When designer meets local culture: The promising learning trajectory on the surface area of polyhedron

Idul Adha; Zulkardi; Ratu Ilma Indra Putri; Somakim

doi:10.22342/jme.v15i3.pp945-960

Download

PDF

Statistic

Read Counter : 329 Download : 99

Downloads

Abstract

Polyhedrons present a challenging topic in elementary geometry education. The Indonesian Realistic Mathematics Education (IRME) approach, when contextualized within the Bukit Sulap tourism area, offers a promising solution to this challenge. This study aims to design a learning trajectory for teaching the surface area of polyhedron using IRME in the context of Bukit Sulap tourism. Employing a research design with a validation study type, the study was conducted in three phases: preparation and design, experimental teaching, and retrospective analysis. The participants were 27 elementary school students from Lubuklinggau City, Indonesia. Data collection instruments included surface area problem-solving worksheets, video recordings of in-depth learning interviews, field notes, and observation sheets. The findings suggest that the Bukit Sulap tourism context significantly enhanced students' understanding of surface area problems, specifically those involving combinations of cuboids and cubes. Additionally, IRME effectively facilitated students' comprehension of abstract mathematical concepts, particularly the surface area formulas for cubes and cuboids. The study concludes that using the Bukit Sulap tourism park context as a starting point for teaching the surface area of polyhedron aligns well with the principles of IRME.

Keywords

Bukit Sulap Tourism Context Cube and Cuboid IRME Surface Area

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Adha, I., Zulkardi, Putri, R. I. I., & Somakim. (2024). When designer meets local culture: The promising learning trajectory on the surface area of polyhedron. Journal on Mathematics Education, 15(3), 945–960. https://doi.org/10.22342/jme.v15i3.pp945-960

