Research Article
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Reflection of Preservice Teachers’ Thoughts about Connecting Mathematics and Real Life Situations on Their Mathematics Learning Activities

Year 2018, Volume: 31 Issue: 1, 177 - 206, 01.06.2018
https://doi.org/10.19171/uefad.450083

Abstract

The importance of constructing connections has been emphasized in many academic works, learning models, standards and teaching programs that illuminates teaching and learning of mathematics. In addition to the connection, the importance of a learning unit which is named as activity has been emphasized in many recent works and thoughts related to teaching and learning of mathematics. This situation moves the activities and activity based learning into the center of mathematics education. In mathematics education, mathematics learning activities are the most appropriate learning unit that could be construct connections with it. In this context, it is thought that it would be beneficial to explain what the connection is and how to construct connection using the existing or developed activities. The main purpose of this study is to identify pre-service secondary mathematics teachers’ (PSMTs) thoughts about what the real life connection is and how this connection could be constructed, and to examine how PSMTs reflected their thoughts on a group of mathematics learning activities that are connected with real life situations. In this work, the case study, which is one of the qualitative research paradigms, was used. The study was conducted with 33 (11 group) PSMTs who had been educated for 4th years in a public university. The PMSTs were asked to write free writings related to what the real life connection is and how to construct real life connections and to develop mathematics learning activities that are connected with real life situations. The collected data was analyzed using content analysis method. It is found that while PSMTs defended the necessity and importance of the real life connection, they had difficulty in reflecting this on mathematics learning activities. 

