Main Article Content

Abstract

Previous research has highlighted the challenges of improving students' mathematical skills, particularly in connecting mathematical concepts to everyday life and developing strong mathematical habits of mind. This research aims to integrate problem-based learning (PBL) into a mathematics module to enhance mathematical connection abilities and mathematical habits of mind. The ADDIE method was employed to achieve this goal, encompassing five stages: Analysis, Design, Development, Implementation, and Evaluation. The findings indicate that media, material, and language experts deemed the module highly suitable. Furthermore, the product was rated as highly practical based on teacher assessments, student responses, and observations during implementation. Effectiveness tests of the product, conducted through MANOVA, t-tests, and N-gain tests, revealed that the module is highly effective in enhancing students' mathematical connection abilities and moderately effective in improving their mathematical habits of mind. These findings underscore the importance of integrating digital learning technologies to increase the module's engagement and accessibility.

Keywords

Elementary school Mathematical connection Mathematical habits of mind Module Problem-based learning

Article Details

References

  1. Andriani, S., Yulianti, K., Ferdias, P., & Fatonah, S. (2017). The effect of mathematical habits of mind learning strategy based on problem toward students’ mathematical creative thinking disposition. IJAEDU- International E-Journal of Advances in Education, 3(9), 689-696. https://doi.org/10.18768/ijaedu.372122

  2. Ayuningtyas, I. N., Amir, M. F., & Wardana, M. D. K. (2024). Elementary school students’ layers of understanding in solving literacy problems based on Sidoarjo context. Infinity Journal, 13(1), 157-174. https://doi.org/10.22460/infinity.v13i1.p157-174

  3. Blöte, A. W., Van der Burg, E., & Klein, A. S. (2001). Students' flexibility in solving two-digit addition and subtraction problems: Instruction effects. Journal of educational psychology, 93(3), 627-638. https://doi.org/10.1037/0022-0663.93.3.627

  4. Bosica, J., Pyper, J. S., & MacGregor, S. (2021). Incorporating problem-based learning in a secondary school mathematics preservice teacher education course. Teaching and Teacher Education, 102, 103335. https://doi.org/10.1016/j.tate.2021.103335

  5. Boye, E. S., & Agyei, D. D. (2023). Effectiveness of problem-based learning strategy in improving teaching and learning of mathematics for pre-service teachers in Ghana. Social Sciences & Humanities Open, 7(1), 100453. https://doi.org/10.1016/j.ssaho.2023.100453

  6. Bülbül, B. Ö. (2021). Factors affecting prospective mathematics teachers’ beliefs about geometric habits of mind. Journal of Pedagogical Research, 5(2), 36-48. https://doi.org/10.33902/JPR.2021068370

  7. Cotič, M., & Zuljan, M. V. (2009). Problem‐based instruction in mathematics and its impact on the cognitive results of the students and on affective‐motivational aspects. Educational Studies, 35(3), 297-310. https://doi.org/10.1080/03055690802648085

  8. Cuoco, A., Paul Goldenberg, E., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375-402. https://doi.org/10.1016/S0732-3123(96)90023-1

  9. Dabbagh, N. (2019). Effects of PBL on critical thinking skills. In M. Moallem, W. Hung, & N. Dabbagh (Eds.), The Wiley Handbook of Problem‐Based Learning (pp. 135-156). https://doi.org/10.1002/9781119173243.ch6

  10. Fennema, E. (1992). Cognitively guided instruction. In NCRMSE research review: The teaching and learning of mathematics.

  11. García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994

  12. Gordon, M. (2011). Mathematical habits of mind: Promoting students’ thoughtful considerations. Journal of Curriculum Studies, 43(4), 457-469. https://doi.org/10.1080/00220272.2011.578664

  13. Harisman, Y., Dwina, F., Nasution, M. L., Amiruddin, M. H., & Syaputra, H. (2023). The development of proton-electron math e-comic to improve special needs students’ mathematical concepts understanding. Infinity Journal, 12(2), 359-376. https://doi.org/10.22460/infinity.v12i2.p359-376

