Araştırma Makalesi
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Voice of Middle School Students: Illuminating Their Conceptual and Procedural Knowledge in Fractions

Yıl 2025, Cilt: 10 Sayı: 2, 233 - 250, 25.12.2025

Bengi Birgili , İpek Saralar

https://doi.org/10.47479/ihead.1796702

Öz

This study explored sixth- and seventh-grade students’ conceptual and procedural fractional knowledge. The participants comprised 30 purposely selected students (aged 12-13) from a private middle school in Istanbul. Employing an explanatory sequential mixed methods design; first, a well established fractions test was utilized to assess the students' conceptual and procedural understanding; this was followed by classroom observations and semi-structured interviews. Findings revealed a statistically significant correlation between conceptual and procedural knowledge, and high-achieving students exhibited a combination of these knowledge domains, while low-achieving students relied predominantly on procedural knowledge. This study underscores the importance of fostering a balanced acquisition of both conceptual and procedural knowledge in fractions to enhance mathematical understanding and skills among middle school students.

Anahtar Kelimeler

Conceptual knowledge Fractions Procedural knowledge Math understanding Middle school

Etik Beyan

We received ethical approval from the MEF University Ethics Committee, numbered MEF-13052019.

Destekleyen Kurum

This research was not supported.

Kaynakça

  • Ahrendt, S., Monson, D., & Cramer, K. (2021). Promoting discourse: Fractions on number lines. Mathematics Teacher: Learning and Teaching PK-12, 114(4), 284–289. National Council of Teachers of Mathematics. https://doi.org/10.5951/mtlt.2020.0184
  • Aksoy, N. C., & Yazlik, D. O. (2017). Student errors in fractions and possible causes of these errors. Journal of Education and Training Studies, 5(11), 219. https://doi.org/10.11114/jets.v5i11.2679
  • Aksu, M. (1997). Student performance in dealing with fractions. The Journal of Educational Research, 90(6), 375–380. https://doi.org/10.1080/00220671.1997.10544595
  • Alacaci, C. (2010). Students’ misconceptions related to fractions. In E. Bingölbali & M. F. Özmantar (Eds.), Mathematical difficulties and solutions in primary education (2nd ed., pp. 63–95). Ankara: Pegem Academy.
  • Anderson, L. W., & Krathwohl, D. R. (2001). A Taxonomy for Learning, Teaching and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives: Complete Edition. Longman.
  • Bach, K.M., Reinhold, F. & Hofer, S.I. (2025). Unlocking math potential in students from lower SES backgrounds – using instructional scaffolds to improve performance. NPJ Science of Learning, 10(1), 66. https://doi.org/10.1038/s41539-025-00358-7
  • Baird, J. (2010). Beliefs and practice in teacher assessment. Assessment in Education: Principles, Policy & Practice, 17(1), 1–5. https://doi.org/10.1080/09695940903562682
  • Baker, W. J., Czarnocha, B., Dias, O., Doyle, K., & Kennis, J. R. (2012). Procedural and conceptual knowledge: Adults reviewing fractions. Adults Learning Mathematics, 7(2), 39–65. https://eric.ed.gov/?id=EJ1068220
  • Birgin, O., & Gürbüz, R. (2009). Examining primary education 2nd grade students’ operational and conceptual knowledge levels of the students in rational numbers. Journal of Uludağ University Faculty of Education, 22(2), 529–550. https://dergipark.org.tr/en/pub/uefad/issue/16690/173458
  • Braithwaite, D. W., & Sprague, L. (2021). Conceptual knowledge, procedural knowledge, and metacognition in routine and nonroutine problem solving. Cognitive Science, 45(10), e13048.
  • Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777–786. https://doi.org/10.1037/0012-1649.27.5.777
  • Byrnes, J. P. (1992). The conceptual basis of procedural learning. Cognitive Development, 7, 235–237. https://doi.org/10.1016/0885-2014(92)90013-H
  • Chan, C.Y., Closser A.Y, Mgo, V., Smith, H., Liu, A.S., & Ottmar, E. (2023). Examining shifts in conceptual knowledge, procedural knowledge and procedural flexibility in the context of two game-based technologies. Journal of Computer-Assisted Learning, 39(4), 1274–1289. https://doi.org/10.1111/jcal.12798
  • Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293–316. https://doi.org/10.1007/s10649-006-9036-2
  • Clements, D. H., & Sarama, J. (2020). Learning and Teaching Early Math: The Learning Trajectories Approach. Routledge.