References

  • Açıl, E. (2011). İlköğretim öğretmenlerinin etkinlik algısı ve uygulanışına ilişkin görüşleri. Yayınlanmamış yüksek lisans tezi, Gaziantep Üniversitesi Sosyal Bilimler Enstitüsü.
  • Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the learning of Mathematics, 14(3), 24-35.
  • Aslan, B. (2010). Matematiksel etkinliklerin uygulanması sırasında ortaya çıkan öğretmen ve öğrenci rolleri. Yayınlanmamış yüksek lisans tezi, Gaziantep Üniversitesi Sosyal Bilimler Enstitüsü. Australian Curriculum Assessment and Reporting Authority (ACARA). (2008). National Assessment Program (NAP). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA267
  • Ball, D. L. (1991). Research on teaching mathematics: Making subject-matter knowledge part of the education. In J. Brophy (Ed.), Advances in research on teaching (Vol. 2, pp. 1–48). Greenwich, CT: JAI Press.
  • Bamberger, H. J., and Oberdorf, C. (2007). Introduction to connections. Portsmouth, NH: Heinemann.
  • Becker, J. P., and Shimada, S. (1997). The Open-Ended Approach: A New Proposal for Teaching Mathematics. National Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA 20191-1593.
  • Berelson, B. (1952). Content analysis in communication research. Glenco, III: Free Press.
  • Boaler, J. (1993). Encouraging the transfer of ‘school’ mathematics to the ‘real world’through the integration of process and content, context and culture. Educational studies in mathematics, 25(4), 341-373.
  • Boaler, J., and Humphreys, C. (2005). Connecting mathematical ideas: Middle school video cases to support teaching and learning (Vol. 1). Heinemann Educational Books.
  • Bonotto, C. (2001). How to connect school mathematics with students’ out-ofschool knowledge. Zentralblatt für Didaktik der Mathematik, 33(3), 75–84.
  • Bossé, M. J. (2003). The beauty of" and" and" or": Connections within mathematics for students with learning differences. Mathematics and Computer Education, 37(1), 105.
  • Brousseau, G. (1997). Theory of didactical situations in mathematics 1970-1990, [Edited and translated M. Cooper, N. Balacheff, R. Sutherland and V. Warfield.] Dordrecht: Kluwer Academic Publishers.
  • Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections (Doctoral dissertation, Faculty of Education-Simon Fraser University).
  • Caine, R. N., and Caine, G. (1990). Understanding a brain-based approach to learning and teaching. Educational Leadership, 48(2), 66-70.
  • Carpenter, T. P., and Lehrer, R. (1999). Teaching and learning mathematics with understanding. Mathematics classrooms that promote understanding, 1932.
  • Chapman, O. (2012). Challenges in mathematics teacher education. Journal of Mathematics Teacher Education, 15(4), 263-270.
  • Chapman, L. R. (Ed.). (2013). The process of learning mathematics: Pergamon International Library of Science, Technology, Engineering and Social Studies. Elsevier.
  • Christiansen, B., and Walther, G. (1986). Task and activity. In Perspectives on mathematics education (pp. 243-307). Springer Netherlands.
  • Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • Coxford, A. F. (1995). The case for connections. Connecting mathematics across the curriculum, 3-12.
  • Creswell J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Los Angeles (CA): Sage Publications.
  • Czerniak, C. M., Weber, W. B., Sandmann, A., and Ahern, J. (1999). A literature review of science and mathematics integration. School Science and Mathematics, 99(8), 421-430.
  • Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159– 199.
  • Eli, J. A., (2009). An exploratory mixed methods study of prospective middle grades teachers’ mathematical connections while completing investiagtive tasks in geometry. Yayınlanmamış Doktora Tezi, University of Kentucky, Lexington, KY.
  • Evitts, T. A., (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula. Yayınlanmamış Doktora Tezi, Pennsylvania State University College of Education.
  • Freudenthal, H., (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1, 3-8.
  • Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219.
  • Gerofsky, S. (2006). Communication: simulation, reality, and mathematical word problems. For the Learning of Mathematics, 26(2), 30-32.
  • Herbst, P. (2008). The teacher and the task. In O. Figuras, J. L. Cortina, S. Alatorre, T. Rojano, & A Sepulveda (Eds.), Proceedings of the 32nd Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 125- 133). Morelia: PME.
  • Hiebert, J., and Carpenter, T., (1992). Learning and Teaching with Understanding. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 65–97). New York: Macmillan.
  • Horoks, J., and Robert, A. (2007). Tasks designed to highlight task-activity relationships. Journal of Mathematics Teacher Education, 10(4-6), 279287.
  • Karakoç, G., ve Alacacı, C. (2015). Real world connections in high school mathematics curriculum and teaching. Turkish Journal of Computer and Mathematics Education, 6(1), 31-46.
  • Kavdır, K. (2011). Matematik öğretmen adaylarının gerçek hayat etkinliği hazırlama süreçlerinin incelenmesi. Yayımlanmamış Yüksek Lisans Tezi, Gazi Üniversitesi Eğitim Bilimleri Enstitüsü.
  • Lee, J. E., (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and Eealuating story problems. Journal of Mathematics Teacher Education, 15(6), 429-452. DOI: 10.1007/s10857012-9220-5
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Margolinas, C. (2013). Task design in mathematics education. Proceedings of ICMI Study 22. ICMI Study 22.
  • Marshall, S. (1995). Schemas in problem solving. Cambridge: Cambridge University Press.
  • Mason, J., and Johnston-Wilder, S. (2006). Designing and using mathematical tasks. Tarquin Pubns.
  • Milli Eğitim Bakanlığı. (2013). Ortaöğretim matematik (9, 10, 11 ve 12. Sınıflar) dersi öğretim programı. Ankara: Yazar.
  • Moschkovich, J. N. (2002). Chapter 1: An introduction to examining everyday and academic mathematical practices. Journal for Research in Mathematics Education. Monograph, 1-11.
  • Muijs, D., and Reynolds, D. (2011). Effective teaching: Evidence and practice (3rd ed.). Los Angels, CA: Sage.
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Curriculum Council (NCC) (2013). National curriculum in England: Mathematics Programmes of study. Retrieved from https://www.gov.uk/government/publications/national-curriculum-inengland-mathematics-programmes-of-study/national-curriculum-inengland-mathematics-programmes-of-study
  • Özgen, K. (2013). Problem çözme bağlamında matematiksel ilişkilendirme becerisi: Öğretmen adayları örneği. E-Journal of New World Sciences Academy, 590.
  • Özmantar, M. F., ve Bingölbali, E. (2009). Etkinlik tasarımı ve temel tasarım prensipleri. İlköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm Önerileri. Pegem Akademi, Ankara.
  • Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the learning of mathematics, 26(1), 42-47.
  • Polya, G. (1962). Mathematical discovery (Vol. 1). New York, NY: Wiley.
  • Singletary, L. M. (2012). Mathematical connections made in practice: An examination of teachers’ beliefs and practices. Unpublished dissertation). Athens, GA: University of Georgia.
  • Sparrow, L. (2008). Real and Relevant Mathematics: Is ıt realıstıc ın the classroom? Australian Primary Mathematics Classroom, 13(2), 4-8.
  • Stein, M. K., Grover, B. W., and Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American educational research journal, 33(2), 455-488.
  • Stein, M. K., and Smith, M. S. (1998). Mathematical tasks As a framework for reflection: From research to practice, Mathematics Teaching in the Middle School, 3(4), 268- 275.
  • Sullivan, P. (2009). Constraints and opportunities when using content- specific openended tasks. Proceedings of the 32nd annual conferences of the Mathematics Education Research Group of Australasia. (July 5-9 2009). Wellington: Massey University.
  • Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Education, 10, 217-237.
  • Swan, M. (2008). Designing a multiple representation learning experience in secondary algebra. Journal of the International Society for Design and Development in Education, 1(1), 1-17.
  • Uğurel, I., ve Bukova-Güzel, E. (2010). Matematiksel öğrenme etkinlikleri üzerine bir tartışma ve kavramsal bir çerçeve önerisi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 39, 333-347.
  • Umay, A. (2007). Eski arkadaşımız okul matematiğinin yeni yüzü. Ankara: Aydan Web Tesisleri.
  • Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri, Ankara: Seçkin Yayınları.

