Conceptual and Procedural Understanding in the Division of Algebraic Fractions
DOI:
https://doi.org/10.32871/rmrj2412.01.17Keywords:
Algebraic Fraction, division, conceptual understanding, procedural understandingAbstract
This study investigated the correlation between conceptual and procedural understanding of the division of algebraic fractions among junior high school students at a government-run university. It utilized descriptive and correlational research designs involving 109 enrolled Grade 8 students as study respondents. A validated algebra test questionnaire was the instrument used for the division of algebraic fractions. The Pearson product-moment correlation or Pearson r was used to assess the correlation between data variables. The findings revealed that the students poorly exhibited conceptual and procedural understanding in the division of algebraic fractions. There was a strong, highly positive, significant correlation between the students’ conceptual and procedural understanding in the division of algebraic fractions, which indicated that students' conceptual understanding goes hand in hand with their procedural understanding. Therefore, the higher the level of student conceptual understanding, the higher the level of procedural understanding and vice-versa.
References
Abocejo, F. T., & Padua, R. N. (2010). An econometric model for determining sustainability of basic education development. CNU Journal of Higher Education. 4(1), 40-53. http://www.jhe.cnu.edu.ph/index.php/cnujhe/article/view/39
Adu-Gyamfi, K., Schwartz, C.S., Sinicrope, R., & Bossé, M. J. (2019). Making sense of fraction division: Domain and representation knowledge of preservice elementary teachers on a fraction division task. Mathematics Education Research Journal, 31, 507–528. https://doi.org/10.1007/s13394-019-00265-2
Agasi, G., Wahyuono, Y., & Rudhito, M. (2017). Junior high school students’ ability to apply algebra in real-world problems. International Journal of Indonesian Education and Teaching, 1(2), 206-215. https://doi.org/10.24071/IJIET.2017.010210
Ahmad, S., Ch, A. H., Batool, A., Sittar, K., & Malik, M. (2016). Play and cognitive development: Formal operational perspective of Piaget's theory. Journal of Education and Practice, 7(28), 72-79. https://files.eric.ed.gov/fulltext/EJ1118552.pdf
Ajai, J.T., & Imoko, B.I. (2015). Gender differences in mathematics achievement and retention scores: A case of problem-based learning method. International Journal of Research in Education and Science (IJRES), 1(1), 45-50. https://files.eric.ed.gov/fulltext/EJ1105194.pdf
Alcock, L., Ansari, D., Batechelor, S., Bison, M., De Smedt, B., Gilmore, C., Göbel, S., Hannula-Sormunen, M, Hodgen, J., Inglis, M., Jones, I., Mazzocco, M., McNeil, N., Scheider, M., Simms, V., & Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2(1), 20– 41. https://doi.org/10.5964/jnc.v2i1.10
Andamon, J. C., & Tan, D. A. (2018). Conceptual understanding, attitude and performance in mathematics of grade 7 students. International Journal of Scientific & Technology Research, 7(8), 96-105. https://www.ijstr.org/final-print/aug2018/Conceptual-Understanding-Attitude-And-Performance-In-Mathematics-Of-Grade-7-Students.pdf
Anjum, S. (2015). Gender difference in mathematics achievement and its relation with reading comprehension of children at upper primary stage. Journal of Education and Practice. 6(16), 71-76. Retrieved from https://files.eric.ed.gov/fulltext/EJ1079951.pdf
Bastürk, S. (2016). Primary student teachers' perspectives of the teaching of fractions. Acta Didactica Napocensia, 9(1), 35-44. https://files.eric.ed.gov/fulltext/EJ1103431.pdf
Brandt, C. F., Bassoi, T. S., & Baccon, A. L. P. (2016). Difficulties of 6th grade elementary school students in solving the four basic fundamental operations: Addition, subtraction, multiplication and division of natural numbers. Creative Education, 7(13), 1820-1833. https://doi.org/10.4236/ce.2016.713185
