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References
- Adelia, V., Putri, R. I. I., & Zulkardi. (2024a). Mathematics teachers in Palembang teaching practice: Numeracy perspective. THE 5TH SRIWIJAYA UNIVERSITY LEARNING AND EDUCATION (SULE) INTERNATIONAL CONFERENCE 2023: Reimagining Learning toward Equitable Education, 020069. https://doi.org/10.1063/5.0201098
- Adelia, V., Putri, R. I. I., & Zulkardi, Z. (2024b). A systematic literature review: how do we support students to become numerate? International Journal of Evaluation and Research in Education (IJERE), 13(3), 1816. https://doi.org/10.11591/ijere.v13i3.26849
- Adelia, V., Putri, R. I. I., Zulkardi, Z., & Mulyono, B. (2022). Learning trajectory for equivalent fraction learning: An insight. Journal of Honai Math, 5(1), 47–60. https://doi.org/10.30862/jhm.v5i1.233
- 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(4), 507–528. https://doi.org/10.1007/s13394-019-00265-2
- Alvarez, I., Guasch, T., & Espasa, A. (2009). University teacher roles and competencies in online learning environments: a theoretical analysis of teaching and learning practices. European Journal of Teacher Education, 32(3), 321–336. https://doi.org/10.1080/02619760802624104
- Amuah, E., & Davis, E. K. (2023). Strategies and Procedural and Conceptual Knowledge of Addition of Unlike Denominator Fractions: The Case of Grade 8 Children in Two Districts of the Central Region of Ghana. African Journal of Research in Mathematics, Science and Technology Education, 27(2), 123–136. https://doi.org/10.1080/18117295.2023.2226546
- Barlovits, S., Caldeira, A., Fesakis, G., Jablonski, S., Koutsomanoli Filippaki, D., Lázaro, C., Ludwig, M., Mammana, M. F., Moura, A., Oehler, D.-X. K., Recio, T., Taranto, E., & Volika, S. (2022). Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. Mathematics, 10(10), 1628. https://doi.org/10.3390/math10101628
- Bennison, A. (2016). A sociocultural approach to understanding identity as an embedder-of-numeracy: A case of numeracy and history. European Educational Research Journal, 15(4), 491–502. https://doi.org/10.1177/1474904116643327
- Čadež, T. H., & Kolar, V. M. (2018). How fifth-grade pupils reason about fractions: a reliance on part-whole subconstructs. Educational Studies in Mathematics, 99(3), 335–357. https://doi.org/10.1007/s10649-018-9838-z
- 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
- Cirneanu, A.-L., & Moldoveanu, C.-E. (2024). Use of Digital Technology in Integrated Mathematics Education. Applied System Innovation, 7(4), 66. https://doi.org/10.3390/asi7040066
- Díez-Palomar, J., Ramis-Salas, M., Močnik, I., Simonič, M., & Hoogland, K. (2023). Challenges for numeracy awareness in the 21st century: making visible the invisible. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1295781
- Drijvers, P. (2015). Digital Technology in Mathematics Education: Why It Works (Or Doesn’t). In Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 135–151). Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_8
- Gaggi, O., Ciraulo, F., & Casagrande, M. (2018). Eating Pizza to learn fractions. Proceedings of the 4th EAI International Conference on Smart Objects and Technologies for Social Good, 220–225. https://doi.org/10.1145/3284869.3284921
- Gal, I., Grotlüschen, A., Tout, D., & Kaiser, G. (2020). Numeracy, adult education, and vulnerable adults: a critical view of a neglected field. ZDM, 52(3), 377–394. https://doi.org/10.1007/s11858-020-01155-9
- Geiger, V., Goos, M., & Dole, S. (2015). The Role of Digital Technologies in Numeracy Teaching and Learning. International Journal of Science and Mathematics Education, 13(5), 1115–1137. https://doi.org/10.1007/s10763-014-9530-4
- Goos, M., Geiger, V., Dole, S., Forgasz, H., & Bennison, A. (2018). Numeracy Across the Curriculum: Research-Based Strategies for Enhancing Teaching and Learning. Routledge.
- Hillmayr, D., Ziernwald, L., Reinhold, F., Hofer, S. I., & Reiss, K. M. (2020). The potential of digital tools to enhance mathematics and science learning in secondary schools: A context-specific meta-analysis. Computers & Education, 153, 103897. https://doi.org/10.1016/j.compedu.2020.103897
- Hoogland, K. (2016). Images of Numeracy Investigating the effects of visual representations of problem situations in contextual mathematical problem solving [Techniesche Universiteit Eindhoven]. https://doi.org/http://dx.doi.org/10.13140/RG.2.2.22839.57767
- Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
- Laughlin, A. J. (2022). Lesson Study and the New Teacher: Adding Fractions with Unlike Denominators, for Grade 4 (8- and 9-year-old) Students. In A. Takahasi, T. McDougal, S. Friedkin, & T. Watanabe (Eds.), Educators’ Learning from Lesson Study (1st ed.). Routledge. https://doi.org/10.4324/9781003230915
- Lithner, J. (2006). A framework for analysing creative and imitative mathematical reasoning.
- Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276. https://doi.org/10.1007/s10649-007-9104-2
- Martin, T., Petrick Smith, C., Forsgren, N., Aghababyan, A., Janisiewicz, P., & Baker, S. (2015). Learning Fractions by Splitting: Using Learning Analytics to Illuminate the Development of Mathematical Understanding. Journal of the Learning Sciences, 24(4), 593–637. https://doi.org/10.1080/10508406.2015.1078244
- Nieveen, N. (2010). Formative Evaluation in Educational Design Research. In T. Plomp & N. Nieveen (Eds.), An Introduction to Educational Design Research (pp. 89–101). SLO.
- Nieveen, N., McKenney, S., & Van Den Akker, J. (2006). Educational Design Research: the Value of Variety. In J. Van Den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational Design Research (pp. 151–158). Routledge.
- Nieveen, N., & van den Akker, J. (1999). Exploring the potential of a computer tool for instructional developers. Educational Technology Research and Development, 47(3), 77–98. https://doi.org/10.1007/BF02299635
- Niss, M., & Jablonka, E. (2014). Mathematical Literacy. In Encyclopedia of Mathematics Education (pp. 391–396). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_100
- O’Donoghue, J. (2002). Numeracy and Mathematics. Irish Mathematical Society Bulletin, 0048, 47–56. https://doi.org/10.33232/BIMS.0048.47.56
- OECD. (2021). The Assessment Frameworks for Cycle 2 of the Programme for the International Assessment of Adult Competencies. OECD. https://doi.org/10.1787/4bc2342d-en
- OECD. (2023). PISA 2022 Assessment and Analytical Framework. OECD. https://doi.org/10.1787/dfe0bf9c-en
- Pedersen, P. L., & Bjerre, M. (2021). Two conceptions of fraction equivalence. Educational Studies in Mathematics, 107(1), 135–157. https://doi.org/10.1007/s10649-021-10030-7
- Plomp, T. (2010). Educational Design Research: an Introduction. In T. Plomp & N. Nieveen (Eds.), An Introduction to Educational Design Research (pp. 9–35). SLO. www.slo.nl
- Pramudiani, P., Herman, T., Turmudi, Dolk, M., & Doorman, M. (2022). How does a missing part become important for primary school students in understanding fractions? Journal on Mathematics Education, 13(4), 565–586. https://doi.org/10.22342/jme.v13i4.pp565-586
- Pusat Asesmen dan Pembelajaran. (2020). AKM dan Implikasinya pada Pembelajaran.
- Santos-Trigo, M., Reyes-Martínez, I., & Aguilar-Magallón, D. (2015). The Use of Digital Technology in Extending Mathematical Problem Solving Reasoning (pp. 298–309). https://doi.org/10.1007/978-3-319-22629-3_24
- Sellars, M. (2017). Numeracy across the curriculum: a pathway to critical thinking. International Journal Innovation Creativity and Change, 3(2), 75–83.
- 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
- Son, J.-W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74(2), 117–142. https://doi.org/10.1007/s10649-010-9229-6
- Sumpter, L. (2018). Grade 9 Students’ Reasoning About Division of Fractions: What Are their Arguments Anchored in? In Students’ and Teachers’ Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms (pp. 135–143). Springer International Publishing. https://doi.org/10.1007/978-3-319-70244-5_13
- Tout, D. (2020). ISSUES IN THE TEACHING OF MATHEMATICS Critical Connections Between Numeracy and Mathematics. https://research.acer.edu.au/learning_processes/29
- 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
- Wahyu, K., Kuzu, T. E., Subarinah, S., Ratnasari, D., & Mahfudy, S. (2020). PARTITIVE FRACTION DIVISION: REVEALING AND PROMOTING PRIMARY STUDENTS’ UNDERSTANDING. Journal on Mathematics Education, 11(2), 237–258. https://doi.org/10.22342/jme.11.2.11062.237-258
- Xiao, F., Barnard-Brak, L., Lan, W., & Burley, H. (2019). Examining problem-solving skills in technology-rich environments as related to numeracy and literacy. International Journal of Lifelong Education, 38(3), 327–338. https://doi.org/10.1080/02601370.2019.1598507
- Zhang, L., Shang, J., Pelton, T., & Pelton, L. F. (2020). Supporting primary students’ learning of fraction conceptual knowledge through digital games. Journal of Computer Assisted Learning, 36(4), 540–548. https://doi.org/10.1111/jcal.12422
- Zulkardi. (2002). DOCTORAL COMMITTEE. University of Twente.