Öğretmen Adaylarının Matematiği Günlük Yaşam ile İlişkilendirme Hakkındaki Düşüncelerinin Geliştirdikleri Öğrenme Etkinliklerine Yansıması

Year 2018, Volume: 31 Issue: 1, 177 - 206, 01.06.2018
https://doi.org/10.19171/uefad.450083

Abstract

Matematik öğretimi ve öğrenimini açıklayan birçok akademik çalışmada, öğrenme modelinde, standartlarda ve öğretim programlarında bağlantı kurma ve ilişkilendirme yapmanın önemi vurgulanmıştır. İlişkilendirmenin yanı sıra, matematik öğretimi ve öğrenimine yönelik çağdaş yaklaşımların pek çoğunda etkinlik adı verilen bir öğrenme birimine vurgu yapılmaktadır. Bu durum etkinlikleri ve etkinlik temelli öğrenmeyi matematik eğitiminin merkezine taşımaktadır. Matematik öğretimi yapılırken ilişkilendirmenin kurulabileceği en uygun öğrenme birimlerinden bir tanesi de matematik öğrenme etkinlikleridir. Bu bağlamda, günlük yaşamla ilişkilendirmenin ne olduğunu, nasıl yapılacağını geliştirilen veya var olan etkinlikler üzerinden incelemenin faydalı olacağı düşünülmektedir. Bu çalışmanın temel amacı ortaöğretim matematik öğretmen adaylarının günlük yaşam ile matematiği ilişkilendirmenin ne olduğu ve nasıl yapılması gerektiği hakkındaki düşüncelerini belirlemek ve düşüncelerini geliştirdikleri bir grup günlük yaşam ile ilişkilendirilmiş matematik öğrenme etkinliğine nasıl yansıttıklarını incelemektir. Çalışmada nitel araştırma paradigmalarından durum çalışması kullanılmıştır. Bu çalışma bir devlet üniversitesinin dördüncü sınıfından eğitim gören 33 (11 grup) matematik öğretmen adayı ile yapılmıştır. Öğretmen adaylarına serbest yazma yaptırılmış ve günlük yaşam ile ilişkilendirilmiş matematik öğrenme etkinliği geliştirmeleri istenmiştir. Toplanan veriler içerik analizi yöntemi ile analiz edilmiştir. Matematik öğretmen adaylarının günlük yaşam ile ilişkilendirmenin gerekliliği ve önemini savunurken, bu durumu geliştirmiş oldukları matematik öğrenme etkinliklerine yansıtmada zorluk çektikleri belirlenmiştir.

