Learning Design of Project-Based Critical Thinking in Intermediate Linear Algebra for Higher Education Students
Keywords:
Learning Design, Project-Based Critical Thinking, Intermediate Linear Algebra
Abstract
This research uses a design-based approach aimed at exploring the critical thinking skills of university students through an advanced linear algebra project. The subjects involved are 32 students enrolled in the Advanced Linear Algebra course during the odd semester of the 2023/2024 academic year. To support the research, the instruments used include a critical thinking skills instrument, Hypothetical Learning Trajectory, Local Instruction Theory, Learning Activity Observation Based on Video, and a Google Drive-Based Portfolio. The data analysis technique involves several stages, starting with data condensation (transcription, coding, categorization, and theme identification), data presentation (process analysis, matrix, iterative processes, and conclusion drawing and verification), and data validity checking (triangulation and generalizability of research results). Based on the research findings, students' critical thinking skills are determined by reviewing five components: interpretation, analysis, evaluation, argumentation, and self-regulation. The harmonization and synchronization across various activities are still in the moderately developed category, indicating the need for dynamic and interactive activities to support proficiency fulfillment.
References
Abdulah, Y., & Winarti, E. R. (2022). Mathematical Critical Thinking Ability in DAPIC Problem Solving Learning with Scientific-RME Approach in Students Learning Independent. Unnes Journal of Mathematics …. https://journal.unnes.ac.id/sju/index.php/ujme/article/view/59931
Açıkyıldız, G., & Kösa, T. (2021). Creating Design Principles of a Learning Environment for Teaching Vector Spaces. Turkish Journal of Computer and Mathematics Education (TURCOMAT). https://doi.org/10.16949/turkbilmat.860627
Al Marri, S., & Obaid, H. (2023). The Impact of the Critical Thinking on Cognitive Building. Islamic Sciences Journal, 12(8), 391–410. https://doi.org/10.25130/jis.21.12.8.17
Alghadari, F., Yundayani, A., & Genç, M. (2022). Learning Habits Shaping Mathematical Literacy: Lens Through the Chronology of Time and Cognitive Processes. In IndoMath: Indonesia Mathematics Education (Vol. 5, Issue 1, p. 42). Universitas Sarjanawiyata Tamansiswa. https://doi.org/10.30738/indomath.v5i1.14
Bachtiar, M. Y. (2022). Inovasi Pembelajaran Daring dan Dampak Bagi PAUD Selama Pandemi Covid-19. 6(2), 1007–1019. https://doi.org/10.31004/obsesi.v6i2.1411
Brashear, R. J., Hall, H. J., Schur, J. D., & Pan, A. A. (1995). Detection of antibodies to Trypanosoma cruzi among blood donors in the southwestern and western United States. II. Evaluation of a supplemental enzyme immunoassay and radioimmunoprecipitation assay for confirmation of seroreactivity. Transfusion, 35(3), 219–225. https://doi.org/10.1046/j.1537-2995.1995.35395184278.x
Catarino, P., & Vasco, P. (2021). Teaching Linear Algebra in Engineering Courses Using Critical Thinking. Open Education Studies, 3(1), 76–83. https://doi.org/10.1515/edu-2020-0141
Çelik, H. C. (2018). Development of symbolic mathematics language literacy perception scale for junior high school students and analysis of literacy perceptions based on certain variables. In International Journal of Mathematical Education in Science and Technology (Vol. 51, Issue 3, pp. 327–343). Informa UK Limited. https://doi.org/10.1080/0020739x.2018.1555724
Coates, H., James, R., & Baldwin, G. (2005). A critical examination of the effects of learning management systems on university teaching and learning. Tertiary Education and Management, 11(1), 19–36. https://doi.org/10.1080/13583883.2005.9967137
Grabinger, S., Dunlap, J. C., & Duffield, J. A. (1997). Rich environments for active learning in action: Problem-based learning. Alt-J, 5(2), 5–17. https://doi.org/10.1080/0968776970050202
Herrington, J., McKenney, S., Reeves, T., & Oliver, R. (2007). Design-based research and doctoral students: Guidelines for preparing a dissertation proposal. World Conference on Educational Multimedia, Hypermedia and Telecommunications, January 2015, 4089–4097. http://researchrepository.murdoch.edu.au/6762/%5Cnpapers3://publication/uuid/373E7103-6768-447C-A4DB-C8E1712589A9
Hillel, J., & Sierpinska, A. (1994). On one persistent mistake in linear algebra. The Proceedings PME, 18(2), 65–72.