Cabuquin, J. C. (2023). An examination of written work and performance task in general mathematics and precalculus of Filipino STEM learners. Jurnal Pendidikan Progresif, 13(2), 375-386. https://doi.org/10.23960/jpp.v13.i2.202317
Cadorna, E. A., Cadorna, E. F., & Taban, J. G. (2021). A cross-sectional study of students’ learning progression in algebra. Universal Journal of Educational Research, 9(3), 449-460. https://doi.org/10.13189/ujer.2021.090304
Cananua-Labid, S. A. (2015). Conceptual and procedural knowledge in mathematics of preservice teachers in the Countryside. The Countryside Development Research Journal, 3(2), 1-6. ojs.ssu.edu.ph/index.php/CDRJ/article/download/55/72/
Cantoria, A. L., & Espinosa E. B. (2016). Predominance of procedural knowledge and between-operation interference as deduced from fraction errors of preservice teachers. Asia Pacific Journal of Multidisciplinary Research, 4(4) 75-79. http://www.apjmr.com/wpcontent/uploads/2016/09/APJMR2016.4.4.11.pdf
Chan, C., Ng, K., Widjaja, W., & Seto, C. (2012). Assessment of primary 5 students' mathematical modelling competencies. Journal of science and Mathematics Education in Southeast Asia, 35(2), 146-178. http://hdl.handle.net/10497/16257
Cherng, H. S. (2017). If they think I can: Teacher bias and youth of color expectations and achievement. Social Science Research, 66, 170-186. https://doi.org/10.1016/j.ssresearch.2017.04.001
Clark, R., Kirschner, P. A., & Sweller, J. (2012). Putting students on the path to learning: The case for fully guided instruction. American Educator, 36(1), 5-11. https://eric.ed.gov/?id=EJ971752
Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344-377. https://doi.org/10.1016/j.dr.2014.10.001
Ervin, H. K. (2017). Fraction multiplication and division models: A practitioner reference paper. International Journal of Research in Education and Science, 3(1), 258-279. https://files.eric.ed.gov/fulltext/EJ1126700.pdf
Escalera-Chávez, M. E., Garcia-Santillán A., Cordova-Rangel, A., Gonzalez-Gómez, S., & Tejada-Peña, E. (2016). Anxiety towards mathematics and educational level: A study on means differences. European Journal of Contemporary Education, 17(3) 311-323. https://eric.ed.gov/?id=EJ1116550.pdf
Devika, R. (2016). Handling fractions and errors in fractions. I-Manager's Journal on Mathematics. 5(3), 1-7. https://doi.org/10.26634/jmat.5.3.8223
Fan, L., & Bokhove, C. (2014). Rethinking the role of algorithms in school mathematics: A conceptual model with focus on cognitive development. ZDM Mathematics Education, 46, 481–492. https://doi.org/10.1007/s11858-014-0590-2
Fernandez, R. C. C., & Abocejo, F. T. (2014). Child labor, poverty and school attendance: Evidences from the Philippines by region. CNU Journal of Higher Education, 8(1), 114-127. http://www.jhe.cnu.edu.ph/index.php/cnujhe/article/view/151
Gabriel, F., Coché, F., Szucs, D., Carette, V., Rey, B., & Content, A. (2013). A componential view of children's difficulties in learning fractions. Frontiers in Psychology, 4, 715. https://doi.org/10.3389/fpsyg.2013.00715
Ghazali, N. H. C., & Zakaria, E. (2011). Students' procedural and conceptual understanding of mathematics. Australian Journal of Basic and Applied Sciences, 5(7), 684-691. http://www.ajbasweb.com/old/ajbas/2011/July-2011/684-691.pdf
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
Hariyani, M., Herman, T., Suryadi, D., & Prabawanto, S. (2022). Exploration of student learning obstacles in solving fraction problems in elementary school. International Journal of Educational Methodology, 8(3), 505–515. https://doi.org/10.12973/ijem.8.3.505
Hord, C., Ladrigan, E., & Saldanha, R. L. (2020). A student with a learning disability and multi-step equations with fractions. Learning Disabilities: A Contemporary Journal, 18(1), 111-121. https://files.eric.ed.gov/fulltext/EJ1264268.pdf