References

  • Açıl, E. (2011). İlköğretim öğretmenlerinin etkinlik algısı ve uygulanışına ilişkin görüşleri. Yayınlanmamış yüksek lisans tezi, Gaziantep Üniversitesi Sosyal Bilimler Enstitüsü.
  • Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the learning of Mathematics, 14(3), 24-35.
  • Aslan, B. (2010). Matematiksel etkinliklerin uygulanması sırasında ortaya çıkan öğretmen ve öğrenci rolleri. Yayınlanmamış yüksek lisans tezi, Gaziantep Üniversitesi Sosyal Bilimler Enstitüsü. Australian Curriculum Assessment and Reporting Authority (ACARA). (2008). National Assessment Program (NAP). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA267
  • Ball, D. L. (1991). Research on teaching mathematics: Making subject-matter knowledge part of the education. In J. Brophy (Ed.), Advances in research on teaching (Vol. 2, pp. 1–48). Greenwich, CT: JAI Press.
  • Bamberger, H. J., and Oberdorf, C. (2007). Introduction to connections. Portsmouth, NH: Heinemann.
  • Becker, J. P., and Shimada, S. (1997). The Open-Ended Approach: A New Proposal for Teaching Mathematics. National Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA 20191-1593.
  • Berelson, B. (1952). Content analysis in communication research. Glenco, III: Free Press.
  • Boaler, J. (1993). Encouraging the transfer of ‘school’ mathematics to the ‘real world’through the integration of process and content, context and culture. Educational studies in mathematics, 25(4), 341-373.
  • Boaler, J., and Humphreys, C. (2005). Connecting mathematical ideas: Middle school video cases to support teaching and learning (Vol. 1). Heinemann Educational Books.
  • Bonotto, C. (2001). How to connect school mathematics with students’ out-ofschool knowledge. Zentralblatt für Didaktik der Mathematik, 33(3), 75–84.
  • Bossé, M. J. (2003). The beauty of" and" and" or": Connections within mathematics for students with learning differences. Mathematics and Computer Education, 37(1), 105.
  • Brousseau, G. (1997). Theory of didactical situations in mathematics 1970-1990, [Edited and translated M. Cooper, N. Balacheff, R. Sutherland and V. Warfield.] Dordrecht: Kluwer Academic Publishers.
  • Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections (Doctoral dissertation, Faculty of Education-Simon Fraser University).
  • Caine, R. N., and Caine, G. (1990). Understanding a brain-based approach to learning and teaching. Educational Leadership, 48(2), 66-70.
  • Carpenter, T. P., and Lehrer, R. (1999). Teaching and learning mathematics with understanding. Mathematics classrooms that promote understanding, 1932.
  • Chapman, O. (2012). Challenges in mathematics teacher education. Journal of Mathematics Teacher Education, 15(4), 263-270.
  • Chapman, L. R. (Ed.). (2013). The process of learning mathematics: Pergamon International Library of Science, Technology, Engineering and Social Studies. Elsevier.
  • Christiansen, B., and Walther, G. (1986). Task and activity. In Perspectives on mathematics education (pp. 243-307). Springer Netherlands.
  • Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • Coxford, A. F. (1995). The case for connections. Connecting mathematics across the curriculum, 3-12.
  • Creswell J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Los Angeles (CA): Sage Publications.
  • Czerniak, C. M., Weber, W. B., Sandmann, A., and Ahern, J. (1999). A literature review of science and mathematics integration. School Science and Mathematics, 99(8), 421-430.
  • Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159– 199.
  • Eli, J. A., (2009). An exploratory mixed methods study of prospective middle grades teachers’ mathematical connections while completing investiagtive tasks in geometry. Yayınlanmamış Doktora Tezi, University of Kentucky, Lexington, KY.
  • Evitts, T. A., (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula. Yayınlanmamış Doktora Tezi, Pennsylvania State University College of Education.
  • Freudenthal, H., (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1, 3-8.
  • Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219.
  • Gerofsky, S. (2006). Communication: simulation, reality, and mathematical word problems. For the Learning of Mathematics, 26(2), 30-32.
  • Herbst, P. (2008). The teacher and the task. In O. Figuras, J. L. Cortina, S. Alatorre, T. Rojano, & A Sepulveda (Eds.), Proceedings of the 32nd Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 125- 133). Morelia: PME.
  • Hiebert, J., and Carpenter, T., (1992). Learning and Teaching with Understanding. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 65–97). New York: Macmillan.