Izquierdo, J., Benítez, J., Berenguer, A., & Lago-Alonso, C. (2016). I decide, therefore i am (relevant!): A project-based learning experience in linear algebra. Computer Applications in Engineering Education, 24(3), 481–492. https://doi.org/10.1002/cae.21725
Kolb, A. Y., & Kolb, D. A. (2022). Experiential Learning Theory as a Guide for Experiential Educators in Higher Education. In Experiential Learning and Teaching in Higher Education (Vol. 1, Issue 1, p. 38). California State University, Office of the Chancellor. https://doi.org/10.46787/elthe.v1i1.3362
Kuzu, A., Çankaya, S., & Abidin Mısırlı, Z. (2011). Tasarım Tabanlı Araştırma ve Öğrenme Ortamlarının Tasarımı ve Geliştirilmesinde Kullanımı Design-Based Research and Its Implementation in the Design and Development of Learning Environments. Anadolu Journal of Educational Sciences International, 1(1).
Margianti, E. S. (2001). Learning Environment , Mathematics Achievement and Student Attitudes Among University Computing Students in Indonesia. October, xiii + 184.
Mcgaghie, W. C., Issenberg, S. B., Barsuk, J. H., & Wayne, D. B. (2014). A critical review of simulation-based mastery learning with translational outcomes. Medical Education, 48(4), 375–385. https://doi.org/10.1111/medu.12391
Moanoang, C., Arsyad, N., & Nasrullah, N. (2021). Desain Pembelajaran Matematika Berbasis Hypothetical Learning Trajectory (HLT) Pada Materi Operasi Bilangan Bulat Siswa Kelas VII SMP Bunda Kasih Sudiang. Issues in Mathematics Education (IMED), 5(2), 100. https://doi.org/10.35580/imed23842
Nasrullah. (2014). Kontribusi Model Pembelajaran Berbasis Proyek terhadap Faktor AIK dalam Pembelajaran Matematika Siswa Kelas II / 3 SMPN 2 Makassar. Kreano, 5(1), 48–55. https://doi.org/http://dx.doi.org/10.15294/kreano.v5i1.3277
Nasrullah. (2015). Teachers’ Creativity in Posing Problems of Mathematics Using Traditional Games as Learning Context. In International Conference on Education and Technology (p. 8).
Nasrullah, & Zulkardi. (2011). Building counting by traditional game: A mathematics program for young children. Journal on Mathematics Education, 2(1). https://doi.org/10.22342/jme.2.1.781.41-54
Oliveira, H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: A focus on functional thinking. Journal on Mathematics Education, 12(2), 257–278. https://doi.org/10.22342/jme.12.2.13745.257-278
Perez, L., & Andrade, R. (2023). Influence of Thinking Style on the Critical Thinking Skills and Creativity in Mathematics. International Journal of Science, Technology, Engineering and Mathematics, 3(4), 30–50. https://doi.org/10.53378/353037
Pimentel, C., Pscheidt, R., Rosa, B., Kemczinski, A., & Gasparini, I. (2022). Gamification of an Exercise Tool of a Virtual Learning Environment. In Proceedings of the 14th International Conference on Computer Supported Education. SCITEPRESS - Science and Technology Publications. https://doi.org/10.5220/0011089300003182
Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2024). Revisiting the Relationship of Arithmetical Thinking and Letter-Symbolic Algebra. International Journal of Science and Mathematics Education, 0123456789. https://doi.org/10.1007/s10763-024-10493-z
Prescott, A., Coupland, M., Angelini, M., & Schuck, S. (2020). Making School Maths Engaging, The Maths Inside Project. https://app.dimensions.ai/details/publication/pub.1131896372%0Ahttps://link.springer.com/content/pdf/bfm%3A978-981-15-9151-8%2F1