  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Earlbaum Associates.
  • Dogan Coskun, S., Tekin Sitrava, R., & Isıksal Bostan, M. (2023). Pre-service elementary teachers’ noticing expertise of students’ mathematical thinking: The case of fractions. International Journal of Mathematical Education in Science and Technology, 54(6), 982-999. https://doi.org/10.1080/0020739X.2021.1979260
  • Creswell, J. W., & Plano-Clark, V. L. (2017). Designing and conducting mixed methods research. Sage Publication.
  • Fisher, E., & Dennis, M. S. (2023). Supporting the fraction magnitude understanding of students with significant behavior problems. Journal of Emotional and Behavioral Disorders, 32(1), 56–67. https://doi.org/10.1177/10634266221149357
  • Fyfe, E. R., DeCaro, M. S., & Rittle‐Johnson, B. (2014). An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge. British Journal of Educational Psychology, 84(3), 502–519.
  • George, D., & Mallery, P., (2018). IBM SPSS Statistics 25 Step: A Simple Guide and Reference. Sage.
  • Gerasimova, D., Miller, A. D., & Hjalmarson, M. A. (2023). Conceptual and procedural teaching: does one teaching approach moderate the relationship between the other teaching approach and algebra achievement? Educational Studies in Mathematics, 114(2), 181–198. https://doi.org/10.1007/s10649-023-10219-y
  • Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102(2), 395–406. https://doi.org/10.1037/a0017486
  • Hecht, S. A. (1998). Toward an information-processing account of individual differences in fraction skills. Journal of Educational Psychology, 90(3), 545–559. https://doi.org/10.1037/0022-0663.90.3.545
  • Hechter, J., Stols, G., & Combrinck, C. (2022). The Reciprocal Relationship Between Conceptual and Procedural Knowledge—A Case Study of Two Calculus Problems. African Journal of Research in Mathematics, Science and Technology Education, 26(2), 111–124. https://doi.org/10.1080/18117295.2022.2101271
  • Heyworth, R. M. (1999). Procedural and conceptual knowledge of expert and novice students for the solving of a basic problem in chemistry. International Journal of Science Education, 21(2), 195–211. https://doi.org/10.1080/095006999290787
  • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1–27). Lawrence Erlbaum Associates, Inc.
  • Hoyles, C., Noss, R., & Pozzi, S. (2001). Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32(1), 4-27. https://doi.org/10.2307/749619
  • Izsák, A., Jacobson, E., & Bradshaw, L. (2019). Surveying middle-grades teachers’ reasoning about fraction arithmetic in terms of measured quantities. Journal for Research in Mathematics Education, 50(2), 156–209. https://doi.org/10.5951/jresematheduc.50.2.0156
  • Kassim, N., Zakaria, E., Salleh, T. S., & Borhan, N. (2017). Effectiveness of the FTI-HOTS module on pupils' conceptual and procedural knowledge in fractions. Man in India, 97(17), 63–78.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49–84). Lawrence Erlbaum Associates.
  • Krathwohl, D. R., & Anderson, L. W. (2010). Merlin C. Wittrock and the revision of Bloom's taxonomy. Educational Psychologist, 45(1), 64–65. https://doi.org/10.1080/00461520903433562
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Ortaokul Öğrencilerinin Sesi: Kesirlerdeki Kavramsal ve İşlemsel Bilgilerinin İncelenmesi

Yıl 2025, Cilt: 10 Sayı: 2, 233 - 250, 25.12.2025

Bengi Birgili , İpek Saralar

https://doi.org/10.47479/ihead.1796702

Öz

Bu çalışma, altıncı ve yedinci sınıf öğrencilerinin kesirlere ilişkin kavramsal ve işlemsel bilgilerini incelemiştir. Katılımcılar, İstanbul’daki özel bir ortaokuldan amaçlı örnekleme yoluyla seçilen 30 öğrenciden (12–13 yaş aralığında) oluşmaktadır. Açıklayıcı sıralı karma yöntem deseninin kullanıldığı araştırmada, öncelikle öğrencilerin kavramsal ve işlemsel bilgi düzeylerini değerlendirmek amacıyla alan yazında geçerliliği kanıtlanmış bir kesir testi uygulanmış; ardından sınıf gözlemleri ve yarı yapılandırılmış görüşmeler gerçekleştirilmiştir. Bulgular, kavramsal ve işlemsel bilgi arasında istatistiksel olarak anlamlı bir korelasyon olduğunu ortaya koymuş; yüksek başarı gösteren öğrencilerin her iki bilgi türünü de bütünleştirerek kullandıkları, düşük başarı gösteren öğrencilerin ise ağırlıklı olarak işlemsel bilgiye dayandıkları belirlenmiştir. Bu çalışma, ortaokul öğrencilerinin matematiksel anlayış ve becerilerini geliştirmek için kavramsal ve işlemsel bilginin dengeli bir şekilde kazandırılmasının önemini vurgulamaktadır.