Download Citation

References

Apsari, R. A., Putri, R. I. I., Abels, M., & Prayitno, S. (2020). Geometry representation to develop algebraic thinking: A recommendation for a pattern investigation in pre-algebra class. Journal on Mathematics Education, 11(1), 45-58. http://doi.org/10.22342/jme.11.1.9535.45-58
Arifah, A. N., & Retnawati, H. (2020). Are students having trouble solving problems polyhedron?. Journal of Physics: Conference Series, 1613(1), 012029. http://doi.org/10.1088/1742-6596/1613/1/012029
Bakker, A. (2018). Design Research in Education (A Practical Guide for Early Career Researchers). Routledge. https://doi.org/10.4324/9780203701010
Elia, I., van den Heuvel-Panhuizen, M., & Gagatsis, A. (2018). Geometry learning in the early years: Developing understanding of shapes and space with a focus on visualization. In Kinnear, V., Lai, M., Muir, T. (eds) Forging Connections in Early Mathematics Teaching and Learning. Early Mathematics Learning and Development. Springer. https://doi.org/10.1007/978-981-10-7153-9_5
Fouze, A. Q., & Amit, M. (2021). Teaching geometry by integrating ethnomathematics of Bedouin values. Creative Education, 12(02), 402–421. https://doi.org/10.4236/ce.2021.122029
Goktepe Yildiz, S., & Ozdemir, A. S. (2020). The effects of engineering design processes on spatial abilities of middle school students. International Journal of Technology and Design Education, 30, 127-148. https://doi.org/10.1007/s10798-018-9491-y
Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teaching in mathematics education. The Elementary School Journal, 109(5), 510–524. https://doi.org/10.1086/596999
Hartutik, Nugroho, K. U. Z., Sukestiyarno, Y. L., Widada, W., Sugiyana, Taçain, J., & Anggoro, S. D. T. (2024). Digital technology literacy skills of participants in religious teacher professional training in Indonesia. Community Practitioner, 21(5), 1228–1245. https://doi.org/10.5281/zenodo.11365010
Hendriana, H., Prahmana, R. C. I., Ristiana, M. G., Rohaeti, E. E., & Hidayat, W. (2022). The theoretical framework on humanist ethno-metaphorical mathematics learning model: An impactful insight in learning mathematics. Frontiers in Education, 7, 1030471. https://doi.org/10.3389/feduc.2022.1030471
Hendroanto, A., Van Galen, F., Van Eerde, D., Prahmana, R. C. I., Setyawan, F., & Istiandaru, A. (2018). Photography activities for developing students’ spatial orientation and spatial visualization. Journal of Physics: Conference Series, 943(1), 012029. https://doi.org/10.1088/1742-6596/943/1/012029
Herawaty, D., Widada, W., Adhitya, A., Sari, R. D. W., & Novianita, L. (2020). Students’ ability to simplify the concept of function through realistic mathematics learning with the ethnomathematics approach. Journal of Physics: Conference Series, 1470(1), 012031. https://doi.org/10.1088/1742-6596/1470/1/012031
Hwang, W. Y., & Hu, S. S. (2013). Analysis of peer learning behaviors using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62, 308-319. https://doi.org/10.1016/j.compedu.2012.10.005
Hwang, W. Y., Zhao, L., Shadiev, R., Lin, L. K., Shih, T. K., & Chen, H. R. (2020). Exploring the effects of ubiquitous geometry learning in real situations. Educational Technology Research and Development, 68, 1121-1147. https://doi.org/10.1016/j.compedu.2012.10.005
Junaedi, Y., Wahyudin, & Juandi, D. (2021). Mathematical creative thinking ability of junior high school students’ on polyhedron. Journal of Physics: Conference Series, 1806(1), 012069. https://doi.org/10.1088/1742-6596/1806/1/012069
Juniarti, A., Jojo, Z., & Prahmana, R. C. I. (2022). Designing the learning trajectory for the topic of circles through a tambourine context. Journal of Honai Math, 5(1), 29-46. https://doi.org/10.30862/jhm.v5i1.239
Kurniawati, L., & Amir, M. F. (2022). Development of learning trajectory of perimeter and area of squares and rectangles through various tasks. Premiere Educandum: Journal of Basic Education and Learning, 12(1), 54-68. https://doi.org/10.25273/pe.v12i1.12121