Rahman, F. (2022). EXPERIENTIAL LEARNING FOR STUDENT ADVANCEMENT: A STATE-OF-THE-ART IN HIGHER EDUCATION. In The Global Conference on Research in Education and Learning. R&R Knowledge Solutions. https://doi.org/10.56790/103.091022
Reeves, T. C. (2000). Enhancing the Worth of Instructional Technology Research through “Design Experiments” and Other Development Research Strategies. Educational Technology, April, 1–15. http://it.coe.uga.edu/~treeves/AERA2000Reeves.pdf
Riconscente, M. M. (2013). Results from a controlled study of the iPad fractions game motion math. Games and Culture, 8(4), 186–214. https://doi.org/10.1177/1555412013496894
Sari, R., Susanti, E., Kurniadi, E., & Sari, N. (2022). Students’ Ability in Making Mathematics Generalizations Through Geogebra Assisted CPS on Straight Line Equations. Proceedings of the 2nd National Conference on Mathematics Education 2021 (NaCoME 2021), 656(January). https://doi.org/10.2991/assehr.k.220403.023
Siregar, T., Syekh, U., Hasan, A., & Padangsidimpuan, A. A. (2024). Improving Student’s Critical Thinking Skill in Learning Mathematics Using Problem Posing Approach. August, 1–20. https://www.researchgate.net/publication/383212501
Suryandari, K. C., Fatimah, S., Sajidan, S., Rahardjo, S. B., & Prasetyo, Z. K. (2018). PROJECT-BASED SCIENCE LEARNING AND PRE-SERVICE TEACHERS’ SCIENCE LITERACY SKILL AND CREATIVE THINKING. In Jurnal Cakrawala Pendidikan (Vol. 37, Issue 3). Universitas Negeri Yogyakarta. https://doi.org/10.21831/cp.v38i3.17229
Terblanche, E. A. J. (2021). A critical thinking competency framework for accounting students. Accounting Education, 30(4), 325–354. https://doi.org/10.1080/09639284.2021.1913614
Treffinger, D. J. (2007). Creative Problem Solving (CPS): Powerful Tools for Managing Change and Developing Talent. Gifted and Talented International, 22(2), 8–18. https://doi.org/10.1080/15332276.2007.11673491
Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education. Encyclopedia of Mathematics Education, 521–525. https://doi.org/10.1007/978-94-007-4978-8
Açıkyıldız, G., & Kösa, T. (2021). Creating Design Principles of a Learning Environment for Teaching Vector Spaces. Turkish Journal of Computer and Mathematics Education (TURCOMAT). https://doi.org/10.16949/turkbilmat.860627
Al Marri, S., & Obaid, H. (2023). The Impact of the Critical Thinking on Cognitive Building. Islamic Sciences Journal, 12(8), 391–410. https://doi.org/10.25130/jis.21.12.8.17
Alghadari, F., Yundayani, A., & Genç, M. (2022). Learning Habits Shaping Mathematical Literacy: Lens Through the Chronology of Time and Cognitive Processes. In IndoMath: Indonesia Mathematics Education (Vol. 5, Issue 1, p. 42). Universitas Sarjanawiyata Tamansiswa. https://doi.org/10.30738/indomath.v5i1.14
Bachtiar, M. Y. (2022). Inovasi Pembelajaran Daring dan Dampak Bagi PAUD Selama Pandemi Covid-19. 6(2), 1007–1019. https://doi.org/10.31004/obsesi.v6i2.1411
Brashear, R. J., Hall, H. J., Schur, J. D., & Pan, A. A. (1995). Detection of antibodies to Trypanosoma cruzi among blood donors in the southwestern and western United States. II. Evaluation of a supplemental enzyme immunoassay and radioimmunoprecipitation assay for confirmation of seroreactivity. Transfusion, 35(3), 219–225. https://doi.org/10.1046/j.1537-2995.1995.35395184278.x