References
Adelia, V., Putri, R. I. I., & Zulkardi. (2024a). Mathematics teachers in Palembang teaching practice: Numeracy perspective. THE 5TH SRIWIJAYA UNIVERSITY LEARNING AND EDUCATION (SULE) INTERNATIONAL CONFERENCE 2023: Reimagining Learning toward Equitable Education, 020069. https://doi.org/10.1063/5.0201098
Adelia, V., Putri, R. I. I., & Zulkardi, Z. (2024b). A systematic literature review: how do we support students to become numerate? International Journal of Evaluation and Research in Education (IJERE), 13(3), 1816. https://doi.org/10.11591/ijere.v13i3.26849
Adelia, V., Putri, R. I. I., Zulkardi, Z., & Mulyono, B. (2022). Learning trajectory for equivalent fraction learning: An insight. Journal of Honai Math, 5(1), 47–60. https://doi.org/10.30862/jhm.v5i1.233
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(4), 507–528. https://doi.org/10.1007/s13394-019-00265-2
Alvarez, I., Guasch, T., & Espasa, A. (2009). University teacher roles and competencies in online learning environments: a theoretical analysis of teaching and learning practices. European Journal of Teacher Education, 32(3), 321–336. https://doi.org/10.1080/02619760802624104
Amuah, E., & Davis, E. K. (2023). Strategies and Procedural and Conceptual Knowledge of Addition of Unlike Denominator Fractions: The Case of Grade 8 Children in Two Districts of the Central Region of Ghana. African Journal of Research in Mathematics, Science and Technology Education, 27(2), 123–136. https://doi.org/10.1080/18117295.2023.2226546
Barlovits, S., Caldeira, A., Fesakis, G., Jablonski, S., Koutsomanoli Filippaki, D., Lázaro, C., Ludwig, M., Mammana, M. F., Moura, A., Oehler, D.-X. K., Recio, T., Taranto, E., & Volika, S. (2022). Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. Mathematics, 10(10), 1628. https://doi.org/10.3390/math10101628
Bennison, A. (2016). A sociocultural approach to understanding identity as an embedder-of-numeracy: A case of numeracy and history. European Educational Research Journal, 15(4), 491–502. https://doi.org/10.1177/1474904116643327
Čadež, T. H., & Kolar, V. M. (2018). How fifth-grade pupils reason about fractions: a reliance on part-whole subconstructs. Educational Studies in Mathematics, 99(3), 335–357. https://doi.org/10.1007/s10649-018-9838-z
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
Cirneanu, A.-L., & Moldoveanu, C.-E. (2024). Use of Digital Technology in Integrated Mathematics Education. Applied System Innovation, 7(4), 66. https://doi.org/10.3390/asi7040066
Díez-Palomar, J., Ramis-Salas, M., Močnik, I., Simonič, M., & Hoogland, K. (2023). Challenges for numeracy awareness in the 21st century: making visible the invisible. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1295781
Drijvers, P. (2015). Digital Technology in Mathematics Education: Why It Works (Or Doesn’t). In Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 135–151). Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_8
Gaggi, O., Ciraulo, F., & Casagrande, M. (2018). Eating Pizza to learn fractions. Proceedings of the 4th EAI International Conference on Smart Objects and Technologies for Social Good, 220–225. https://doi.org/10.1145/3284869.3284921
Gal, I., Grotlüschen, A., Tout, D., & Kaiser, G. (2020). Numeracy, adult education, and vulnerable adults: a critical view of a neglected field. ZDM, 52(3), 377–394. https://doi.org/10.1007/s11858-020-01155-9
Geiger, V., Goos, M., & Dole, S. (2015). The Role of Digital Technologies in Numeracy Teaching and Learning. International Journal of Science and Mathematics Education, 13(5), 1115–1137. https://doi.org/10.1007/s10763-014-9530-4
Goos, M., Geiger, V., Dole, S., Forgasz, H., & Bennison, A. (2018). Numeracy Across the Curriculum: Research-Based Strategies for Enhancing Teaching and Learning. Routledge.
Hillmayr, D., Ziernwald, L., Reinhold, F., Hofer, S. I., & Reiss, K. M. (2020). The potential of digital tools to enhance mathematics and science learning in secondary schools: A context-specific meta-analysis. Computers & Education, 153, 103897. https://doi.org/10.1016/j.compedu.2020.103897
Hoogland, K. (2016). Images of Numeracy Investigating the effects of visual representations of problem situations in contextual mathematical problem solving [Techniesche Universiteit Eindhoven]. https://doi.org/http://dx.doi.org/10.13140/RG.2.2.22839.57767
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
Laughlin, A. J. (2022). Lesson Study and the New Teacher: Adding Fractions with Unlike Denominators, for Grade 4 (8- and 9-year-old) Students. In A. Takahasi, T. McDougal, S. Friedkin, & T. Watanabe (Eds.), Educators’ Learning from Lesson Study (1st ed.). Routledge. https://doi.org/10.4324/9781003230915
Lithner, J. (2006). A framework for analysing creative and imitative mathematical reasoning.