Lisnani, Putri, R. I. I., Zulkardi, & Somakim. (2023). Web-based realistic mathematics learning environment for 21st-century skills in primary school students. Journal on Mathematics Education, 14(2), 253–274. https://doi.org/10.22342/jme.v14i2.pp253-274
Lowrie, T., Logan, T., & Hegarty, M. (2019). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. Journal of Cognition and Development, 20(5), 729-751. https://doi.org/10.1080/15248372.2019.1653298
McKenney, S., & Reeves, T. C. (2014). Educational design research. In Spector, J., Merrill, M., Elen, J., Bishop, M. (eds) Handbook of Research on Educational Communications and Technology. Springer. https://doi.org/10.1007/978-1-4614-3185-5_11
Mensah, J. Y. & Nabie, M. J. (2021). The effect of PowerPoint instruction on high school students’ achievement and motivation to learn geometry. International Journal of Technology in Education (IJTE), 4(3), 331-350. https://doi.org/10.46328/ijte.55
Meryansumayeka, Zulkardi, Putri, R. I. I., & Hiltrimartin, C. (2022). Designing geometrical learning activities assisted with ICT media for supporting students’ higher order thinking skills. Journal on Mathematics Education, 13(1), 135–148. https://doi.org/10.22342/jme.v13i1.pp135-148
Nagy-Kondor, R., & Esmailnia, S. (2021). Polyhedrons vs. curved surfaces with mental cutting: Impact of spatial ability. Acta Polytechnica Hungarica, 18(6), 71-83. http://dx.doi.org/10.12700/APH.18.6.2021.6.4
Naidoo, J., & Kapofu, W. (2020). Exploring female learners’ perceptions of learning geometry in mathematics. South African Journal of Education, 40(1), 1-11. https://hdl.handle.net/10520/EJC-1c03576684
Nailurrohmah, A., & Murdiyani, N. M. (2022). Developing realistic mathematics education learning set in polyhedron subject to improve mathematical concepts understanding skills. AIP Conference Proceedings, 2575(1), 050009. https://doi.org/10.1063/5.0107950
Nursyahidah, F., & Albab, I. U. (2021). Learning design on surface area and volume of cylinder using Indonesian ethno-mathematics of traditional cookie maker assisted by GeoGebra. Mathematics Teaching Research Journal, 13(4), 79-98. https://files.eric.ed.gov/fulltext/EJ1332350.pdf
Plomp, T. & Nieveen, N. (2013). Educational Design Research. SLO. https://www.fi.uu.nl/publicaties/literatuur/educational-design-research-part-a.pdf
Prahmana, R. C. I., & D'Ambrosio, U. (2020). Learning geometry and values from patterns: Ethnomathematics on the batik patterns of Yogyakarta, Indonesia. Journal on Mathematics Education, 11(3), 439-456. https://doi.org/10.22342/jme.11.3.12949.439-456
Prahmana, R. C. I., Sagita, L., Hidayat, W., & Utami, N. W. (2020). Two decades of realistic mathematics education research in Indonesia: A survey. Infinity Journal, 9(2), 223-246. https://doi.org/10.22460/infinity.v9i2.p223-246
Quiroz, S. M. R., Orrego, S. M. L., & López, C. M. J. (2015). Measurement of area and volume in an authentic context: An alternative learning experience through mathematical modelling. In Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 229-240). Springer. https://doi.org/10.1007/978-3-319-18272-8_18
Richit, A., Tomkelski, M. L., & Richit, A. (2021). Understandings of perimeter and area mobilized with an exploratory approach in a lesson study. Acta Scientiae, 23(5), 1-36. https://doi.org/10.17648/acta.scientiae.6226
Risdiyanti, I., Zulkardi, Putri, R. I. I., Prahmana, R. C. I., & Nusantara, D. S. (2024). Ratio and proportion through realistic mathematics education and Pendidikan matematika realistik Indonesia approach: A systematic literature review. Jurnal Elemen, 10(1), 158-180. https://doi.org/10.29408/jel.v10i1.24445
Romero, I., Rodríguez-Martínez, J. A., & Rodríguez, J. L. (2023). Optimizing the surface of orthohedra with virtual reality in primary school. Eurasia Journal of Mathematics, Science and Technology Education, 19(9), em2325. https://doi.org/10.29333/ejmste/13508