Catarino, P., & Vasco, P. (2021). Teaching Linear Algebra in Engineering Courses Using Critical Thinking. Open Education Studies, 3(1), 76–83. https://doi.org/10.1515/edu-2020-0141
Çelik, H. C. (2018). Development of symbolic mathematics language literacy perception scale for junior high school students and analysis of literacy perceptions based on certain variables. In International Journal of Mathematical Education in Science and Technology (Vol. 51, Issue 3, pp. 327–343). Informa UK Limited. https://doi.org/10.1080/0020739x.2018.1555724
Coates, H., James, R., & Baldwin, G. (2005). A critical examination of the effects of learning management systems on university teaching and learning. Tertiary Education and Management, 11(1), 19–36. https://doi.org/10.1080/13583883.2005.9967137
Grabinger, S., Dunlap, J. C., & Duffield, J. A. (1997). Rich environments for active learning in action: Problem-based learning. Alt-J, 5(2), 5–17. https://doi.org/10.1080/0968776970050202
Herrington, J., McKenney, S., Reeves, T., & Oliver, R. (2007). Design-based research and doctoral students: Guidelines for preparing a dissertation proposal. World Conference on Educational Multimedia, Hypermedia and Telecommunications, January 2015, 4089–4097. http://researchrepository.murdoch.edu.au/6762/%5Cnpapers3://publication/uuid/373E7103-6768-447C-A4DB-C8E1712589A9
Hillel, J., & Sierpinska, A. (1994). On one persistent mistake in linear algebra. The Proceedings PME, 18(2), 65–72.
Izquierdo, J., Benítez, J., Berenguer, A., & Lago-Alonso, C. (2016). I decide, therefore i am (relevant!): A project-based learning experience in linear algebra. Computer Applications in Engineering Education, 24(3), 481–492. https://doi.org/10.1002/cae.21725
Kolb, A. Y., & Kolb, D. A. (2022). Experiential Learning Theory as a Guide for Experiential Educators in Higher Education. In Experiential Learning and Teaching in Higher Education (Vol. 1, Issue 1, p. 38). California State University, Office of the Chancellor. https://doi.org/10.46787/elthe.v1i1.3362
Kuzu, A., Çankaya, S., & Abidin Mısırlı, Z. (2011). Tasarım Tabanlı Araştırma ve Öğrenme Ortamlarının Tasarımı ve Geliştirilmesinde Kullanımı Design-Based Research and Its Implementation in the Design and Development of Learning Environments. Anadolu Journal of Educational Sciences International, 1(1).
Margianti, E. S. (2001). Learning Environment , Mathematics Achievement and Student Attitudes Among University Computing Students in Indonesia. October, xiii + 184.
Mcgaghie, W. C., Issenberg, S. B., Barsuk, J. H., & Wayne, D. B. (2014). A critical review of simulation-based mastery learning with translational outcomes. Medical Education, 48(4), 375–385. https://doi.org/10.1111/medu.12391
Moanoang, C., Arsyad, N., & Nasrullah, N. (2021). Desain Pembelajaran Matematika Berbasis Hypothetical Learning Trajectory (HLT) Pada Materi Operasi Bilangan Bulat Siswa Kelas VII SMP Bunda Kasih Sudiang. Issues in Mathematics Education (IMED), 5(2), 100. https://doi.org/10.35580/imed23842
Nasrullah. (2014). Kontribusi Model Pembelajaran Berbasis Proyek terhadap Faktor AIK dalam Pembelajaran Matematika Siswa Kelas II / 3 SMPN 2 Makassar. Kreano, 5(1), 48–55. https://doi.org/http://dx.doi.org/10.15294/kreano.v5i1.3277
Nasrullah. (2015). Teachers’ Creativity in Posing Problems of Mathematics Using Traditional Games as Learning Context. In International Conference on Education and Technology (p. 8).
