Pengetahuan Konseptual dan Prosedural dalam Matematik: Satu Sorotan Literatur Sistematik
Keywords:
pengetahuan konseptual, pengetahuan prosedural, penguasaan, matematik
Abstract
Pengetahuan konseptual dan prosedural merupakan dua jenis pengetahuan yang harus dimiliki oleh pelajar untuk menguasai matematik. Kedua-dua pengetahuan ini mempunyai kepentingan tersendiri dan memberikan pengaruh terhadap tahap penguasaan pelajar dalam matematik. Sorotan literatur bersistematik dijalankan bagi menganalisis kajian lepas berhubung kaitan pengetahuan konseptual dan prosedural dengan tahap pencapaian matematik pelajar. Kajian ini juga dijalankan untuk meninjau pendekatan dan kaedah yang digunakan untuk meningkatkan pengetahuan konseptual dan prosedural pelajar. Sebanyak 30 kajian dalam tempoh lima tahun terkini telah terpilih dalam kajian sistematik ini dan kajian-kajian tersebut diperoleh melalui pangkalan data Scopus, Web of Science dan ERIC. Dapatan kajian menunjukkan terdapat banyak pendekatan dan kaedah yang digunakan untuk meningkatkan pengetahuan konseptual pelajar. Peningkatan dalam pengetahuan konseptual ini meningkatkan tahap penguasaan matematik pelajar. Dapatan kajian ini boleh dimanfaatkan oleh semua pihak terutamanya guru-guru dan institusi pendidikan bagi meningkatkan tahap penguasaan pelajar dalam matematik. Kajian ini juga boleh dijadikan sebagai panduan dalam penghasilan model atau kaedah pembelajaran yang bertujuan untuk meningkatkan pengetahuan konseptual dan prosedural pelajar dalam usaha untuk membantu meningkatkan pencapaian pelajar dalam matematik.
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References
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Blume, F., Dresler, T., Gawrilow, C., Ehlis, A. C., Goellner, R., & Moeller, K. (2021). Examining the relevance of basic numerical skills for mathematical achievement in secondary school using a within-task assessment approach. Acta Psychologica, 215, 103289. https://doi.org/10.1016/j.actpsy.2021.103289
Chang, Y. P., Krawitz, J., Schukajlow, S., & Yang, K. L. (2020). Comparing German and Taiwanese secondary school students’ knowledge in solving mathematical modelling tasks requiring their assumptions. ZDM - Mathematics Education, 52(1), 59–72. https://doi.org/10.1007/s11858-019-01090-4
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Kadijevich, D. M. (2018). Relating procedural and conceptual knowledge. Teaching of Mathematics, 21(1), 15–28.
Lai, M. Y., Kinnear, V., & Fung, C. I. (2019). Teaching Mathematics for Understanding in Primary Schools: Could Teaching for Mathematising Be a Solution?. International Journal for Mathematics Teaching and Learning, 20(1), 1–17.
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Namkung, J. M., & Bricko, N. (2020). The Effects of Algebraic Equation Solving Intervention for Students With Mathematics Learning Difficulties. https://doi.org/10.1177/0022219420930814
Ocal, M. F. (2017). The Effect of Geogebra on Students’ Conceptual and Procedural Knowledge: The Case of Applications of Derivative. Higher Education Studies, 7(2), 67. https://doi.org/10.5539/hes.v7n2p67
Otun, W. I., & Olaoye, A. A. (2019). Enhancing the Conceptual, Procedural and Flexible Procedural Knowledge of Pre-Service Mathematics Teachers in Algebra. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 4(2), 66–78. https://doi.org/10.23917/jramathedu.v4i2.8363
Radmehr, F., & Drake, M. (2020). Exploring students’ metacognitive knowledge: The case of integral calculus. Education Sciences, 10(3). https://doi.org/10.3390/educsci10030055
Rahman, A., & Ahmar, A. S. (2016). Exploration of mathematics problem solving process based on the thinking level of students in junior high school. International Journal of Environmental and Science Education, 11(14), 7278–7285. https://doi.org/10.5281/zenodo.240664