Anahtar Kelimeler

İşlemsel bilgi Kavramsal bilgi Kesirler Matematik anlayışı Ortaokul seviyesi

Etik Beyan

Çalışmamız MEF Üniversitesi Etik Kurulu’ndan MEF-13052019 numaralı etik onayını almıştır.

Destekleyen Kurum

Araştırma herhangi bir kurum tarafından desteklenmemektedir.

Kaynakça

  • Ahrendt, S., Monson, D., & Cramer, K. (2021). Promoting discourse: Fractions on number lines. Mathematics Teacher: Learning and Teaching PK-12, 114(4), 284–289. National Council of Teachers of Mathematics. https://doi.org/10.5951/mtlt.2020.0184
  • Aksoy, N. C., & Yazlik, D. O. (2017). Student errors in fractions and possible causes of these errors. Journal of Education and Training Studies, 5(11), 219. https://doi.org/10.11114/jets.v5i11.2679
  • Aksu, M. (1997). Student performance in dealing with fractions. The Journal of Educational Research, 90(6), 375–380. https://doi.org/10.1080/00220671.1997.10544595
  • Alacaci, C. (2010). Students’ misconceptions related to fractions. In E. Bingölbali & M. F. Özmantar (Eds.), Mathematical difficulties and solutions in primary education (2nd ed., pp. 63–95). Ankara: Pegem Academy.
  • Anderson, L. W., & Krathwohl, D. R. (2001). A Taxonomy for Learning, Teaching and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives: Complete Edition. Longman.
  • Bach, K.M., Reinhold, F. & Hofer, S.I. (2025). Unlocking math potential in students from lower SES backgrounds – using instructional scaffolds to improve performance. NPJ Science of Learning, 10(1), 66. https://doi.org/10.1038/s41539-025-00358-7
  • Baird, J. (2010). Beliefs and practice in teacher assessment. Assessment in Education: Principles, Policy & Practice, 17(1), 1–5. https://doi.org/10.1080/09695940903562682
  • Baker, W. J., Czarnocha, B., Dias, O., Doyle, K., & Kennis, J. R. (2012). Procedural and conceptual knowledge: Adults reviewing fractions. Adults Learning Mathematics, 7(2), 39–65. https://eric.ed.gov/?id=EJ1068220
  • Birgin, O., & Gürbüz, R. (2009). Examining primary education 2nd grade students’ operational and conceptual knowledge levels of the students in rational numbers. Journal of Uludağ University Faculty of Education, 22(2), 529–550. https://dergipark.org.tr/en/pub/uefad/issue/16690/173458
  • Braithwaite, D. W., & Sprague, L. (2021). Conceptual knowledge, procedural knowledge, and metacognition in routine and nonroutine problem solving. Cognitive Science, 45(10), e13048.
  • Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777–786. https://doi.org/10.1037/0012-1649.27.5.777
  • Byrnes, J. P. (1992). The conceptual basis of procedural learning. Cognitive Development, 7, 235–237. https://doi.org/10.1016/0885-2014(92)90013-H
  • Chan, C.Y., Closser A.Y, Mgo, V., Smith, H., Liu, A.S., & Ottmar, E. (2023). Examining shifts in conceptual knowledge, procedural knowledge and procedural flexibility in the context of two game-based technologies. Journal of Computer-Assisted Learning, 39(4), 1274–1289. https://doi.org/10.1111/jcal.12798
  • Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293–316. https://doi.org/10.1007/s10649-006-9036-2
  • Clements, D. H., & Sarama, J. (2020). Learning and Teaching Early Math: The Learning Trajectories Approach. Routledge.
  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Earlbaum Associates.
  • Dogan Coskun, S., Tekin Sitrava, R., & Isıksal Bostan, M. (2023). Pre-service elementary teachers’ noticing expertise of students’ mathematical thinking: The case of fractions. International Journal of Mathematical Education in Science and Technology, 54(6), 982-999. https://doi.org/10.1080/0020739X.2021.1979260
  • Creswell, J. W., & Plano-Clark, V. L. (2017). Designing and conducting mixed methods research. Sage Publication.
  • Fisher, E., & Dennis, M. S. (2023). Supporting the fraction magnitude understanding of students with significant behavior problems. Journal of Emotional and Behavioral Disorders, 32(1), 56–67. https://doi.org/10.1177/10634266221149357
  • Fyfe, E. R., DeCaro, M. S., & Rittle‐Johnson, B. (2014). An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge. British Journal of Educational Psychology, 84(3), 502–519.
  • George, D., & Mallery, P., (2018). IBM SPSS Statistics 25 Step: A Simple Guide and Reference. Sage.
  • Gerasimova, D., Miller, A. D., & Hjalmarson, M. A. (2023). Conceptual and procedural teaching: does one teaching approach moderate the relationship between the other teaching approach and algebra achievement? Educational Studies in Mathematics, 114(2), 181–198. https://doi.org/10.1007/s10649-023-10219-y
  • Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102(2), 395–406. https://doi.org/10.1037/a0017486
  • Hecht, S. A. (1998). Toward an information-processing account of individual differences in fraction skills. Journal of Educational Psychology, 90(3), 545–559. https://doi.org/10.1037/0022-0663.90.3.545
