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References
- Anderson, L. W., & Krathwohl, D. R. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Longman.
- Baek, J. M., Wickstrom, M. H., Tobias, J. M., Miller, A. L., Safak, E., Wessman-Enzinger, N., & Kirwan, J. V. (2017). Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem. Journal of Mathematical Behavior, 45, 1–14. https://doi.org/10.1016/j.jmathb.2016.10.005
- Brousseau, G. (2002). Theory of Didactical Situations in Mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (eds.); Vol. 19). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2
- Bütüner, S. Ö. (2021). Content and Problem Analysis in Turkish and Singaporean Mathematics Textbooks: The Case of Multiplying Fractions. Journal of Research in Mathematics Education, 10(2), 117. https://doi.org/10.17583/redimat.2021.4379
- Byrnes, J. P., & Wasik, B. A. (1991). Role of Conceptual Knowledge in Mathematical Procedural Learning. Developmental Psychology, 27(5), 777–786. https://doi.org/10.1037/0012-1649.27.5.777
- Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations: results from a national sample of elementary school teachers. Educational Studies in Mathematics, 107(3), 525–545. https://doi.org/10.1007/s10649-021-10033-4
- Greer, B. (1992). Multiplication and division as models of situations. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–295). Macmillan.
- 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
- Hallett, D., Nunes, T., Bryant, P., & Thorpe, C. M. (2012). Individual differences in conceptual and procedural fraction understanding: The role of abilities and school experience. Journal of Experimental Child Psychology, 113(4), 469–486. https://doi.org/10.1016/j.jecp.2012.07.009
- Izsák, A. (2008). Mathematical Knowledge for Teaching Fraction Multiplication. Cognition and Instruction, 26(1), 95–143. https://doi.org/10.1080/07370000701798529
- Khairunnisak, C., Maghfirotun, S., Juniati, A. D., & De Haan, D. (2012). Supporting fifth graders in learning multiplication of fraction with whole number. Journal on Mathematics Education, 3(1). https://doi.org/10.22342/jme.3.1.615.71-86
- Kilpatrick, J., Swafford, J., & Findell, B. (2001). The strands of mathematical proficiency. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Adding it up: Helping children learn mathematics (pp. 115–118). National Academy Press.
- Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge University Press.
- Li, G., Luo, H., Lei, J., Xu, S., & Chen, T. (2022). Effects of First-Time Experiences and Self-Regulation on College Students’ Online Learning Motivation: Based on a National Survey during COVID-19. Education Sciences, 12(4). https://doi.org/10.3390/educsci12040245
- Purnomo, Y. W., Arlini, R., Nuriadin, I., & Aziz, T. A. (2021). Learning trajectory based on fractional sub-constructs: Using fractions as quotients to introduce fractions. Mathematics Teaching-Research Journal, 13(3), 183–207. https://commons.hostos.cuny.edu/mtrj/wp-content/uploads/sites/30/2021/10/v13n3-Learning-trajectory-based-on-fractional-sub-constructs.pdf
- Purnomo, Y. W., Kowiyah, K., Alyani, F., & Assiti, S. S. (2014). Assessing Number Sense Performance of Indonesian Elementary School Students. International Education Studies, 7(8), 74–84. https://doi.org/10.5539/ies.v7n8p74
- Purnomo, Y. W., Widowati, C., Aziz, T. A., & Pramudiani, P. (2017). Fractions division knowledge of elementary school student: The case of Lala. AIP Conference Proceedings, 1868. https://doi.org/10.1063/1.4995148
- Purnomo, Y. W., Widowati, C., & Ulfah, S. (2019). Incomprehension of the Indonesian Elementary School Students on Fraction Division Problem. Infinity Journal, 8(1), 57. https://doi.org/10.22460/infinity.v8i1.p57-74
- Putra, Z. H. (2016). Evaluation of Elementary Teachers ’ Knowledge on Fraction Multiplication using Anthropological Theory of The Didactic. 13th International Congress on Mathematical Education, 24-31 July 2016.
