critical thinking in kindergarten and elementary school: Studies on the impact of philosophical praxis in pupils. In the Routledge İnternational Handbook of Philosophy for Children, 268-276. Routledge. https://doi.org/10.4324/9781315726625
• Dawes, L. (2004). Talk and learning in classroom science. International Journal of Science Education, 26(6), 677–695. https://doi.org/10.1080/0950069032000097424
• DeWaelsche, S. A. (2015). Critical thinking, questioning and student engagement in Korean university English courses. Linguistics and Education, 32, 131-147. https://doi.org/10.1016/j.linged.2015.10.003
• Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science & Education, 10, 391-408. https://doi.org/10.1023/A:1011205014608
• Freitas, A. L., Gollwitzer, P., & Trope, Y. (2004). The influence of abstract and concrete mindsets on anticipating and guiding others' self-regulatory efforts. Journal of Experimental Social Psychology, 40(6), 739-752. https://doi.org/10.1016/j.jesp.2004.04.003
• Fujita, K., Trope, Y., & Liberman, N. (2006). The role of mental construalin self-control. Social Psychology and Economics, eds D. DeCremer, M. Zeelenberg, and J. K. Murnighan (New York, NY: Sage), 193–211. (17). https://doi.org/10.4324/9780203726594
• Gorard, S., Siddiqui, N., & See, B. H. (2015). Philosophy for children: Evaluation report and executive summary. Education Endowment Foundation. Erişim Tarihi: 18.08.2023 (https://files.eric.ed.gov/fulltext/ED581147.pdf).
• Hakkarainen, K., & Sintonen, M. (2002). The interrogative model of inquiry and computer-supported collaborative learning. Science & Education, 11, 25-43. https://doi.org/10.1023/A:1013076706416
• Harper, K. A., Etkina, E., & Lin, Y. (2003). Encouraging and analyzing student questions in a large physics course: Meaningful patterns for instructors. Journal of Research in Science Teaching: The Official Journal of the National Association for Research in Science Teaching, 40(8), 776-791. https://doi.org/10.1002/tea.10111
• Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 33–46. https://doi.org/10.2307/749455
• Hernández, Y. P., & Díaz, L. A. M. (2021). El aprendizaje de las matemáticas desde filosofía para/con niños [Learning mathematics from philosophy for/with children]. Childhood & Philosophy, 17. Erişim Tarihi: 18.08.2023 (https://www.e-publicacoes.uerj.br/index.php/childhood/article/download/58661/40834).
• Hofstein, A., Shore, R., & Kipnis, N. (2004). Providing high school students with opportunities to develop learning skills in an inquiry-type laboratory. International Journal of Science Education, 26(1), 47–62. https://doi.org/10.1080/0950069032000070342
• Jaisnski, I., & Lewis, T. (2015). Community of infancy: Suspending the sovereignty of the teacher's voice. Journal of Philosophy of Education, 4(50), 538-553. https://doi.org/10.1111/1467-9752.12154
• Kefeli, İ., ve Kara, U. (2008). Çocukta Felsefi ve Eleştirel Düşünmenin Gelişimi. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 41 (1), 339-357. https://doi.org/10.1501/Egifak_0000000193
• King, A. (1994). Guiding knowledge construction in the classroom: Effects of teaching children how to question and how to explain. American Educational Research Journal, 31(2), 338-368. https://doi.org/10.3102/00028312031002338
• Lam, C. M. (2012). Continuing Lipman's and Sharp's pioneering work on philosophy for children: Using harry to foster critical thinking in hong kong students. Educational Research and Evaluation, 18(2), 187-203. https://doi.org/10.1080/13803611.2012.658669
• Lester, F. K., Garafalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behaviour. In D. B. Mcleod & V. M. Adams (Eds.), Affect and Mathematical Problem Solving, 75–88. New York, NY: Springer. http://dx.doi.org/10.1007/978-1-4612-3614-6
• Lewis, L., & Chandley, N. (Eds.). (2012). Philosophy for Children Through the Secondary Curriculum. Bloomsbury Publishing.