  • Hechter, J., Stols, G., & Combrinck, C. (2022). The Reciprocal Relationship Between Conceptual and Procedural Knowledge—A Case Study of Two Calculus Problems. African Journal of Research in Mathematics, Science and Technology Education, 26(2), 111–124. https://doi.org/10.1080/18117295.2022.2101271
  • Heyworth, R. M. (1999). Procedural and conceptual knowledge of expert and novice students for the solving of a basic problem in chemistry. International Journal of Science Education, 21(2), 195–211. https://doi.org/10.1080/095006999290787
  • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1–27). Lawrence Erlbaum Associates, Inc.
  • Hoyles, C., Noss, R., & Pozzi, S. (2001). Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32(1), 4-27. https://doi.org/10.2307/749619
  • Izsák, A., Jacobson, E., & Bradshaw, L. (2019). Surveying middle-grades teachers’ reasoning about fraction arithmetic in terms of measured quantities. Journal for Research in Mathematics Education, 50(2), 156–209. https://doi.org/10.5951/jresematheduc.50.2.0156
  • Kassim, N., Zakaria, E., Salleh, T. S., & Borhan, N. (2017). Effectiveness of the FTI-HOTS module on pupils' conceptual and procedural knowledge in fractions. Man in India, 97(17), 63–78.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49–84). Lawrence Erlbaum Associates.
  • Krathwohl, D. R., & Anderson, L. W. (2010). Merlin C. Wittrock and the revision of Bloom's taxonomy. Educational Psychologist, 45(1), 64–65. https://doi.org/10.1080/00461520903433562
  • Lamon, S. J. (2020). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Routledge.
  • Lenz, K., & Wittmann, G. (2020). Individual differences in conceptual and procedural fraction knowledge: What makes the difference and what does it look like? International Electronic Journal of Mathematics Education, 16(1), em0615. https://doi.org/10.29333/iejme/9282
  • Lewis, C. C., & Perry, R. R. (2017). Lesson study to scale up research-based knowledge: A randomized, controlled trial of fractions learning. Journal for Research in Mathematics Education, 48(3), 261–299. https://doi.org/10.5951/jresematheduc.48.3.0261
  • Li, H.-C. (2025). Examining procedural proficiency in fraction addition: Comparative insights from England and Taiwan. International Journal of Instruction, 18(1), 325-340. https://www.e-iji.net/dosyalar/iji_2025_1_18.pdf
  • Majeed, B. H., & AlRikabi, H. T. (2022). Effect of augmented reality technology on spatial intelligence among high school students. International Journal of Emerging Technologies in Learning, 17(24), 131. https://doi.org/10.3991/ijet.v17i24.35977
  • Miles, M.B., Huberman, A.M., & Saldana, J. (2014) Qualitative data analysis: A methods sourcebook. Sage.
  • Mitchell, A., & Clarke, D. M. (2004). When is three quarters not three quarters? Listening for conceptual understanding in children’s explanations in a fractions interview. Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 367–373).
  • Ministry of National Education. (2024). Middle School Mathematics Education Programme. MoNE Publications. Moore. D., Notz. W., & Fligner. M. (2012). The Basic Practice of Statistics. W. H. Freeman and Company.
  • Nahdi, D. S., & Jatisunda, M. G. (2020, March). Conceptual understanding and procedural knowledge: A case study on learning mathematics of fractional material in elementary school. In Journal of Physics: Conference Series (Vol. 1477, No. 4, p. 042037). IOP Publishing.
  • Ncube, M., & Luneta, K. (2025). Concept-based instruction: Improving learner performance in mathematics through conceptual understanding. Pythagoras, 46(1), 1-18.
  • Novikasari, I., & Dede, Y. (2023). Toward proficiency: developing a multiplication mathematical content knowledge test for pre-service mathematics teachers in Indonesia and Türkiye. Journal on Mathematics Education, 15(1), 115–130. https://eric.ed.gov/?id=EJ1413487
  • Örmeci, Ş. (2012). Seventh grade students' conceptual and procedural understanding of fractions: Comparison between successful and less successful students [Unpublished Master’s Thesis]. Bilkent University.
  • Özpınar, İ., & Arslan, S. (2021). Investigation of basic mathematical knowledge of preservice maths teachers: procedural or conceptual? International Journal of Mathematical Education in Science and Technology, 53(8), 2115–2132. https://doi.org/10.1080/0020739x.2020.1867915
  • Patterson, C. L., Parrott, A., & Belnap, J. (2020). Strategies for assessing mathematical knowledge for teaching in mathematics content courses. The Mathematics Enthusiast, 17(2), 807–842.
  • Pesen, C. (2007). Students’ misconception about fractions Education and Science, 32(143), 79–88.
  • Prediger, S., Dröse, J., Stahnke, R., & Ademmer, C. (2023). Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth. Journal of Mathematics Teacher Education, 26(4), 481508. https://doi.org/10.1007/s10857-022-09538-3
  • Ratner, B. (2009). The correlation coefficient: Its values range between+ 1/− 1, or do they? Journal of Targeting, Measurement and Analysis for Marketing, 17(2), 139-142. https://doi.org/10.1057/jt.2009.5
