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Abstract
Fractions remain predominantly one of the most challenging topics to teach and learn. Brunei Darussalam is no exception, where a few local researches reported that students performed poorly in fraction topics. To understand this situation, this study focuses on pupils’ understanding in solving problems on fractions. Specifically, this study investigated Year 5 pupils’ conceptual and procedural performance on the addition of fractions. This study employed a quantitative research approach involving 572 primary school children. A test consisting of six carefully planned questions on fractions was used as the research instrument. The questions were divided into two sections to test pupils’ conceptual and procedural understanding laterally. The findings from this study revealed that children performed better in the procedural than in the conceptual questions. It can be concluded that most Year 5 pupils can correctly attempt the addition of fractions via procedural approach without understanding the essential concepts involved. Recommendation for future research was also discussed.
DOI : https://doi.org/10.22342/jpm.16.2.17811.227-238
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Copyright (c) 2022 Nor’ Arifahwati Abbas, Nor Azura Abdullah, Masitah Shahrill, Khairul Amilin Tengah
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References
- Abbas, N. A. H., Shahrill, M., & Prahmana, R. C. I. (2020). Understanding primary school children’s learning on addition of fractions. Journal of Physics: Conference Series, 1613(1), 012046. https://doi:10.1088/1742-6596/1613/1/012046
- Abdullah, N. A., & Leung, F. K. S. (2019). Exploring teachers’ values and valuing process in school- based lesson study: A Brunei Darussalam case study. In P. Clarkson, W. Seah, & J. Pang (Eds.), Values and Valuing in Mathematics Education. ICME-13 Monographs (pp. 129–142). Cham: Springer. https://doi.org/10.1007/978-3-030-16892-6_9
- Davis, E. J. (2000). Guest editorial: Understanding numerical concepts and skills—Some differences. The Mathematics Educator, 9(1), 1–4.
- Finti, H. N. F. M. M., Shahrill, M., & Salleh, S. M. (2016). Integrating virtual manipulative with the use of iPad in the teaching and learning of fractions. Knowledge Management & E-Learning: An International Journal, 8(4), 581–601. https://doi.org/10.34105/j.kmel.2016.08.036
- Gani, M. A., Tengah, K. A., & Said, H. (2019). Bar model as intervention in solving word problem of percentage. International Journal on Emerging Mathematics Education, 3(1), 69–76. https://dx.doi.org/10.12928/ijeme.v3i1.11093
- Ginting, M. S., Prahmana, R. C. I., Isa, M., & Murni, M. (2018). Improving the reasoning ability of elementary school student through the Indonesian realistic mathematics education. Journal on Mathematics Education, 9(1), 41–54. http://dx.doi.org/10.22342/jme.9.1.5049.41-54
- Harun, Z. (2003). The development of fraction and decimal concepts among form 4 N-level students at a girls’ secondary school in Brunei Darussalam. Unpublished Master Thesis. Brunei Darussalam: Universiti Brunei Darussalam.
- Harun, H. Z. H. (2011). Evaluating the teaching and learning of fractions through modelling in Brunei: Measurement and semiotic analyses. Unpublished Doctoral Thesis. United Kingdom: The University of Manchester.
- Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102, 843–859. https://doi.org/10.1037/a0019824
- 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). Hillsdale: Erlbaum.
- Idris, N., & Narayanan, L. M. (2011). Error patterns in addition and subtraction of fractions among form two students. Journal of Mathematics Education, 4(2), 35–54.
- Japar, I., Asamoah, D., & Shahrill, M. (2022). Addressing student learning gaps in fractions: How effective is synchronous videoconferencing? Jurnal Pendidikan Matematika, 16(1), 103–120. https://doi.org/10.22342/jpm.14.2.11261.101-116
- Julie, H., Suwarsono, S., & Juniati, D. (2013). First cycle developing teaching materials for integers in grade four with realistic mathematics education. Journal on Mathematics Education, 4(2), 172–187. https://doi.org/10.22342/jme.4.2.415.172-187
- Karika, T., & Csíkos, C. (2022). A test for understanding simple fractions among 5th grade students at the beginning of lower secondary education. EURASIA Journal of Mathematics, Science and Technology Education, 18(2), em2081. https://doi.org/10.29333/ejmste/11654
- Kerslake, D. (1986). Fractions: Children’s strategies and errors. A report of the strategies and errors in secondary mathematics project. NFER-NELSON.