- 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., & Schneider, M. (2014). Developing Conceptual and Procedural Knowledge of Mathematics (R. Cohen Kadosh & A. Dowker (eds.); Vol. 1, Issue March 2019). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014
- Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (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
- Rosli, R., Goldsby, D., Onwuegbuzie, A. J., Capraro, M. M., Capraro, R. M., & Gonzalez, E. G. Y. (2020). Elementary preservice teachers’ knowledge, perceptions and attitudes towards fractions: A mixed-analysis. Journal on Mathematics Education, 11(1). https://doi.org/10.22342/jme.11.1.9482.59-76
- Schneider, M., & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178–192. https://doi.org/10.1037/a0016701
- Sidney, P. G., Thompson, C. A., & Rivera, F. D. (2019). Number lines, but not area models, support children’s accuracy and conceptual models of fraction division. Contemporary Educational Psychology, 58, 288–298. https://doi.org/10.1016/j.cedpsych.2019.03.011
- Simon, M. A., Kara, M., Norton, A., & Placa, N. (2018). Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication: A study of the Learning Through Activity research program. Journal of Mathematical Behavior, 52, 151–173. https://doi.org/10.1016/j.jmathb.2018.03.002
- Skemp, R. R. (1987). The Psychology of Learning Mathematics: Expanded American Edition. Lawrence Elbaum Associates, Inc. Publishers.
- Son, J.-W., & Lee, J.-E. (2016). Pre-service Teachers’ Understanding of Fraction Multiplication, Representational Knowledge, and Computational Skills. Mathematics Teacher Education and Development, 182, 5–28.
- Star, J. R., & Stylianides, G. J. (2013). Procedural and Conceptual Knowledge: Exploring the Gap Between Knowledge Type and Knowledge Quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169–181. https://doi.org/10.1080/14926156.2013.784828
- Tall, D. (2002). Advanced mathematical thinking (Mathematic, Vol. 11). Springer Science & Business Media.
- Webel, C., & DeLeeuw, W. W. (2016). Meaning for fraction multiplication: Thematic analysis of mathematical talk in three fifth grade classes. The Journal of Mathematical Behavior, 41, 123–140. https://doi.org/http://dx.doi.org/10.1016/j.jmathb.2015.12.003
- Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
- Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Veldhuis, M. (2018). Opportunity-to-Learn to Solve Context-based Mathematics Tasks and Students’ Performance in Solving these Tasks – Lessons from Indonesia. EURASIA Journal of Mathematics, Science and Technology Education, 14(10). https://doi.org/10.29333/ejmste/93420
References
Anderson, L. W., & Krathwohl, D. R. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Longman.
Baek, J. M., Wickstrom, M. H., Tobias, J. M., Miller, A. L., Safak, E., Wessman-Enzinger, N., & Kirwan, J. V. (2017). Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem. Journal of Mathematical Behavior, 45, 1–14. https://doi.org/10.1016/j.jmathb.2016.10.005
Brousseau, G. (2002). Theory of Didactical Situations in Mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (eds.); Vol. 19). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2
Bütüner, S. Ö. (2021). Content and Problem Analysis in Turkish and Singaporean Mathematics Textbooks: The Case of Multiplying Fractions. Journal of Research in Mathematics Education, 10(2), 117. https://doi.org/10.17583/redimat.2021.4379
Byrnes, J. P., & Wasik, B. A. (1991). Role of Conceptual Knowledge in Mathematical Procedural Learning. Developmental Psychology, 27(5), 777–786. https://doi.org/10.1037/0012-1649.27.5.777
Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations: results from a national sample of elementary school teachers. Educational Studies in Mathematics, 107(3), 525–545. https://doi.org/10.1007/s10649-021-10033-4
Greer, B. (1992). Multiplication and division as models of situations. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–295). Macmillan.
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
Hallett, D., Nunes, T., Bryant, P., & Thorpe, C. M. (2012). Individual differences in conceptual and procedural fraction understanding: The role of abilities and school experience. Journal of Experimental Child Psychology, 113(4), 469–486. https://doi.org/10.1016/j.jecp.2012.07.009
Izsák, A. (2008). Mathematical Knowledge for Teaching Fraction Multiplication. Cognition and Instruction, 26(1), 95–143. https://doi.org/10.1080/07370000701798529
Khairunnisak, C., Maghfirotun, S., Juniati, A. D., & De Haan, D. (2012). Supporting fifth graders in learning multiplication of fraction with whole number. Journal on Mathematics Education, 3(1). https://doi.org/10.22342/jme.3.1.615.71-86
Kilpatrick, J., Swafford, J., & Findell, B. (2001). The strands of mathematical proficiency. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Adding it up: Helping children learn mathematics (pp. 115–118). National Academy Press.