  • Rayner, V., Pitsolantis, N., & Osana, H. (2009). Mathematics anxiety in preservice teachers: Its relationship to their conceptual and procedural knowledge of fractions. Mathematics Education Research Journal, 21(3), 60–85. https://doi-org.ezproxy.uow.edu.au/10.1007/BF03217553
  • Rittle‐Johnson, B. (2017). Developing mathematics knowledge. Child Development Perspectives, 11(3), 184–190. https://doi.org/10.1111/cdep.12229
  • Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189. https://doi.org/10.1037/0022-0663.91.1.175
  • Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skills (pp. 75–110). Psychology Press/Taylor & Francis.
  • Rittle-Johnson, B., & Siegler, R. S. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362. https://doi.org/10.1037/0022-0663.93.2.346
  • Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587–597. https://doi.org/10.1007/s10648-015-9302-x
  • Rosli, F. A. B., Hong, Z., Boon, J., Han, T., Cheong, S. H., Teoh, L. A., & Anthonysamy, A. (2024). Assessment of fraction concept among lower secondary students. Library Progress International, 44(3), 6043–6048.
  • Saralar-Aras, İ., & Tütüncü, S. (2025, February 4-8). The role of digital tools in enhancing classroom assessment practices. [Oral presentation]. The 14th Congress of the European Society for Research in Mathematics Education (CERME-14), Bozen-Bolzano, Italy.
  • Saralar-Aras, İ., & Tütüncü, S. (2024). Utilization of technology for assessment purposes among mathematics teachers. In J. Morska & A. Rogerson (Eds.), Proceeedings of the Mathematics Education for the Future Project’s 2024 Symposium on New Ways of Teaching & Learning (pp. 291-296). WTM Publications. https://doi.org/10.37626/GA9783959872881.0.51
  • Schneider, M., & Stern, E. (2005). Conceptual and procedural knowledge of a mathematics problem: Their measurement and their causal interrelations. Presented at the 27th Annual Conference of the Cognitive Science Society.
  • Schwarzmeier, S., & Obersteiner, A. (2025). Is counting a bad idea? Complex relations among children’s fraction knowledge, eye movements, and performance in visual fraction comparisons. Journal of Experimental Child Psychology, 252, 106181. https://doi.org/10.1016/j.jecp.2024.106181
  • Sformo, T. (2008). Practical Problems in Mathematics: For Automotive Technicians. Cengage Learning. Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: the new frontier for theories of numerical development. Trends Cognitive Science, 17(1), 13-19. https://doi.org/10.1016/j.tics.2012.11.004
  • Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296. https://doi.org/10.1016/j.cogpsych.2011.03.001
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  • Steffe, L. P., & Olive, J. (2010). Children’s Fractional Knowledge. Springer. https://doi.org/10.1007/978-1-4419-0591-8
  • Stovner, R. B., & Klette, K. (2022). Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: A video study in lower secondary mathematics classrooms. Teaching and Teacher Education, 110, 103593. https://doi.org/10.1016/j.tate.2021.103593
  • Sullivan, P. L., Barnett, J. E., & Killion, K. (2023). Beware of “gaps” in students’ fraction conceptions. Mathematics Teacher: Learning and Teaching PK-12, 116(12), 912–922. National Council of Teachers of Mathematics. https://doi.org/10.5951/mtlt.2023.0109
  • Tan, A. L., Ong, Y. S., Ng, Y. S., & Tan, J. H. J. (2023). STEM problem solving: Inquiry, concepts, and reasoning. Science & Education, 32(2), 381–397.
  • Tian, J., & Siegler, R. S. (2017). Fractions learning in children with mathematics difficulties. Journal of Learning Disabilities, 50(6), 614-620. https://doi.org/10.1177/002221941666203
  • Van de Walle, J. A. (1990). Elementary School Mathematics: Teaching Developmentally (1st ed). Pearson Education.
  • Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Pearson Education.
  • Van Hoof, J., Janssen, R., Verschaffel, L., & Van Dooren, W. (2015). In search for the natural number bias in secondary school students’ interpretation of graphs. Learning and Instruction, 39(1), 1–11. https://doi.org/10.1016/j.learninstruc.2014.03.004
  • Wong, M., & Evans, D. (2007). Students’ conceptual understanding of equivalent fractions. Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 824–833). https://acuresearchbank.acu.edu.au/item/86x87/students-conceptual-understanding-of-equivalent-fractions
  • Xu, C., Di Lonardo Burr, S., Rodgers, L. J., Wylie, J., Si, J., Huang, B., Guo, K., & Li, H. (2025). A longitudinal investigation of the codevelopment and bidirectional relations among whole number arithmetic and conceptual and procedural fraction knowledge. Journal of Educational Psychology (Advance online publication). https://doi.org/10.1037/edu0000942
  • Zohar, A., & Ben-Ari, G. (2022). Teachers’ knowledge and professional development for metacognitive instruction in the context of higher order thinking. Metacognition and Learning, 17(3), 855–895.
Toplam 76 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik Eğitimi
Bölüm Araştırma Makalesi
Yazarlar