• Liberman, N., & Trope, Y. (1998). The role of feasibility and desirability considerations in near and distant future decisions: A test of temporal construal theory. Journal of personality and social psychology, 75(1), 5. https://doi.org/10.1037/0022-3514.75.1.5
• Lipman, M. (2011). Philosophy for children: Some assumptions and implications. Ethics in Progress, 2(1), 3-16. https://doi.org/10.14746/eip.2011.1.2
• Malboeuf-Hurtubise, C., Tomaso, C., Lefrançois, D., Mageau, G., Taylor, G., Either, M., … ve Leger-Goodes, T. (2021). Existential Therapy for Children: Impact of a Philosophy for Children Intervention on Positive and Negative Indicators of Mental Health in Elementary School Children. IJERPH, 23(18), 12332. https://doi.org/10.3390/ijerph182312332
• Marbach-Ad., G., & Sokolove, P. G. (2000). Can undergraduate biology students learn to ask higher level questions? Journal of Research in Science Teaching, 37(8), 854–870. https://doi.org/10.1002/1098-2736(200010)37:8<854: AID-TEA6>3.0.CO;2-5
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
• Mishra, P., & Brewer, W. F. (2003). Theories as a form of mental representation and their role in the recall of text information. Contemporary Educational Psychology. 28, 277–303. https://doi.org/10.1016/s0361-476x(02)00040-1
• Murris, K. (2008). Philosophy with children, the stingray and the educative value of disequilibrium. Journal of Philosophy of Education, 3-4(42), 667-685. https://doi.org/10.1111/j.1467-9752.2008.00640.x
• Murris K. S., (2017). P4C and picturebooks. Naji S. ve Hashim R. (eds.), In History, Theory and Practices of Philosophy for Children: International Perspectives. Routledge. https://doi.org/10.4324/9781315208732
• Oliveira, A. W. (2010). Developing elementary teachers’ understanding of the discourse structure of inquiry-based science classrooms. International Journal of Science and Mathematics Education, 8(2), 247–269. https://doi.org/10.1007/s10763-009-9172-0
• Palinscar, A. S., & Brown, A. L. (1984). Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction, 1(2), 117-175. Erişim Tarihi: 18.08.2023 (https://www.jstor.org/stable/3233567).
• Povey, H., Demissie, A., & Adams, G. (2019). What are the affordances and limitations of the philosophy for children (P4C) pedagogy for teaching and learning mathematics? Erişim Tarihi: 18.08.2023 (https://bsrlm.org.uk/wp-content/uploads/2019/07/BSRLM-CP-39-1-08.pdf ).
• Reznitskaya, A., & Anderson, R. C. (2006). Analyzing argumentation in rich, natural contexts. Informal Logic, 26(2), 175-198. https://doi.org/10.22329/il.v26i2.442
• R Reznitskaya, A., Glina, M., Carolan, B., Michaud, O., Rogers, J., & Sequeira, L. (2012). Examining transfer effects from dialogic discussions to new tasks and contexts. Contemporary Educational Psychology, 37(4), 288-306. https://doi.org/10.1016/j.cedpsych.2012.02.003
• Rowe, A. D., Bullock, P. R., Polkey, C. E., & Morris, R. G. (2001). Theory of mind'impairments and their relationship to executive functioning following frontal lobe excisions. Brain, 124(3), 600-616. https://doi.org/10.1093/brain/124.3.600
• Rumelhart, D. E. (1980). Schemata: The building blocks of cognition. In R. J. Spiro, B. C. Bruce, & W. F. Brewer (Eds.), Theoretical Issues in Reading and Comprehension, 33–58. Hillsdale, NJ: Erlbaum. https://doi.org/10.4324/9781315107493
• Scardamalia, M., & Bereiter, C. (1992). Text-based and knowledge based questioning by children. Cognition and Instruction. 9(3), 177-199. Erişim Tarihi: 18.08.2023 (https://www.jstor.org/stable/3233513).
• Sharp, A. M. (1987). What is a ‘community of inquiry'? Journal of Moral Education, 16(1), 37-45. https://doi.org/10.1080/0305724870160104.
• Sintonen, M. (1990), How to put questions to nature, in D. Knowles (ed.), Explanation and its Limits, Cambridge University Press, Cambridge, 267–284. https://doi.org/10.1017/S1358246100005142
• Slaughter, V., Dennis, M. J., & Pritchard, M. (2002). Theory of mind and peer acceptance in preschool children. British Journal of Developmental Psychology 20(4). 545–564. Wiley. https://doi.org/10.1348/026151002760390945
• Snelson, C. (2008). Web-based video in education: Possibilities and pitfalls. Proceedings of the Technology, Colleges and Community. Worldwide Online Conference (TCC) (pp. 214–221). Hawaii, Apr 15–1 Erişim Tarihi: 18.08.2023 (https://www.learntechlib.org/p/43828/.)