Rittle-Johnson, B. (2017). Developing Mathematics Knowledge. Child Development Perspectives, 11(3), 184–190. https://doi.org/10.1111/cdep.12229
Rittle-Johnson, B., Fyfe, E. R., & Loehr, A. M. (2016). Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson. British Journal of Educational Psychology, 86(4), 576–591. https://doi.org/10.1111/bjep.12124
Rittle-Johnson, B., & Schneider, M. (2015). Developing Conceptual and Procedural Knowledge of Mathematics. Oxford Handbook of Numerical Cognition, 1, 1118–1134. http://oxfordhandbooks.com/view/10.1093/oxfordhb/9780199642342.001.0001/oxfordhb-9780199642342-e-014
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(4), 587–597. https://doi.org/10.1007/s10648-015-9302-x
Saiman, Wahyuningsih, P., & Hamdani. (2017). Conceptual or procedural mathematics for engineering students at University of Samudra. Journal of Physics: Conference Series, 855(1). https://doi.org/10.1088/1742-6596/855/1/012041
Satsangi, R., Hammer, R., & Bouck, E. C. (2020). Using Video Modeling to Teach Geometry Word Problems: A Strategy for Students With Learning Disabilities. Remedial and Special Education, 41(5), 309–320. https://doi.org/10.1177/0741932518824974
Stoyle, K. L., & Morris, B. J. (2017). Blogging mathematics: Using technology to support mathematical explanations for learning fractions. Computers and Education, 111, 114–127. https://doi.org/10.1016/j.compedu.2017.04.007
Sylviyani, H. (2017). Etnomatematika: Aplikasi bangun datar segiempat pada candi Muaro Jambi. 8(2), 99–110.
Torres-Carrion, P. V., Soledad, C., Aciar, S., & Rodriguez-Morales, G. (2018). Methodology for Systematic Literature Review applied to Engineering and Education. 1364–1373.
Vamvakoussi, X., Bempeni, M., Poulopoulou, S., & Tsiplaki, I. (2019). Theoretical and methodological issues in the study of conceptual and procedural knowledge : Reflections on a series of studies on Greek secondary students ’ knowledge of fractions. 6(2), 82–96.
Watson, S. M. R., Lopes, J., Oliveira, C., & Judge, S. (2018). Error patterns in Portuguese students’ addition and subtraction calculation tasks: Implications for teaching. Journal for Multicultural Education, 12(1), 67–82. https://doi.org/10.1108/JME-01-2017-0002
Wawan, Talib, A., & Djam’an, N. (2019). Analisis Pemahaman Konseptual dan Prosedural Siswa dalam Menyelesaikan Soal Matematika Berdasarkan Gaya Belajar. Issues in Mathematics Education (IMED), 1(2), 101–106.
Yummiyati, K., Sujadi, I., & Indriati, D. (2019). Cognitive Level Profile At the Tenth Grade of Senior High School Students in Mathematics Problem. Nternational Online Journal of Education and Teaching (IOJET), 6(3). http://iojet.org/index.php/IOJET/article/view/535, diakses Jumat 2 Juli 2021
Yurniwati. (2019). Improving the Conceptual and Procedural Knowledge of Prospective Teachers through Multisensory Approach: Experience from Indonesia. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(2), 106–117. https://doi.org/10.23917/jramathedu.v3i2.6783
Zulnaidi, H., & Zamri, S. N. A. S. (2017). The effectiveness of the geogebra software: The intermediary role of procedural knowledge on students’ conceptual knowledge and their achievement in mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 13(6), 2155–2180. https://doi.org/10.12973/eurasia.2017.01219a
Aydin, U. (2018). Conceptual and Procedural Angle Knowledge: Do Gender and Grade Level Make a Difference? International Journal for Mathematics Teaching and Learning, 19(1), 22–46.
Aydın, U., & Özgeldi, M. (2019). The PISA Tasks: Unveiling Prospective Elementary Mathematics Teachers’ Difficulties with Contextual, Conceptual, and Procedural Knowledge. Scandinavian Journal of Educational Research, 63(1), 105–123. https://doi.org/10.1080/00313831.2017.1324906
Beilstein, S. O. (2019). Supporting Children’s Conceptual Understanding of Fractions With Manipulative and Gesture. In Αγαη (Vol. 8, Issue 5).