Bengi Birgili 0000-0002-2990-6717

İpek Saralar 0000-0002-4942-4408

Gönderilme Tarihi 3 Ekim 2025
Kabul Tarihi 26 Kasım 2025
Yayımlanma Tarihi 25 Aralık 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 10 Sayı: 2

Kaynak Göster

APA Birgili, B., & Saralar, İ. (2025). Voice of Middle School Students: Illuminating Their Conceptual and Procedural Knowledge in Fractions. Ihlara Eğitim Araştırmaları Dergisi, 10(2), 233-250. https://doi.org/10.47479/ihead.1796702
Değerli Meslektaşlarımız,
IHEAD'ın son sayısının (Cilt 10-Sayı 2) yayımlandığını bildirmekten mutluluk duymaktayız. Sayının yayımlanmasında emeği geçen editör kurulu üyelerine, hakemlere ve yazarlara değerli katkılarından dolayı özel teşekkürlerimizi sunarız. Ayrıca, IHEAD'ın gelecek sayısını (Cilt 11-Sayı 1) Haziran 2026 itibariyle yayımlamayı planlamaktayız. Ocak 2024 tarihinden itibaren dergimize Türkçe makalelerin yanı sıra İngilizce makaleler de kabul etmekteyiz. Eğitimle ile ilgili makalelerinizi değerlendirmekten büyük bir memnuniyet duyacağımızı bildirir katkılarınız için şimdiden teşekkür ederiz.
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