Sagita, L., Setiyani, & Sumiarsih. (2021). Designing teaching materials based on process skills approach to mathematical representation ability in polyhedron. Journal of Physics: Conference Series, 1957(1), 012015. http://doi.org/10.1088/1742-6596/1957/1/012015
Sarkar, P., Kadam, K., & Pillai, J. S. (2020). Learners' approaches, motivation and patterns of problem-solving on lines and angles in geometry using augmented reality. Smart Learning Environments, 7, 1-23. https://doi.org/10.1186/s40561-020-00124-9
Schwarz, B. B., Swidan, O., Prusak, N., & Palatnik, A. (2021). Collaborative learning in mathematics classrooms: Can teachers understand progress of concurrent collaborating groups?. Computers & Education, 165, 104151. https://doi.org/10.1016/j.compedu.2021.104151
Seah, R. T. K., & Horne, M. (2020). The influence of spatial reasoning on analysing about measurement situations. Mathematics Education Research Journal, 32, 365-386. https://doi.org/10.1007/s13394-020-00327-w
Sitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: Implementation of realistic mathematics education. Thinking Skills and Creativity, 22, 111-120. https://doi.org/10.1016/j.tsc.2016.09.007
Smith III, J. P., Males, L. M., & Gonulates, F. (2016). Conceptual limitations in curricular presentations of area measurement: One nation’s challenges. Mathematical Thinking and Learning, 18(4), 239-270. https://doi.org/10.1080/10986065.2016.1219930
Sukasno, Zulkardi, Putri, R. I. I., & Somakim. (2024). Students’ cognitive processes in understanding fractions through the tourist context. Jurnal Pendidikan Matematika, 18(1), 27–38. https://doi.org/10.22342/jpm.v18i1.pp27-38
Sukestiyarno, Y. L., Nugroho, K. U. Z., Sugiman, & Waluya, B. (2023). Learning trajectory of non-Euclidean geometry through ethnomathematics learning approaches to improve spatial ability. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), em2285. https://doi.org/10.29333/ejmste/13269
Sukirwan, Darhim, Herman, T., & Prahmana, R. C. I. (2018). The students’ mathematical argumentation in geometry. Journal of Physics: Conference Series, 943(1), 012026. https://doi.org/10.1088/1742-6596/943/1/012026
Taylor, A., & Jones, G. (2009). Proportional reasoning ability and concepts of scale: Surface area to volume relationships in science. International Journal of Science Education, 31(9), 1231-1247. https://doi.org/10.1080/09500690802017545
Toheri, Winarso, W., & Haqq, A. A. (2020). Where exactly for enhance critical and creative thinking: The use of problem posing or contextual learning. European Journal of Educational Research, 9(2), 877-887. https://doi.org/10.12973/eu-jer.9.2.877
Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic Mathematics Education. In Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-15789-0_170
Velten, K., Schmidt, D. M., & Kahlen, K. (2024). Mathematical modeling and simulation: Introduction for scientists and engineers. John Wiley & Sons.
Widodo, S. A., Prahmana, R. C. I., Purnami, A. S., & Turmudi. (2018). Teaching materials of algebraic equation. Journal of Physics: Conference Series, 943(1), 012017. https://doi.org/10.1088/1742-6596/943/1/012017
Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., ... & Ogbuehi, P. (2012). Improving Mathematical Problem Solving in Grades 4 through 8. IES Practice Guide. NCEE 2012-4055. What Works Clearinghouse. https://files.eric.ed.gov/fulltext/ED532215.pdf
Zulkardi, & Putri, R. I. I. (2019). New School Mathematics Curricula, PISA and PMRI in Indonesia. In Vistro-Yu, C., Toh, T. (eds) School Mathematics Curricula. Mathematics Education – An Asian Perspective. Springer. https://doi.org/10.1007/978-981-13-6312-2_3
Zulkardi, Putri, R. I. I., & Wijaya, A. (2019). Two Decades of Realistic Mathematics Education in Indonesia. Springer International Publishing. https://doi.org/10.1007/978-3-030-20223-1_18