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276. https://doi.org/10.1007/s10649-007-9104-2
Martin, T., Petrick Smith, C., Forsgren, N., Aghababyan, A., Janisiewicz, P., & Baker, S. (2015). Learning Fractions by Splitting: Using Learning Analytics to Illuminate the Development of Mathematical Understanding. Journal of the Learning Sciences, 24(4), 593–637. https://doi.org/10.1080/10508406.2015.1078244
Nieveen, N. (2010). Formative Evaluation in Educational Design Research. In T. Plomp & N. Nieveen (Eds.), An Introduction to Educational Design Research (pp. 89–101). SLO.
Nieveen, N., McKenney, S., & Van Den Akker, J. (2006). Educational Design Research: the Value of Variety. In J. Van Den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational Design Research (pp. 151–158). Routledge.
Nieveen, N., & van den Akker, J. (1999). Exploring the potential of a computer tool for instructional developers. Educational Technology Research and Development, 47(3), 77–98. https://doi.org/10.1007/BF02299635
Niss, M., & Jablonka, E. (2014). Mathematical Literacy. In Encyclopedia of Mathematics Education (pp. 391–396). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_100
O’Donoghue, J. (2002). Numeracy and Mathematics. Irish Mathematical Society Bulletin, 0048, 47–56. https://doi.org/10.33232/BIMS.0048.47.56
OECD. (2021). The Assessment Frameworks for Cycle 2 of the Programme for the International Assessment of Adult Competencies. OECD. https://doi.org/10.1787/4bc2342d-en
OECD. (2023). PISA 2022 Assessment and Analytical Framework. OECD. https://doi.org/10.1787/dfe0bf9c-en
Pedersen, P. L., & Bjerre, M. (2021). Two conceptions of fraction equivalence. Educational Studies in Mathematics, 107(1), 135–157. https://doi.org/10.1007/s10649-021-10030-7
Plomp, T. (2010). Educational Design Research: an Introduction. In T. Plomp & N. Nieveen (Eds.), An Introduction to Educational Design Research (pp. 9–35). SLO. www.slo.nl
Pramudiani, P., Herman, T., Turmudi, Dolk, M., & Doorman, M. (2022). How does a missing part become important for primary school students in understanding fractions? Journal on Mathematics Education, 13(4), 565–586. https://doi.org/10.22342/jme.v13i4.pp565-586
Pusat Asesmen dan Pembelajaran. (2020). AKM dan Implikasinya pada Pembelajaran.
Santos-Trigo, M., Reyes-Martínez, I., & Aguilar-Magallón, D. (2015). The Use of Digital Technology in Extending Mathematical Problem Solving Reasoning (pp. 298–309). https://doi.org/10.1007/978-3-319-22629-3_24
Sellars, M. (2017). Numeracy across the curriculum: a pathway to critical thinking. International Journal Innovation Creativity and Change, 3(2), 75–83.
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
Son, J.-W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74(2), 117–142. https://doi.org/10.1007/s10649-010-9229-6
Sumpter, L. (2018). Grade 9 Students’ Reasoning About Division of Fractions: What Are their Arguments Anchored in? In Students’ and Teachers’ Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms (pp. 135–143). Springer International Publishing. https://doi.org/10.1007/978-3-319-70244-5_13
Tout, D. (2020). ISSUES IN THE TEACHING OF MATHEMATICS Critical Connections Between Numeracy and Mathematics. https://research.acer.edu.au/learning_processes/29
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
Wahyu, K., Kuzu, T. E., Subarinah, S., Ratnasari, D., & Mahfudy, S. (2020). PARTITIVE FRACTION DIVISION: REVEALING AND PROMOTING PRIMARY STUDENTS’ UNDERSTANDING. Journal on Mathematics Education, 11(2), 237–258. https://doi.org/10.22342/jme.11.2.11062.237-258
Xiao, F., Barnard-Brak, L., Lan, W., & Burley, H. (2019). Examining problem-solving skills in technology-rich environments as related to numeracy and literacy. International Journal of Lifelong Education, 38(3), 327–338. https://doi.org/10.1080/02601370.2019.1598507
Zhang, L., Shang, J., Pelton, T., & Pelton, L. F. (2020). Supporting primary students’ learning of fraction conceptual knowledge through digital games. Journal of Computer Assisted Learning, 36(4), 540–548. https://doi.org/10.1111/jcal.12422
Zulkardi. (2002). DOCTORAL COMMITTEE. University of Twente.