  • Horoks, J., and Robert, A. (2007). Tasks designed to highlight task-activity relationships. Journal of Mathematics Teacher Education, 10(4-6), 279287.
  • Karakoç, G., ve Alacacı, C. (2015). Real world connections in high school mathematics curriculum and teaching. Turkish Journal of Computer and Mathematics Education, 6(1), 31-46.
  • Kavdır, K. (2011). Matematik öğretmen adaylarının gerçek hayat etkinliği hazırlama süreçlerinin incelenmesi. Yayımlanmamış Yüksek Lisans Tezi, Gazi Üniversitesi Eğitim Bilimleri Enstitüsü.
  • Lee, J. E., (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and Eealuating story problems. Journal of Mathematics Teacher Education, 15(6), 429-452. DOI: 10.1007/s10857012-9220-5
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Margolinas, C. (2013). Task design in mathematics education. Proceedings of ICMI Study 22. ICMI Study 22.
  • Marshall, S. (1995). Schemas in problem solving. Cambridge: Cambridge University Press.
  • Mason, J., and Johnston-Wilder, S. (2006). Designing and using mathematical tasks. Tarquin Pubns.
  • Milli Eğitim Bakanlığı. (2013). Ortaöğretim matematik (9, 10, 11 ve 12. Sınıflar) dersi öğretim programı. Ankara: Yazar.
  • Moschkovich, J. N. (2002). Chapter 1: An introduction to examining everyday and academic mathematical practices. Journal for Research in Mathematics Education. Monograph, 1-11.
  • Muijs, D., and Reynolds, D. (2011). Effective teaching: Evidence and practice (3rd ed.). Los Angels, CA: Sage.
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Curriculum Council (NCC) (2013). National curriculum in England: Mathematics Programmes of study. Retrieved from https://www.gov.uk/government/publications/national-curriculum-inengland-mathematics-programmes-of-study/national-curriculum-inengland-mathematics-programmes-of-study
  • Özgen, K. (2013). Problem çözme bağlamında matematiksel ilişkilendirme becerisi: Öğretmen adayları örneği. E-Journal of New World Sciences Academy, 590.
  • Özmantar, M. F., ve Bingölbali, E. (2009). Etkinlik tasarımı ve temel tasarım prensipleri. İlköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm Önerileri. Pegem Akademi, Ankara.
  • Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the learning of mathematics, 26(1), 42-47.
  • Polya, G. (1962). Mathematical discovery (Vol. 1). New York, NY: Wiley.
  • Singletary, L. M. (2012). Mathematical connections made in practice: An examination of teachers’ beliefs and practices. Unpublished dissertation). Athens, GA: University of Georgia.
  • Sparrow, L. (2008). Real and Relevant Mathematics: Is ıt realıstıc ın the classroom? Australian Primary Mathematics Classroom, 13(2), 4-8.
  • Stein, M. K., Grover, B. W., and Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American educational research journal, 33(2), 455-488.
  • Stein, M. K., and Smith, M. S. (1998). Mathematical tasks As a framework for reflection: From research to practice, Mathematics Teaching in the Middle School, 3(4), 268- 275.
  • Sullivan, P. (2009). Constraints and opportunities when using content- specific openended tasks. Proceedings of the 32nd annual conferences of the Mathematics Education Research Group of Australasia. (July 5-9 2009). Wellington: Massey University.
  • Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Education, 10, 217-237.
  • Swan, M. (2008). Designing a multiple representation learning experience in secondary algebra. Journal of the International Society for Design and Development in Education, 1(1), 1-17.
  • Uğurel, I., ve Bukova-Güzel, E. (2010). Matematiksel öğrenme etkinlikleri üzerine bir tartışma ve kavramsal bir çerçeve önerisi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 39, 333-347.
  • Umay, A. (2007). Eski arkadaşımız okul matematiğinin yeni yüzü. Ankara: Aydan Web Tesisleri.
  • Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri, Ankara: Seçkin Yayınları.
There are 57 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Melike Yiğit Koyunkaya

İşıkhan Uğurel

Berna Tataroğlu Taşdan

Publication Date June 1, 2018
Submission Date June 23, 2017
Published in Issue Year 2018 Volume: 31 Issue: 1

Cite

APA Yiğit Koyunkaya, M., Uğurel, İ., & Tataroğlu Taşdan, B. (2018). Reflection of Preservice Teachers’ Thoughts about Connecting Mathematics and Real Life Situations on Their Mathematics Learning Activities. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 31(1), 177-206. https://doi.org/10.19171/uefad.450083