  14. Hiebert, J., & Wearne, D. (1992). Links between teaching and learning place value with understanding in first grade. Journal for Research in Mathematics Education JRME, 23(2), 98-122. https://doi.org/10.5951/jresematheduc.23.2.0098

  15. Houghton, J. (2023). Learning modules: problem-based learning, blended learning and flipping the classroom. The Law Teacher, 57(3), 271-294. https://doi.org/10.1080/03069400.2023.2208017

  16. Kurniansyah, M. Y., Hidayat, W., & Rohaeti, E. E. (2022). Development of combined module using contextual scientific approach to enhance students' cognitive and affective. Infinity Journal, 11(2), 349-366. https://doi.org/10.22460/infinity.v11i2.p349-366

  17. Kusmaryono, I., Aminudin, M., Ubaidah, N., & Chamalah, E. (2024). The bridging understanding of language and mathematical symbols between teachers and students: An effort to increase mathematical literacy. Infinity Journal, 13(1), 251-270. https://doi.org/10.22460/infinity.v13i1.p251-270

  18. Li, A., Bilgic, E., Keuhl, A., & Sibbald, M. (2022). Does your group matter? How group function impacts educational outcomes in problem-based learning: a scoping review. BMC Medical Education, 22(1), 900. https://doi.org/10.1186/s12909-022-03966-8

  19. Lianghuo, F., & Mei, Y. S. (2007). Integrating oral presentation into mathematics teaching and learning: An exploratory study with Singapore secondary students. The Montana Mathematics Enthusiast, Monograph, 3, 81-98.

  20. Ma, X., Millman, R., & Wells, M. (2008). Infusing assessment into mathematics content courses for pre-service elementary school teachers. Educational Research for Policy and Practice, 7(3), 165-181. https://doi.org/10.1007/s10671-008-9050-5

  21. Maarif, S., & Fitriani, N. (2023). Mathematical resilience, habits of mind, and sociomathematical norms by senior high school students in learning mathematics: A structured equation model. Infinity Journal, 12(1), 117-132. https://doi.org/10.22460/infinity.v12i1.p117-132

  22. McFeetors, P. J., & Palfy, K. (2018). Educative experiences in a games context: Supporting emerging reasoning in elementary school mathematics. The Journal of Mathematical Behavior, 50, 103-125. https://doi.org/10.1016/j.jmathb.2018.02.003

  23. Moallem, M. (2019). Effects of PBL on Learning Outcomes, Knowledge Acquisition, and Higher-Order Thinking Skills. In M. Moallem, W. Hung, & N. Dabbagh (Eds.), The Wiley Handbook of Problem‐Based Learning (pp. 107-133). https://doi.org/10.1002/9781119173243.ch5

  24. Moallem, M., Hung, W., & Dabbagh, N. (2019). The Wiley handbook of problem-based learning. John Wiley & Sons. https://doi.org/10.1002/9781119173243

  25. Moust, J., Roebertsen, H., Savelberg, H., & De Rijk, A. (2005). Revitalising PBL groups: Evaluating PBL with study teams. Education for Health, 18(1), 62-73.

  26. Muhtarom, M., Pratiwi, A. D., & Murtianto, Y. H. (2021). Profile of prospective teachers' mathematical communication ability reviewed from adversity quotient. Infinity Journal, 10(1), 93-108. https://doi.org/10.22460/infinity.v10i1.p93-108

  27. Munawaroh, M., Setyani, N. S., Susilowati, L., & Rukminingsih, R. (2022). The effect of e-problem based learning on students’ interest, motivation and achievement. International Journal of Instruction, 15(3), 503-518. https://doi.org/10.29333/iji.2022.15328a

  28. Nabillah, R., Herwin, H., & Tandukar, K. (2023). How is the mathematical connection ability of post-pandemic class IV elementary school students in whole numbers material? Pythagoras, 18(1), 1-13. https://doi.org/10.21831/pythagoras.v18i1.58448

  29. Nardo, M. T. B. (2017). Modular instruction enhances learner autonomy. American Journal of Educational Research, 5(10), 1024-1034.

