Main Article Content
Abstract
Despite the growing emphasis on numeracy as a critical outcome of mathematics education, many instructional approaches fail to connect numeracy learning with students’ reasoning development in meaningful ways. Existing research has not sufficiently explored the integration of technology-supported environments for fostering numeracy through theoretically grounded task design. Addressing this gap, the present study introduces a novel web-based learning environment grounded in numeracy theory and task design principles aimed at enhancing students' numeracy competence and mathematical reasoning. The development and implementation process involved iterative trials with 25 fifth-grade students: a one-to-one trial (n = 2), a small-group trial (n = 5), and a field trial (n = 18). Data were collected from students’ written responses on the web-based platform and their oral explanations. Findings demonstrate that the developed environment meets three key criteria: validity, as it aligns with relevant theoretical and empirical foundations; practicality, based on its usability and feasibility for students; and effectiveness, as evidenced by improved reasoning skills. These results highlight the potential of well-designed web-based learning environments to meaningfully support the development of numeracy competence while simultaneously fostering mathematical reasoning in primary education.
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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. (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, & 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.
- Guskey, T. R. (2000). Evaluating professional development (Vol. 1). Corwin press.
- 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]. 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 [AKM and its implications for learning].
- 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
- Wirth, L., & Greefrath, G. (2024). Working with an instructional video on mathematical modeling: Upper-secondary students’ perceived advantages and challenges. ZDM–Mathematics Education, 56(4), 573-587. https://doi.org/10.1007/s11858-024-01546-2
- 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). Developing a learning environment on realistic mathematics education for Indonesian student teachers. Doctoral dissertation. 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. (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, & 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.
Guskey, T. R. (2000). Evaluating professional development (Vol. 1). Corwin press.
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]. 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 [AKM and its implications for learning].
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
Wirth, L., & Greefrath, G. (2024). Working with an instructional video on mathematical modeling: Upper-secondary students’ perceived advantages and challenges. ZDM–Mathematics Education, 56(4), 573-587. https://doi.org/10.1007/s11858-024-01546-2
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). Developing a learning environment on realistic mathematics education for Indonesian student teachers. Doctoral dissertation. University of Twente.