Hurrell, D. (2021). Conceptual knowledge or procedural knowledge or conceptual knowledge and procedural knowledge: Why the conjunction is important to teachers. Australian Journal of Teacher Education (Online), 46(2), 57-71. https://search.informit.org/doi/10.3316/informit.757709794375494
Hwang, J., & Riccomini, P. J. (2021). A descriptive analysis of the error patterns observed in the fraction-computation solution pathways of students with and without learning disabilities. Assessment for Effective Intervention, 46(2), 132–142. https://doi.org/10.1177/1534508419872256
Ibañez, E. D., & Pentang, J. (2021). Socio-constructivist learning and teacher education students’ conceptual understanding and attitude toward fractions. Indonesian Research Journal in Education, 5(1), 22-44. https://online-journal.unja.ac.id/irje/article/ download/12187/10849
Iskenderoglu, T.A. (2018). Fraction multiplication and division word problems posed by different years of preservice elementary mathematics teachers. European Journal of Educational Research, 7(2), 373-385. https://doi.org/10.12973/eu-jer.7.2.373
Jankvist, U. T., & Niss, M. (2018). Counteracting destructive student misconceptions of mathematics. Education Sciences, 8(2), 53. https://doi.org/10.26822/iejee.2023.283
Jayanthi, M., Gersten, R., Schumacher, R. F., Dimino, J., Smolkowski, K., & Spallone, S. (2021). Improving struggling Fifth-Grade students’ understanding of fractions: a randomized controlled trial of an intervention that stresses both concepts and procedures. Exceptional Children, 88(1), 81–100. https://doi.org/10.1177/00144029211008851
Jolejole-Caube, C., Dumlao, A. B., & Abocejo, F. T. (2019). Anxiety towards mathematics and mathematics performance of grade 7 learners. European Journal of Education Studies, 6(1), 334-360. http://dx.doi.org/10.5281/zenodo.2694050
Joutsenlahti, J., & Kulju, P. (2017). Multimodal languaging as a pedagogical model—A case study of the concept of division in school mathematics. Education Science, 7(9), 1-9. https://doi.org/10.3390/educsci7010009
Kang, H. J. (2022). Preservice elementary teachers understanding of fraction multiplication and division in multiple contexts. International Electronic Journal of Elementary Education, 15(2), 109-121. https://doi.org/10.26822/iejee.2023.283
Kusuma, U., & Retnawati, H. (2019). Analysis of sixth graders’ difficulties in solving Mathematics word problems on whole numbers, fractions, and decimals. Journal of Physics: Conference Series, 1320. https://doi.org/10.1088/1742-6596/1320/1/012008
Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2017). How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569-578. https://doi.org/10.12973/ejmste/76959
Lauritzen, P. (2012). Conceptual and procedural knowledge of mathematical functions [Doctoral dissertation, University of Eastern Finland]. University of Eastern Finland Digital Repository. http://epublications.uef.fi/pub/urn_isbn_978-952-61-0893-3/urn_isbn_978-952-61-0893-3.pdf
Lee, H. J., & Boyadzhiev, I. (2020). Underprepared college students' understanding of and misconceptions with fractions. International Electronic Journal of Mathematics Education, 15(3), 1-12. https://doi.org/10.29333/iejme/7835
Maass, K., Geiger, V., Ariza, M. R., & Goos, M. (2019). The role of mathematics in interdisciplinary STEM education. ZDM Mathematics Education, 51, 869-884. https://doi.org/10.1007/s11858-019-01100-5
Maelasari, E., & Jupri, A. (2017). Analysis of student errors on division of fractions. Journal of Physics: Conference Series, 812(1), 012033. https://doi.org/10.1088/1742-6596/812/1/012033
Makhubele, Y. E. (2021). The analysis of grade 8 fractions errors displayed by learners due to deficient mastery of prerequisite concepts. International Electronic Journal of Mathematics Education, 16(3), em0645. https://doi.org/10.29333/iejme/11004