- Khairunnisak, C., Amin, S. M., Juniati, D., & de Haan, D. (2012). Supporting fifth graders in learning multiplication of fraction with whole number. Journal on Mathematics Education, 3(1), 71–86. http://dx.doi.org/10.22342/jme.3.1.615.71-86
- Laidin, D. R., & Tengah, K. A. (2021). Applying butterfly method in the learning of addition and subtraction of fractions. Jurnal Pendidikan Matematika, 15(2), 161–174. https://doi.org/10.22342/jpm.15.2.13934.161-174
- Li, H. C. (2014). A comparative analysis of British and Taiwanese students’ conceptual and procedural knowledge of fraction addition. International Journal of Mathematical Education in Science and Technology, 45(7), 968–979. https://doi.org/10.1080/0020739X.2014.892163
- Low, J., Shahrill, M., & Zakir, N. (2020). Solving fractions by applying the bar model concept with the butterfly method. Jurnal Pendidikan Matematika, 14(2), 101–116. https://doi.org/10.22342/jpm.14.2.11261.101-116
- Lubis, N. H. A. M. N., Tengah, K. A., Shahrill, M., Leong, E. (2017). Enhancing mathematics students’ mental computation in calculating percentage by using the bubble method. In S. De Silva (Ed.), Proceedings for the 3rd International Conference on Education 2017 (Vol. 3, pp. 155–165). Pitakotte, Sri Lanka: The International Institute of Knowledge Management. https://doi.org/10.17501/icedu.2017.3117
- Nasution, M. F., & Putri, R. I. I. (2018). Rowing sport in learning fractions of the fourth grade students. Journal on Mathematics Education, 9(1), 69–80. http://dx.doi.org/10.22342/jme.9.1.4270.69-80
- Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19. https://doi.org/10.1016/j.tics.2012.11.004
- Simpol, N. S. H., Shahrill, M., Li, H. C., & Prahmana, R. C. I. (2017). Implementing thinking aloud pair and Pólya problem solving strategies in fractions. Journal of Physics: Conference Series, 943(1), 012013. https://doi.org/10.1088/1742-6596/943/1/012013
- Suffolk, J., & Clements, M. A. (2003). Fractions concepts and skills of form 1 and form 2 students in Brunei Darussalam. In H. S. Dhindsa, S. B. Lim, P. Achleitner, & M. A. Clements (Eds.), Studies in Science, Mathematics and Technical Education (pp. 145–154). Brunei Darussalam: Universiti Brunei Darussalam.
- Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5–13. https://doi.org/10.1016/j.learninstruc.2014.03.002
- Tsai, T. L., & Li, H. C. (2017). Towards a framework for developing students’ fraction proficiency. International Journal of Mathematical Education in Science and Technology, 48(2), 244–255. https://doi.org/10.1080/0020739X.2016.1238520
- Yusof, J. (2003). Mathematics errors in fractions work: A longitudinal study of primary level pupils in Brunei. Unpublished Doctoral Thesis. Perth, Australia: Curtin University.
- Yusof, J., & Langkan, J. (2016). Word problems involving fractions: A case of year 5 pupils in Brunei Darussalam. In 6th International Conference on Language, Education, and Innovation, Malaysia (pp. 47–53).
- Yusof, J., & Malone, J. (2003). Mathematical errors in fractions: A case of Bruneian primary 5 pupils. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics Education Research: Innovation, Networking, Opportunity (Vol. 2, pp. 783–790). Geelong, Victoria: Mathematics Education Research Group of Australasia.
References
Abbas, N. A. H., Shahrill, M., & Prahmana, R. C. I. (2020). Understanding primary school children’s learning on addition of fractions. Journal of Physics: Conference Series, 1613(1), 012046. https://doi:10.1088/1742-6596/1613/1/012046
Abdullah, N. A., & Leung, F. K. S. (2019). Exploring teachers’ values and valuing process in school- based lesson study: A Brunei Darussalam case study. In P. Clarkson, W. Seah, & J. Pang (Eds.), Values and Valuing in Mathematics Education. ICME-13 Monographs (pp. 129–142). Cham: Springer. https://doi.org/10.1007/978-3-030-16892-6_9
Davis, E. J. (2000). Guest editorial: Understanding numerical concepts and skills—Some differences. The Mathematics Educator, 9(1), 1–4.
Finti, H. N. F. M. M., Shahrill, M., & Salleh, S. M. (2016). Integrating virtual manipulative with the use of iPad in the teaching and learning of fractions. Knowledge Management & E-Learning: An International Journal, 8(4), 581–601. https://doi.org/10.34105/j.kmel.2016.08.036
Gani, M. A., Tengah, K. A., & Said, H. (2019). Bar model as intervention in solving word problem of percentage. International Journal on Emerging Mathematics Education, 3(1), 69–76. https://dx.doi.org/10.12928/ijeme.v3i1.11093
Ginting, M. S., Prahmana, R. C. I., Isa, M., & Murni, M. (2018). Improving the reasoning ability of elementary school student through the Indonesian realistic mathematics education. Journal on Mathematics Education, 9(1), 41–54. http://dx.doi.org/10.22342/jme.9.1.5049.41-54
Harun, Z. (2003). The development of fraction and decimal concepts among form 4 N-level students at a girls’ secondary school in Brunei Darussalam. Unpublished Master Thesis. Brunei Darussalam: Universiti Brunei Darussalam.