References

Apsari, R. A., Putri, R. I. I., Abels, M., & Prayitno, S. (2020). Geometry representation to develop algebraic thinking: A recommendation for a pattern investigation in pre-algebra class. Journal on Mathematics Education, 11(1), 45-58. http://doi.org/10.22342/jme.11.1.9535.45-58

Arifah, A. N., & Retnawati, H. (2020). Are students having trouble solving problems polyhedron?. Journal of Physics: Conference Series, 1613(1), 012029. http://doi.org/10.1088/1742-6596/1613/1/012029

Bakker, A. (2018). Design Research in Education (A Practical Guide for Early Career Researchers). Routledge. https://doi.org/10.4324/9780203701010

Elia, I., van den Heuvel-Panhuizen, M., & Gagatsis, A. (2018). Geometry learning in the early years: Developing understanding of shapes and space with a focus on visualization. In Kinnear, V., Lai, M., Muir, T. (eds) Forging Connections in Early Mathematics Teaching and Learning. Early Mathematics Learning and Development. Springer. https://doi.org/10.1007/978-981-10-7153-9_5

Fouze, A. Q., & Amit, M. (2021). Teaching geometry by integrating ethnomathematics of Bedouin values. Creative Education, 12(02), 402–421. https://doi.org/10.4236/ce.2021.122029

Goktepe Yildiz, S., & Ozdemir, A. S. (2020). The effects of engineering design processes on spatial abilities of middle school students. International Journal of Technology and Design Education, 30, 127-148. https://doi.org/10.1007/s10798-018-9491-y

Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teaching in mathematics education. The Elementary School Journal, 109(5), 510–524. https://doi.org/10.1086/596999

Hartutik, Nugroho, K. U. Z., Sukestiyarno, Y. L., Widada, W., Sugiyana, Taçain, J., & Anggoro, S. D. T. (2024). Digital technology literacy skills of participants in religious teacher professional training in Indonesia. Community Practitioner, 21(5), 1228–1245. https://doi.org/10.5281/zenodo.11365010

Hendriana, H., Prahmana, R. C. I., Ristiana, M. G., Rohaeti, E. E., & Hidayat, W. (2022). The theoretical framework on humanist ethno-metaphorical mathematics learning model: An impactful insight in learning mathematics. Frontiers in Education, 7, 1030471. https://doi.org/10.3389/feduc.2022.1030471

Hendroanto, A., Van Galen, F., Van Eerde, D., Prahmana, R. C. I., Setyawan, F., & Istiandaru, A. (2018). Photography activities for developing students’ spatial orientation and spatial visualization. Journal of Physics: Conference Series, 943(1), 012029. https://doi.org/10.1088/1742-6596/943/1/012029

Herawaty, D., Widada, W., Adhitya, A., Sari, R. D. W., & Novianita, L. (2020). Students’ ability to simplify the concept of function through realistic mathematics learning with the ethnomathematics approach. Journal of Physics: Conference Series, 1470(1), 012031. https://doi.org/10.1088/1742-6596/1470/1/012031

Hwang, W. Y., & Hu, S. S. (2013). Analysis of peer learning behaviors using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62, 308-319. https://doi.org/10.1016/j.compedu.2012.10.005

Hwang, W. Y., Zhao, L., Shadiev, R., Lin, L. K., Shih, T. K., & Chen, H. R. (2020). Exploring the effects of ubiquitous geometry learning in real situations. Educational Technology Research and Development, 68, 1121-1147. https://doi.org/10.1016/j.compedu.2012.10.005

Junaedi, Y., Wahyudin, & Juandi, D. (2021). Mathematical creative thinking ability of junior high school students’ on polyhedron. Journal of Physics: Conference Series, 1806(1), 012069. https://doi.org/10.1088/1742-6596/1806/1/012069

Juniarti, A., Jojo, Z., & Prahmana, R. C. I. (2022). Designing the learning trajectory for the topic of circles through a tambourine context. Journal of Honai Math, 5(1), 29-46. https://doi.org/10.30862/jhm.v5i1.239

Kurniawati, L., & Amir, M. F. (2022). Development of learning trajectory of perimeter and area of squares and rectangles through various tasks. Premiere Educandum: Journal of Basic Education and Learning, 12(1), 54-68. https://doi.org/10.25273/pe.v12i1.12121

Lisnani, Putri, R. I. I., Zulkardi, & Somakim. (2023). Web-based realistic mathematics learning environment for 21st-century skills in primary school students. Journal on Mathematics Education, 14(2), 253–274. https://doi.org/10.22342/jme.v14i2.pp253-274

Lowrie, T., Logan, T., & Hegarty, M. (2019). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. Journal of Cognition and Development, 20(5), 729-751. https://doi.org/10.1080/15248372.2019.1653298

McKenney, S., & Reeves, T. C. (2014). Educational design research. In Spector, J., Merrill, M., Elen, J., Bishop, M. (eds) Handbook of Research on Educational Communications and Technology. Springer. https://doi.org/10.1007/978-1-4614-3185-5_11