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge University Press.
Li, G., Luo, H., Lei, J., Xu, S., & Chen, T. (2022). Effects of First-Time Experiences and Self-Regulation on College Students’ Online Learning Motivation: Based on a National Survey during COVID-19. Education Sciences, 12(4). https://doi.org/10.3390/educsci12040245
Purnomo, Y. W., Arlini, R., Nuriadin, I., & Aziz, T. A. (2021). Learning trajectory based on fractional sub-constructs: Using fractions as quotients to introduce fractions. Mathematics Teaching-Research Journal, 13(3), 183–207. https://commons.hostos.cuny.edu/mtrj/wp-content/uploads/sites/30/2021/10/v13n3-Learning-trajectory-based-on-fractional-sub-constructs.pdf
Purnomo, Y. W., Kowiyah, K., Alyani, F., & Assiti, S. S. (2014). Assessing Number Sense Performance of Indonesian Elementary School Students. International Education Studies, 7(8), 74–84. https://doi.org/10.5539/ies.v7n8p74
Purnomo, Y. W., Widowati, C., Aziz, T. A., & Pramudiani, P. (2017). Fractions division knowledge of elementary school student: The case of Lala. AIP Conference Proceedings, 1868. https://doi.org/10.1063/1.4995148
Purnomo, Y. W., Widowati, C., & Ulfah, S. (2019). Incomprehension of the Indonesian Elementary School Students on Fraction Division Problem. Infinity Journal, 8(1), 57. https://doi.org/10.22460/infinity.v8i1.p57-74
Putra, Z. H. (2016). Evaluation of Elementary Teachers ’ Knowledge on Fraction Multiplication using Anthropological Theory of The Didactic. 13th International Congress on Mathematical Education, 24-31 July 2016.
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., & Schneider, M. (2014). Developing Conceptual and Procedural Knowledge of Mathematics (R. Cohen Kadosh & A. Dowker (eds.); Vol. 1, Issue March 2019). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (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
Rosli, R., Goldsby, D., Onwuegbuzie, A. J., Capraro, M. M., Capraro, R. M., & Gonzalez, E. G. Y. (2020). Elementary preservice teachers’ knowledge, perceptions and attitudes towards fractions: A mixed-analysis. Journal on Mathematics Education, 11(1). https://doi.org/10.22342/jme.11.1.9482.59-76
Schneider, M., & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178–192. https://doi.org/10.1037/a0016701
Sidney, P. G., Thompson, C. A., & Rivera, F. D. (2019). Number lines, but not area models, support children’s accuracy and conceptual models of fraction division. Contemporary Educational Psychology, 58, 288–298. https://doi.org/10.1016/j.cedpsych.2019.03.011
Simon, M. A., Kara, M., Norton, A., & Placa, N. (2018). Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication: A study of the Learning Through Activity research program. Journal of Mathematical Behavior, 52, 151–173. https://doi.org/10.1016/j.jmathb.2018.03.002
Skemp, R. R. (1987). The Psychology of Learning Mathematics: Expanded American Edition. Lawrence Elbaum Associates, Inc. Publishers.
Son, J.-W., & Lee, J.-E. (2016). Pre-service Teachers’ Understanding of Fraction Multiplication, Representational Knowledge, and Computational Skills. Mathematics Teacher Education and Development, 182, 5–28.
Star, J. R., & Stylianides, G. J. (2013). Procedural and Conceptual Knowledge: Exploring the Gap Between Knowledge Type and Knowledge Quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169–181. https://doi.org/10.1080/14926156.2013.784828
Tall, D. (2002). Advanced mathematical thinking (Mathematic, Vol. 11). Springer Science & Business Media.
Webel, C., & DeLeeuw, W. W. (2016). Meaning for fraction multiplication: Thematic analysis of mathematical talk in three fifth grade classes. The Journal of Mathematical Behavior, 41, 123–140. https://doi.org/http://dx.doi.org/10.1016/j.jmathb.2015.12.003
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Veldhuis, M. (2018). Opportunity-to-Learn to Solve Context-based Mathematics Tasks and Students’ Performance in Solving these Tasks – Lessons from Indonesia. EURASIA Journal of Mathematics, Science and Technology Education, 14(10). https://doi.org/10.29333/ejmste/93420