Nasrullah, & Zulkardi. (2011). Building counting by traditional game: A mathematics program for young children. Journal on Mathematics Education, 2(1). https://doi.org/10.22342/jme.2.1.781.41-54
Oliveira, H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: A focus on functional thinking. Journal on Mathematics Education, 12(2), 257–278. https://doi.org/10.22342/jme.12.2.13745.257-278
Perez, L., & Andrade, R. (2023). Influence of Thinking Style on the Critical Thinking Skills and Creativity in Mathematics. International Journal of Science, Technology, Engineering and Mathematics, 3(4), 30–50. https://doi.org/10.53378/353037
Pimentel, C., Pscheidt, R., Rosa, B., Kemczinski, A., & Gasparini, I. (2022). Gamification of an Exercise Tool of a Virtual Learning Environment. In Proceedings of the 14th International Conference on Computer Supported Education. SCITEPRESS - Science and Technology Publications. https://doi.org/10.5220/0011089300003182
Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2024). Revisiting the Relationship of Arithmetical Thinking and Letter-Symbolic Algebra. International Journal of Science and Mathematics Education, 0123456789. https://doi.org/10.1007/s10763-024-10493-z
Prescott, A., Coupland, M., Angelini, M., & Schuck, S. (2020). Making School Maths Engaging, The Maths Inside Project. https://app.dimensions.ai/details/publication/pub.1131896372%0Ahttps://link.springer.com/content/pdf/bfm%3A978-981-15-9151-8%2F1
Rahman, F. (2022). EXPERIENTIAL LEARNING FOR STUDENT ADVANCEMENT: A STATE-OF-THE-ART IN HIGHER EDUCATION. In The Global Conference on Research in Education and Learning. R&R Knowledge Solutions. https://doi.org/10.56790/103.091022
Reeves, T. C. (2000). Enhancing the Worth of Instructional Technology Research through “Design Experiments” and Other Development Research Strategies. Educational Technology, April, 1–15. http://it.coe.uga.edu/~treeves/AERA2000Reeves.pdf
Riconscente, M. M. (2013). Results from a controlled study of the iPad fractions game motion math. Games and Culture, 8(4), 186–214. https://doi.org/10.1177/1555412013496894
Sari, R., Susanti, E., Kurniadi, E., & Sari, N. (2022). Students’ Ability in Making Mathematics Generalizations Through Geogebra Assisted CPS on Straight Line Equations. Proceedings of the 2nd National Conference on Mathematics Education 2021 (NaCoME 2021), 656(January). https://doi.org/10.2991/assehr.k.220403.023
Siregar, T., Syekh, U., Hasan, A., & Padangsidimpuan, A. A. (2024). Improving Student’s Critical Thinking Skill in Learning Mathematics Using Problem Posing Approach. August, 1–20. https://www.researchgate.net/publication/383212501
Suryandari, K. C., Fatimah, S., Sajidan, S., Rahardjo, S. B., & Prasetyo, Z. K. (2018). PROJECT-BASED SCIENCE LEARNING AND PRE-SERVICE TEACHERS’ SCIENCE LITERACY SKILL AND CREATIVE THINKING. In Jurnal Cakrawala Pendidikan (Vol. 37, Issue 3). Universitas Negeri Yogyakarta. https://doi.org/10.21831/cp.v38i3.17229
Terblanche, E. A. J. (2021). A critical thinking competency framework for accounting students. Accounting Education, 30(4), 325–354. https://doi.org/10.1080/09639284.2021.1913614
Treffinger, D. J. (2007). Creative Problem Solving (CPS): Powerful Tools for Managing Change and Developing Talent. Gifted and Talented International, 22(2), 8–18. https://doi.org/10.1080/15332276.2007.11673491
Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education. Encyclopedia of Mathematics Education, 521–525. https://doi.org/10.1007/978-94-007-4978-8
Published
2025-08-03
How to Cite
Nasrullah, Khadijah, & Ahyani Mirah Liani. (2025). Learning Design of Project-Based Critical Thinking in Intermediate Linear Algebra for Higher Education Students. International Journal of Education, Vocational and Social Science , 4(03), 650-668. https://doi.org/10.63922/ijevss.v4i03.2170
Contact Person +6282139474255
Email : ijevss@citakonsultindo.or.id / editor.ijevss@gmail.com