Mensah, J. Y. & Nabie, M. J. (2021). The effect of PowerPoint instruction on high school students’ achievement and motivation to learn geometry. International Journal of Technology in Education (IJTE), 4(3), 331-350. https://doi.org/10.46328/ijte.55

Meryansumayeka, Zulkardi, Putri, R. I. I., & Hiltrimartin, C. (2022). Designing geometrical learning activities assisted with ICT media for supporting students’ higher order thinking skills. Journal on Mathematics Education, 13(1), 135–148. https://doi.org/10.22342/jme.v13i1.pp135-148

Nagy-Kondor, R., & Esmailnia, S. (2021). Polyhedrons vs. curved surfaces with mental cutting: Impact of spatial ability. Acta Polytechnica Hungarica, 18(6), 71-83. http://dx.doi.org/10.12700/APH.18.6.2021.6.4

Naidoo, J., & Kapofu, W. (2020). Exploring female learners’ perceptions of learning geometry in mathematics. South African Journal of Education, 40(1), 1-11. https://hdl.handle.net/10520/EJC-1c03576684

Nailurrohmah, A., & Murdiyani, N. M. (2022). Developing realistic mathematics education learning set in polyhedron subject to improve mathematical concepts understanding skills. AIP Conference Proceedings, 2575(1), 050009. https://doi.org/10.1063/5.0107950

Nursyahidah, F., & Albab, I. U. (2021). Learning design on surface area and volume of cylinder using Indonesian ethno-mathematics of traditional cookie maker assisted by GeoGebra. Mathematics Teaching Research Journal, 13(4), 79-98. https://files.eric.ed.gov/fulltext/EJ1332350.pdf

Plomp, T. & Nieveen, N. (2013). Educational Design Research. SLO. https://www.fi.uu.nl/publicaties/literatuur/educational-design-research-part-a.pdf

Prahmana, R. C. I., & D'Ambrosio, U. (2020). Learning geometry and values from patterns: Ethnomathematics on the batik patterns of Yogyakarta, Indonesia. Journal on Mathematics Education, 11(3), 439-456. https://doi.org/10.22342/jme.11.3.12949.439-456

Prahmana, R. C. I., Sagita, L., Hidayat, W., & Utami, N. W. (2020). Two decades of realistic mathematics education research in Indonesia: A survey. Infinity Journal, 9(2), 223-246. https://doi.org/10.22460/infinity.v9i2.p223-246

Quiroz, S. M. R., Orrego, S. M. L., & López, C. M. J. (2015). Measurement of area and volume in an authentic context: An alternative learning experience through mathematical modelling. In Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 229-240). Springer. https://doi.org/10.1007/978-3-319-18272-8_18

Richit, A., Tomkelski, M. L., & Richit, A. (2021). Understandings of perimeter and area mobilized with an exploratory approach in a lesson study. Acta Scientiae, 23(5), 1-36. https://doi.org/10.17648/acta.scientiae.6226

Risdiyanti, I., Zulkardi, Putri, R. I. I., Prahmana, R. C. I., & Nusantara, D. S. (2024). Ratio and proportion through realistic mathematics education and Pendidikan matematika realistik Indonesia approach: A systematic literature review. Jurnal Elemen, 10(1), 158-180. https://doi.org/10.29408/jel.v10i1.24445

Romero, I., Rodríguez-Martínez, J. A., & Rodríguez, J. L. (2023). Optimizing the surface of orthohedra with virtual reality in primary school. Eurasia Journal of Mathematics, Science and Technology Education, 19(9), em2325. https://doi.org/10.29333/ejmste/13508

Sagita, L., Setiyani, & Sumiarsih. (2021). Designing teaching materials based on process skills approach to mathematical representation ability in polyhedron. Journal of Physics: Conference Series, 1957(1), 012015. http://doi.org/10.1088/1742-6596/1957/1/012015