Bergsten, C., Engelbrecht, J., & Kågesten, O. (2017). Conceptual and procedural approaches to mathematics in the engineering curriculum - comparing views of junior and senior engineering students in two countries. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 533–553. https://doi.org/10.12973/eurasia.2017.00631a
Blume, F., Dresler, T., Gawrilow, C., Ehlis, A. C., Goellner, R., & Moeller, K. (2021). Examining the relevance of basic numerical skills for mathematical achievement in secondary school using a within-task assessment approach. Acta Psychologica, 215, 103289. https://doi.org/10.1016/j.actpsy.2021.103289
Chang, Y. P., Krawitz, J., Schukajlow, S., & Yang, K. L. (2020). Comparing German and Taiwanese secondary school students’ knowledge in solving mathematical modelling tasks requiring their assumptions. ZDM - Mathematics Education, 52(1), 59–72. https://doi.org/10.1007/s11858-019-01090-4
Daubert, E. N., & Ramani, G. B. (2019). Math and Memory in Bilingual Preschoolers: The Relations Between Bilingualism, Working Memory, and Numerical Knowledge. Journal of Cognition and Development, 20(3), 314–333. https://doi.org/10.1080/15248372.2019.1565536
Engelbrecht, J., Bergsten, C., & Kågesten, O. (2017). Conceptual and procedural approaches to mathematics in the engineering curriculum: views of qualified engineers*. European Journal of Engineering Education, 42(5), 570–586. https://doi.org/10.1080/03043797.2017.1343278
Herppich, S., & Wittwer, J. (2018). Preservice teachers’ beliefs about students’ mathematical knowledge structure as a foundation for formative assessments. Teaching and Teacher Education, 76, 242–254. https://doi.org/10.1016/j.tate.2018.06.011
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, 46(2), 57–71. https://doi.org/10.14221/ajte.2021v46n2.4
Kadijevich, D. M. (2018). Relating procedural and conceptual knowledge. Teaching of Mathematics, 21(1), 15–28.
Lai, M. Y., Kinnear, V., & Fung, C. I. (2019). Teaching Mathematics for Understanding in Primary Schools: Could Teaching for Mathematising Be a Solution?. International Journal for Mathematics Teaching and Learning, 20(1), 1–17.
Legesse, M., Luneta, K., & Ejigu, T. (2020). Studies in Educational Evaluation Analyzing the e ff ects of mathematical discourse-based instruction on eleventh-grade students ’ procedural and conceptual understanding of probability and statistics. Studies in Educational Evaluation, 67(July), 100918. https://doi.org/10.1016/j.stueduc.2020.100918
Lenz, K., Dreher, A., Holzäpfel, L., & Wittmann, G. (2020). Are conceptual knowledge and procedural knowledge empirically separable? The case of fractions. British Journal of Educational Psychology, 90(3), 809–829. https://doi.org/10.1111/bjep.12333
Levin, M. (2018). Conceptual and Procedural Knowledge During Strategy Construction: A Complex Knowledge Systems Perspective. Cognition and Instruction, 36(3), 247–278. https://doi.org/10.1080/07370008.2018.1464003
Ling, C. Y., Osman, S., Daud, M. F., & Hussin, W. N. W. (2019). Application of vee diagram as a problem-solving strategy in developing students’ conceptual and procedural knowledge. International Journal of Innovative Technology and Exploring Engineering, 8(10), 2796–2800. https://doi.org/10.35940/ijitee.J9591.0881019
Mairing, J. P. (2016). Thinking Process of Naive Problem Solvers to Solve Mathematical Problems. International Education Studies, 10(1), 1. https://doi.org/10.5539/ies.v10n1p1
Morales, N., Dartnell, P., & Gómez, D. M. (2020). A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students. Frontiers in Psychology, 11(June), 1–14. https://doi.org/10.3389/fpsyg.2020.01190
Namkung, J. M., & Bricko, N. (2020). The Effects of Algebraic Equation Solving Intervention for Students With Mathematics Learning Difficulties. https://doi.org/10.1177/0022219420930814
Ocal, M. F. (2017). The Effect of Geogebra on Students’ Conceptual and Procedural Knowledge: The Case of Applications of Derivative. Higher Education Studies, 7(2), 67. https://doi.org/10.5539/hes.v7n2p67