Mbeki, N., & Mbekwa, M. O. (2022). Grade 9 learners’ ways of working with Algebraic fractions: Errors and misconceptions. In K.R. Langenhoven, & C.H. Stevenson-Milln (Eds.), Book of proceedings of the 30th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (76-106). SAARMSTE. https://wdetest.com/saarmste/wp-content/uploads/2022/01/Book-of-Proceedings_Long-Papers_30th-Conference.pdf#page=76
Musa, A. K. J., Dauda, B., & Umar, M. A. (2016). Gender differences in achievement goals and performances in English language and mathematics of senior secondary schools’ students in Borno State, Nigeria. Journal of Education and Practice, 7(27), 165-175. https://files.eric.ed.gov/fulltext/EJ1115862.pdf
Nahdi, D. S., & Jatisunda, M. G. (2020). Conceptual understanding and procedural knowledge: A case study on learning mathematics of fractional material in elementary school. Journal of Physics: Conference Series, 1477(4), 042037. https://files.eric.ed.gov/fulltext/EJ1296887.pdf
Owi, W. P., & Ang, K. H. (2015). Mathematical operations from teacher to student: A case study of applied division wheel in primary school. International Journal of Scientific Engineering and Research, 3(9), 2347-3878. https://www.ijser.in/archives/v3i9/IJSER15480.pdf
Rittle-Johnson, B. Schneider, M. & Star, J. (2015). Not a one-way street: Bi-directional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587-597. https://doi.org/10.1007/s10648-015-9302-x
Rodriguez, K. F. R., & Abocejo, F. T. (2018). Competence vis-à-vis performance of special education preservice teachers. European Academic Research, 6(7), 3474-3498. Retrieved from http://www.euacademic.org/UploadArticle/3707.pdf
Rosa, M., & Orey, D. C. (2015). A trivium curriculum for mathematics based on literacy, matheracy, and technoracy: An ethnomathematics perspective. ZDM Mathematics Education, 47(4), 587-598. https://doi.org/10.1007/s11858-015-0688-1
Saleh, S. F., Sirajuddin, N., Ernawati, N., & Damayanti, N. (2023). Analysis of Students’ Mathematical Ability in Solving Fraction Problems at Elementary School Level. AULADUNA Jurnal Pendidikan Dasar Islam, 10(1), 116–125. https://doi.org/10.24252/10.24252/auladuna.v10i1a9.2023
Saraspe, L. D., & Abocejo, F. T. (2020). Effectiveness of descriptive praise on the English composition skill of bridging students. European Journal of English Language Teaching, 5(4), 18-38. http://dx.doi.org/10.46827/ejel.v5i4.3140
Suryadi, Mahardika, I. K., Supeno, & Sudarti. (2021). Data literacy of high school students on physics learning. Journal of Physics: Conference Series, 1839(1), 012025. https://doi.org/10.1088/1742-6596/1839/1/012025
Thomson, M. M., DiFrancesca, D., Carrier, S., & Lee, C. (2017). Teaching efficacy: Exploring relationships between mathematics and science self-efficacy beliefs, PCK and domain knowledge among preservice teachers from the United States. Teacher Development, 21(1), 1-20. https://doi.org/10.1080/13664530.2016.1204355
Torio, M. Z. C. (2015). Development of instructional material using algebra as a tool in problem-solving. International Journal of Education and Research, 3(1), 569-586. http://ijern.com/journal/2015/January-2015/48.pdf
Yorulmaz, A., & Önal, H. (2017). Examination of the views of class teachers regarding the errors primary school students make in four operations. Universal Journal of Educational Research, 5(11), 1885-1895. https://doi.org/10.13189/ujer.2017.051105
Yuan, S. (2013). Incorporating Polya’s problem solving method in remedial math. Journal of Humanistic Mathematics, 3(1), 96-107. https://scholarship.claremont.edu/jhm/vol3/iss1/8
Zembat, I. O. (2015). An alternative route to teaching fraction division: Abstraction of common denominator algorithm. International Electronic Journal of Elementary Education, 7(3), 399-422. https://files.eric.ed.gov/fulltext/EJ1068041.pdf
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 University of San Jose-Recoletos
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright of the Journal belongs to the University of San Jose-Recoletos
