Research Article
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Voice of Middle School Students: Illuminating Their Conceptual and Procedural Knowledge in Fractions

Year 2025, Volume: 10 Issue: 2, 233 - 250, 25.12.2025

Bengi Birgili , İpek Saralar

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

Abstract

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.

Keywords

Conceptual knowledge Fractions Procedural knowledge Math understanding Middle school

Ethical Statement

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

Supporting Institution

This research was not supported.

References

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  • 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
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  • 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
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  • 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
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  • 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.
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Ortaokul Öğrencilerinin Sesi: Kesirlerdeki Kavramsal ve İşlemsel Bilgilerinin İncelenmesi

Year 2025, Volume: 10 Issue: 2, 233 - 250, 25.12.2025

Bengi Birgili , İpek Saralar

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

Abstract

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.

Keywords

İşlemsel bilgi Kavramsal bilgi Kesirler Matematik anlayışı Ortaokul seviyesi

Ethical Statement

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

Supporting Institution

Araştırma herhangi bir kurum tarafından desteklenmemektedir.

References

  • 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.
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There are 76 citations in total.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Research Article
Authors

Bengi Birgili 0000-0002-2990-6717

İpek Saralar 0000-0002-4942-4408

Submission Date October 3, 2025
Acceptance Date November 26, 2025
Publication Date December 25, 2025
Published in Issue Year 2025 Volume: 10 Issue: 2

Cite

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

Dear Colleagues,
We are very pleased to announce that the latest issue of IHEAD (Vol. 10- Iss. 2) has been released. We kindly want to express our speacial thanks to the editorial board members, reviewers, and authors for their invaluable contribution to this issue. Also, we are delighted to announce that the next issue (Vol. 11- Iss. 1) of the IHEAD will be available online in June, 2026. As of January, 2024, IHEAD has been accepting submissions in English along with Turkish. Handling your papers within the scope education for the next issue will be a great pleasure for us. Many thanks in advance for your contributions.
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