Otun, W. I., & Olaoye, A. A. (2019). Enhancing the Conceptual, Procedural and Flexible Procedural Knowledge of Pre-Service Mathematics Teachers in Algebra. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 4(2), 66–78. https://doi.org/10.23917/jramathedu.v4i2.8363
Radmehr, F., & Drake, M. (2020). Exploring students’ metacognitive knowledge: The case of integral calculus. Education Sciences, 10(3). https://doi.org/10.3390/educsci10030055
Rahman, A., & Ahmar, A. S. (2016). Exploration of mathematics problem solving process based on the thinking level of students in junior high school. International Journal of Environmental and Science Education, 11(14), 7278–7285. https://doi.org/10.5281/zenodo.240664
Rittle-Johnson, B. (2017). Developing Mathematics Knowledge. Child Development Perspectives, 11(3), 184–190. https://doi.org/10.1111/cdep.12229
Rittle-Johnson, B., Fyfe, E. R., & Loehr, A. M. (2016). Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson. British Journal of Educational Psychology, 86(4), 576–591. https://doi.org/10.1111/bjep.12124
Rittle-Johnson, B., & Schneider, M. (2015). Developing Conceptual and Procedural Knowledge of Mathematics. Oxford Handbook of Numerical Cognition, 1, 1118–1134. http://oxfordhandbooks.com/view/10.1093/oxfordhb/9780199642342.001.0001/oxfordhb-9780199642342-e-014
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(4), 587–597. https://doi.org/10.1007/s10648-015-9302-x
Saiman, Wahyuningsih, P., & Hamdani. (2017). Conceptual or procedural mathematics for engineering students at University of Samudra. Journal of Physics: Conference Series, 855(1). https://doi.org/10.1088/1742-6596/855/1/012041
Satsangi, R., Hammer, R., & Bouck, E. C. (2020). Using Video Modeling to Teach Geometry Word Problems: A Strategy for Students With Learning Disabilities. Remedial and Special Education, 41(5), 309–320. https://doi.org/10.1177/0741932518824974
Stoyle, K. L., & Morris, B. J. (2017). Blogging mathematics: Using technology to support mathematical explanations for learning fractions. Computers and Education, 111, 114–127. https://doi.org/10.1016/j.compedu.2017.04.007
Sylviyani, H. (2017). Etnomatematika: Aplikasi bangun datar segiempat pada candi Muaro Jambi. 8(2), 99–110.
Torres-Carrion, P. V., Soledad, C., Aciar, S., & Rodriguez-Morales, G. (2018). Methodology for Systematic Literature Review applied to Engineering and Education. 1364–1373.
Vamvakoussi, X., Bempeni, M., Poulopoulou, S., & Tsiplaki, I. (2019). Theoretical and methodological issues in the study of conceptual and procedural knowledge : Reflections on a series of studies on Greek secondary students ’ knowledge of fractions. 6(2), 82–96.
Watson, S. M. R., Lopes, J., Oliveira, C., & Judge, S. (2018). Error patterns in Portuguese students’ addition and subtraction calculation tasks: Implications for teaching. Journal for Multicultural Education, 12(1), 67–82. https://doi.org/10.1108/JME-01-2017-0002
Wawan, Talib, A., & Djam’an, N. (2019). Analisis Pemahaman Konseptual dan Prosedural Siswa dalam Menyelesaikan Soal Matematika Berdasarkan Gaya Belajar. Issues in Mathematics Education (IMED), 1(2), 101–106.
Yummiyati, K., Sujadi, I., & Indriati, D. (2019). Cognitive Level Profile At the Tenth Grade of Senior High School Students in Mathematics Problem. Nternational Online Journal of Education and Teaching (IOJET), 6(3). http://iojet.org/index.php/IOJET/article/view/535, diakses Jumat 2 Juli 2021
Yurniwati. (2019). Improving the Conceptual and Procedural Knowledge of Prospective Teachers through Multisensory Approach: Experience from Indonesia. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(2), 106–117. https://doi.org/10.23917/jramathedu.v3i2.6783
Zulnaidi, H., & Zamri, S. N. A. S. (2017). The effectiveness of the geogebra software: The intermediary role of procedural knowledge on students’ conceptual knowledge and their achievement in mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 13(6), 2155–2180. https://doi.org/10.12973/eurasia.2017.01219a