Sarkar, P., Kadam, K., & Pillai, J. S. (2020). Learners' approaches, motivation and patterns of problem-solving on lines and angles in geometry using augmented reality. Smart Learning Environments, 7, 1-23. https://doi.org/10.1186/s40561-020-00124-9

Schwarz, B. B., Swidan, O., Prusak, N., & Palatnik, A. (2021). Collaborative learning in mathematics classrooms: Can teachers understand progress of concurrent collaborating groups?. Computers & Education, 165, 104151. https://doi.org/10.1016/j.compedu.2021.104151

Seah, R. T. K., & Horne, M. (2020). The influence of spatial reasoning on analysing about measurement situations. Mathematics Education Research Journal, 32, 365-386. https://doi.org/10.1007/s13394-020-00327-w

Sitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: Implementation of realistic mathematics education. Thinking Skills and Creativity, 22, 111-120. https://doi.org/10.1016/j.tsc.2016.09.007

Smith III, J. P., Males, L. M., & Gonulates, F. (2016). Conceptual limitations in curricular presentations of area measurement: One nation’s challenges. Mathematical Thinking and Learning, 18(4), 239-270. https://doi.org/10.1080/10986065.2016.1219930

Sukasno, Zulkardi, Putri, R. I. I., & Somakim. (2024). Students’ cognitive processes in understanding fractions through the tourist context. Jurnal Pendidikan Matematika, 18(1), 27–38. https://doi.org/10.22342/jpm.v18i1.pp27-38

Sukestiyarno, Y. L., Nugroho, K. U. Z., Sugiman, & Waluya, B. (2023). Learning trajectory of non-Euclidean geometry through ethnomathematics learning approaches to improve spatial ability. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), em2285. https://doi.org/10.29333/ejmste/13269

Sukirwan, Darhim, Herman, T., & Prahmana, R. C. I. (2018). The students’ mathematical argumentation in geometry. Journal of Physics: Conference Series, 943(1), 012026. https://doi.org/10.1088/1742-6596/943/1/012026

Taylor, A., & Jones, G. (2009). Proportional reasoning ability and concepts of scale: Surface area to volume relationships in science. International Journal of Science Education, 31(9), 1231-1247. https://doi.org/10.1080/09500690802017545

Toheri, Winarso, W., & Haqq, A. A. (2020). Where exactly for enhance critical and creative thinking: The use of problem posing or contextual learning. European Journal of Educational Research, 9(2), 877-887. https://doi.org/10.12973/eu-jer.9.2.877

Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic Mathematics Education. In Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-15789-0_170

Velten, K., Schmidt, D. M., & Kahlen, K. (2024). Mathematical modeling and simulation: Introduction for scientists and engineers. John Wiley & Sons.

Widodo, S. A., Prahmana, R. C. I., Purnami, A. S., & Turmudi. (2018). Teaching materials of algebraic equation. Journal of Physics: Conference Series, 943(1), 012017. https://doi.org/10.1088/1742-6596/943/1/012017

Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., ... & Ogbuehi, P. (2012). Improving Mathematical Problem Solving in Grades 4 through 8. IES Practice Guide. NCEE 2012-4055. What Works Clearinghouse. https://files.eric.ed.gov/fulltext/ED532215.pdf

Zulkardi, & Putri, R. I. I. (2019). New School Mathematics Curricula, PISA and PMRI in Indonesia. In Vistro-Yu, C., Toh, T. (eds) School Mathematics Curricula. Mathematics Education – An Asian Perspective. Springer. https://doi.org/10.1007/978-981-13-6312-2_3

Zulkardi, Putri, R. I. I., & Wijaya, A. (2019). Two Decades of Realistic Mathematics Education in Indonesia. Springer International Publishing. https://doi.org/10.1007/978-3-030-20223-1_18

When designer meets local culture: The promising learning trajectory on the surface area of polyhedron

Article Sidebar

Downloads

Main Article Content

Abstract

Keywords

Article Details

References

References

Most read articles by the same author(s)