  30. NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.

  31. OECD. (2019). PISA 2018 Results (Volume I): What students know and can do. OECD Publishing.

  32. OECD. (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD Publishing. https://doi.org/10.1787/53f23881-en

  33. Polman, J., Hornstra, L., & Volman, M. (2021). The meaning of meaningful learning in mathematics in upper-primary education. Learning Environments Research, 24(3), 469-486. https://doi.org/10.1007/s10984-020-09337-8

  34. Purnomo, Y. W. (2015). Pengembangan desain pembelajaran berbasis penilaian dalam pembelajaran matematika [Development of assessment-based learning designs in mathematics learning]. Cakrawala Pendidikan, XXXIV(2), 182-191. https://doi.org/10.21831/cp.v2i2.4823

  35. Purnomo, Y. W. (2016). Perbaikan instruksional dalam implementasi assessment-based learning di kelas matematika [Instructional improvements in implementing assessment-based learning in mathematics classes]. Cakrawala Pendidikan, XXXV(3), 403-411. https://doi.org/10.21831/cp.v35i3.8821

  36. Purnomo, Y. W., Widowati, C., & Ulfah, S. (2019). Incomprehension of the Indonesian elementary school students on fraction division problem. Infinity Journal, 8(1), 57-74. https://doi.org/10.22460/infinity.v8i1.p57-74

  37. Rachmawati, L. N., Cholily, Y. M., & Zukhrufurrohmah, Z. (2021). Mathematics communication mistakes in solving HOTs problems. Infinity Journal, 10(1), 69-80. https://doi.org/10.22460/infinity.v10i1.p69-80

  38. Rafi, I., & Retnawati, H. (2022). Exploring the use of portfolio assessment in fostering students’ mathematical creativity and self-regulated learning in an era of uncertainty. AIP Conference Proceedings, 2575(1), 040016. https://doi.org/10.1063/5.0111225

  39. Rahmawati, R. D., Sulistyani, N., Purnomo, Y. W., Fitriya, Y., & Ramadhani, D. (2023). Relationship between elementary school students' numeracy and number sense. The New Educational Review, 74, 73-88. https://doi.org/10.15804/tner.23.74.4.06

  40. Rodríguez-Nieto, C. A., Font Moll, V., Borji, V., & Rodríguez-Vásquez, F. M. (2022). Mathematical connections from a networking of theories between extended theory of mathematical connections and onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(9), 2364-2390. https://doi.org/10.1080/0020739X.2021.1875071

  41. Rotgans, J. I., & Schmidt, H. G. (2019). Effects of Problem-Based Learning on Motivation, Interest, and Learning. In M. Moallem, W. Hung, & N. Dabbagh (Eds.), The Wiley Handbook of Problem‐Based Learning (pp. 157-179). https://doi.org/10.1002/9781119173243.ch7

  42. Smith, P. L., & Ragan, T. J. (2004). Instructional design. John Wiley & Sons.

  43. Tan, O.-S. (2003). Problem-based learning innovation: Using problems to power learning in the 21st century. Gale Cengage Learning.

  44. Westwood, P. (2011). The problem with problems: Potential difficulties in implementing problem-based learning as the core method in primary school mathematics. Australian Journal of Learning Difficulties, 16(1), 5-18. https://doi.org/10.1080/19404158.2011.563475

  45. Wijaya, T. T., Hidayat, W., Hermita, N., Alim, J. A., & Talib, C. A. (2024). Exploring contributing factors to PISA 2022 mathematics achievement: Insights from Indonesian teachers. Infinity Journal, 13(1), 139-156. https://doi.org/10.22460/infinity.v13i1.p139-156

  46. Wijnia, L., Noordzij, G., Arends, L. R., Rikers, R. M. J. P., & Loyens, S. M. M. (2024). The effects of problem-based, project-based, and case-based learning on students’ motivation: A meta-analysis. Educational Psychology Review, 36(1), 29. https://doi.org/10.1007/s10648-024-09864-3

  47. Yustinah, N., Rohaeti, E. E., & Yuliani, A. (2023). The effect of habits of mind on mathematical problem-solving ability of junior high school students. (JIML) Journal of Innovative Mathematics Learning, 6(1), 12-19. https://doi.org/10.22460/jiml.v6i1.15259