• Splitter, L. (2011). Identity, citizenship and moral education. Educational Philosophy and Theory, 43(5), 484-505. https://doi:10.1111/j.1469-5812.2009.00626.x
• Telaumbanua, Y. N., Dewi, I., & Simamora, E. (2023). Philosophy perspective of mathematics education as a field of knowledge. EDUTEC: Journal of Education And Technology, 6(3), 703-710. https://doi.org/10.29062/edu.v6i3.479
• Tian, S., & Liao, P. (2016). Philosophy for children with learners of english as a foreign language. JPS, 1(3). https://doi.org/10.21913/jps.v3i1.1299
• Topping, K. J., & Trickey, S. (2007). Collaborative philosophical enquiry for school children: Cognitive effects at 10–12 years. British Journal of Educational Psychology, 77(2), 271-288. https://doi.org/10.1348/000709906x105328
• Trickey, S., & Topping, K. (2013). Assessing the outcome of philosophical thinking with children. In S. Goering, N. Shudak & T. Wartenberg (Eds.), Philosophy in schools: An introduction for philosophers and teachers (pp. 288–298). Routledge. https://doi.org/10.4324/9780203082652
• Tunç, A. İ. (2017). Çocuklarla felsefe. Çocuk ve Medeniyet, 2(4), 71-90.
• United Nations (2022), Transforming education summit report, Erişim Tarihi: 07.10.2023 (https://www.un.org/en/transforming-education-summit)
• Wang, J. (2020). Creating moral winds and nurturing moral growth in a P4C classroom community in Taiwan. Journal of Philosophy in Schools, 1(7), 16. https://doi.org/10.46707/jps.v7i.107
• Webb, N. M. (2009). The teacher's role in promoting collaborative dialogue in the classroom. British Journal of Educational Psychology, 79(1), 1-28. https://doi.org/10.1348/000709908X380772
• Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76, 329-344. https://doi.org/10.1007/s10649-010-9292-z
• Wellman, H. M., Cross, D., & Watson, J. (2001). Meta-analysis of theory of mind development: The truth about false belief. Child Development, 72(3), 655-684. https://doi.org/10.1111/1467-8624.00304
• Wu, C. (2021). Training teachers in China to use the philosophy for children approach and its impact on critical thinking skills: a pilot study. Education Sciences, 5(11), 206. https://doi.org/10.3390/educsci11050206
• Yıldırım, A., ve Şimşek, H. (2011). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.
• Youmans, G. L. (2004). Theory of mind performance of individuals with alzheimer-type dementia profiles (Doctoral dissertation, The Florida State University). Erişim Tarihi: 18.08.2023 (http://purl.flvc.org/fsu/fd/FSU_migr_etd-0866)
• Zekâ Var. (2023a, 5 Ağustos). Matematik Hikayeleri 1. Bölüm Mısırda Doğan Güneş [Video]. Youtube. https://www.youtube.com/watch?v=IPct6tRG4Cc&list=PLZS1HXr9JNQ_CzE9_wRsz9ofJERw0ZN2o&index=1
• Zekâ Var. (2023b, 5 Ağustos). Matematik Hikayeleri 2. Bölüm Sayıların Babası Pisagor [Video]. Youtube. https://www.youtube.com/watch?v=wXqC7aj3ZCQ&list=PLZS1HXr9JNQ_CzE9_wRsz9ofJERw0ZN2o&index=2
• Zekâ Var. (2023c, 5 Ağustos). Matematik Hikayeleri 6. Bölüm Leonardo Fibonacci [Video]. Youtube. https://www.youtube.com/watch?v=VY8JpUCG8A0&list=PLZS1HXr9JNQ_CzE9_wRsz9ofJERw0ZN2o&index=6 Zekâ Var. (2023d, 5 Ağustos). Matematik Hikayeleri 14. Bölüm Sıfır [Video]. Youtube. https://www.youtube.com/watch?v=4qnCxDSk6vg&list=PLZS1HXr9JNQ_CzE9_wRsz9ofJERw0ZN2o&index=15
• Zekâ Var. (2023e, 5 Ağustos). Matematik Hikayeleri 29. Bölüm Eratosthenes [Video]. Youtube. https://www.youtube.com/watch?v=djerIzIdVJs&list=PLZS1HXr9JNQ_CzE9_wRsz9ofJERw0ZN2o&index=33
• Zhang, J., Scardamalia, M., Lamon, M., Messina, R., & Reeve, R. (2007). Socio-cognitive dynamics of knowledge building in the work of 9- and 10-year-olds. Educational Technology Research and Development, 55, 117–145. https://doi.org/10.1007/s11423-006-9019-0
• Zulkifli, H., ve Hashim, R. (2020). Philosophy for children (P4C) in improving critical thinking in a secondary moral education class. IJLTER, 2(19), 29-45. https://doi.org/10.26803/ijlter.19.2.3