Harun, H. Z. H. (2011). Evaluating the teaching and learning of fractions through modelling in Brunei: Measurement and semiotic analyses. Unpublished Doctoral Thesis. United Kingdom: The University of Manchester.
Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102, 843–859. https://doi.org/10.1037/a0019824
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). Hillsdale: Erlbaum.
Idris, N., & Narayanan, L. M. (2011). Error patterns in addition and subtraction of fractions among form two students. Journal of Mathematics Education, 4(2), 35–54.
Japar, I., Asamoah, D., & Shahrill, M. (2022). Addressing student learning gaps in fractions: How effective is synchronous videoconferencing? Jurnal Pendidikan Matematika, 16(1), 103–120. https://doi.org/10.22342/jpm.14.2.11261.101-116
Julie, H., Suwarsono, S., & Juniati, D. (2013). First cycle developing teaching materials for integers in grade four with realistic mathematics education. Journal on Mathematics Education, 4(2), 172–187. https://doi.org/10.22342/jme.4.2.415.172-187
Karika, T., & Csíkos, C. (2022). A test for understanding simple fractions among 5th grade students at the beginning of lower secondary education. EURASIA Journal of Mathematics, Science and Technology Education, 18(2), em2081. https://doi.org/10.29333/ejmste/11654
Kerslake, D. (1986). Fractions: Children’s strategies and errors. A report of the strategies and errors in secondary mathematics project. NFER-NELSON.
Khairunnisak, C., Amin, S. M., Juniati, D., & de Haan, D. (2012). Supporting fifth graders in learning multiplication of fraction with whole number. Journal on Mathematics Education, 3(1), 71–86. http://dx.doi.org/10.22342/jme.3.1.615.71-86
Laidin, D. R., & Tengah, K. A. (2021). Applying butterfly method in the learning of addition and subtraction of fractions. Jurnal Pendidikan Matematika, 15(2), 161–174. https://doi.org/10.22342/jpm.15.2.13934.161-174
Li, H. C. (2014). A comparative analysis of British and Taiwanese students’ conceptual and procedural knowledge of fraction addition. International Journal of Mathematical Education in Science and Technology, 45(7), 968–979. https://doi.org/10.1080/0020739X.2014.892163
Low, J., Shahrill, M., & Zakir, N. (2020). Solving fractions by applying the bar model concept with the butterfly method. Jurnal Pendidikan Matematika, 14(2), 101–116. https://doi.org/10.22342/jpm.14.2.11261.101-116
Lubis, N. H. A. M. N., Tengah, K. A., Shahrill, M., Leong, E. (2017). Enhancing mathematics students’ mental computation in calculating percentage by using the bubble method. In S. De Silva (Ed.), Proceedings for the 3rd International Conference on Education 2017 (Vol. 3, pp. 155–165). Pitakotte, Sri Lanka: The International Institute of Knowledge Management. https://doi.org/10.17501/icedu.2017.3117
Nasution, M. F., & Putri, R. I. I. (2018). Rowing sport in learning fractions of the fourth grade students. Journal on Mathematics Education, 9(1), 69–80. http://dx.doi.org/10.22342/jme.9.1.4270.69-80
Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19. https://doi.org/10.1016/j.tics.2012.11.004
Simpol, N. S. H., Shahrill, M., Li, H. C., & Prahmana, R. C. I. (2017). Implementing thinking aloud pair and Pólya problem solving strategies in fractions. Journal of Physics: Conference Series, 943(1), 012013. https://doi.org/10.1088/1742-6596/943/1/012013
Suffolk, J., & Clements, M. A. (2003). Fractions concepts and skills of form 1 and form 2 students in Brunei Darussalam. In H. S. Dhindsa, S. B. Lim, P. Achleitner, & M. A. Clements (Eds.), Studies in Science, Mathematics and Technical Education (pp. 145–154). Brunei Darussalam: Universiti Brunei Darussalam.
Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5–13. https://doi.org/10.1016/j.learninstruc.2014.03.002
Tsai, T. L., & Li, H. C. (2017). Towards a framework for developing students’ fraction proficiency. International Journal of Mathematical Education in Science and Technology, 48(2), 244–255. https://doi.org/10.1080/0020739X.2016.1238520
Yusof, J. (2003). Mathematics errors in fractions work: A longitudinal study of primary level pupils in Brunei. Unpublished Doctoral Thesis. Perth, Australia: Curtin University.
Yusof, J., & Langkan, J. (2016). Word problems involving fractions: A case of year 5 pupils in Brunei Darussalam. In 6th International Conference on Language, Education, and Innovation, Malaysia (pp. 47–53).
Yusof, J., & Malone, J. (2003). Mathematical errors in fractions: A case of Bruneian primary 5 pupils. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics Education Research: Innovation, Networking, Opportunity (Vol. 2, pp. 783–790). Geelong, Victoria: Mathematics Education Research Group of Australasia.