Evaluation of Students' Difficulties in Learning Mathematics in Complex Variable Material

Jitu Halomoan Lumbantoruan

doi:10.23887/jere.v7i3.60532

Authors

Jitu Halomoan Lumbantoruan Universitas Kristen Indonesia, Jakarta, Indonesia

DOI:

https://doi.org/10.23887/jere.v7i3.60532

Keywords:

Evaluation, Mathematical Difficulty, Complex Variables

Abstract

Prospective mathematics teachers are required to be able to master facts and be able to give examples that exist in everyday life. A prospective mathematics teacher is expected to be skilled and mature in using media when operating, explaining and demonstrating direct objects that exist in any complex variable material. The aim of this study is to analyze the obstacles and difficulties of students in Mathematics. Two indicators for assessing mathematics learning outcomes: 1) Direct objects (Facts, Concepts, Skills, and Principles), and 2) Indirect objects (Internet and friends). Mixed methods research method. The subject of the complex variable mathematics course and the student object. Qualitative data collection techniques by observation, interviews, documentation and quantitative survey method collection techniques by distributing instruments. Analysis with, presentation, reduction, presenting bar charts, data synchronization and drawing conclusions. The findings, students' difficulties lie in the direct object, namely mastery of mathematical facts 95.55% and concept difficulties 91.11%, principle (formula) difficulties 91.11% and algorithms 75.55%. Students who get good grades online are assisted by indirect objects, namely the internet and other student discussion partners. In conclusion, students' obstacles and difficulties lie in the direct objects of fact indicators (definitions) and concepts. Material design, facts and concepts with group discussion models are learning solutions.

References

Alam, A. (2020). Challenges and possibilities in teaching and learning of calculus: A case study of India. Journal for the Education of Gifted Young Scientists, 8(1), 407–433. https://doi.org/10.17478/jegys.660201.

Alban Conto, C., Akseer, S., Dreesen, T., Kamei, A., Mizunoya, S., & Rigole, A. (2021). Potential effects of COVID-19 school closures on foundational skills and Country responses for mitigating learning loss. International Journal of Educational Development, 87(December 2020), 102434.1-11. https://doi.org/10.1016/j.ijedudev.2021.102434.

Alberto, R., Shvarts, A., Drijvers, P., & Bakker, A. (2022). International Journal of Child-Computer Interaction Action-based embodied design for mathematics learning : A decade of variations on a theme. International Journal of Child-Computer Interaction, 32(6), 100419.1-23. https://doi.org/10.1016/j.ijcci.2021.100419.

Aningsih, Zulela, M. S., Neolaka, A., Iasha, V., & Setiawan, B. (2022). How is the Education Character Implemented? The Case Study in Indonesian Elementary School. Journal of Educational and Social Research, 12(1), 371–380. https://doi.org/10.36941/jesr-2022-0029.

Anne, R., Kim, S., Pilon-thomas, S., & Enderling, H. (2022). Mathematical modeling of radiotherapy and its impact on tumor interactions with the immune system. Neoplasia, 28(C), 100796. 1-13. https://doi.org/10.1016/j.neo.2022.100796.

Anthony J. Onwuegbuzie, R. B. J. (2021). The routledge reviewer’s guide to mixed methods analysis. In The Routledge Reviewer’s Guide to Mixed Methods Analysis. https://doi.org/10.4324/9780203729434.

Basilotta-Gómez-Pablos, V., Matarranz, M., Casado-Aranda, L. A., & Otto, A. (2022). Teachers’ digital competencies in higher education: a systematic literature review. International Journal of Educational Technology in Higher Education, 19(1), 1-16. https://doi.org/10.1186/s41239-021-00312-8.

Booth, J. L., McGinn, K. M., Barbieri, C., Begolli, K. N., Chang, B., Miller-Cotto, D., Young, L. K., & Davenport, J. L. (2017). Evidence for Cognitive Science Principles that Impact Learning in Mathematics. In Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts. Elsevier Inc. https://doi.org/10.1016/b978-0-12-805086-6.00013-8.

Borch, C. (2022). Machine learning, knowledge risk, and principal-agent problems in automated trading. Technology in Society, 68(October 2021), 101852.1-10. https://doi.org/10.1016/j.techsoc.2021.101852.

Brouwer, N., Joling, E., & Kaper, W. (2022). Effect of a person-centred, tailor-made, teaching practice-oriented training programme on continuous professional development of STEM lecturers. Teaching and Teacher Education, 119(11), 103848.1-17. https://doi.org/10.1016/j.tate.2022.103848.

Budi, S., Darmawan, H., & Saputro, M. (2020). Analysis of Mathematic Communication Ability to be Reviewed From Student Learning Creativity In Statistical Materials. Daya Matematis: Jurnal Inovasi Pendidikan Matematika, 8(1), 105. https://doi.org/10.26858/jds.v8i1.13325.

Chai, Y., Li, W., Li, T., Gong, Z., & You, X. (2016). Engineering Analysis with Boundary Elements Analysis of underwater acoustic scattering problems using stable node-based smoothed fi nite element method. Engineering Analysis With Boundary Elements, 72(11), 27–41. https://doi.org/10.1016/j.enganabound.2016.08.005.

Chang, Y. M., & Lai, C. L. (2021). Exploring the experiences of nursing students in using immersive virtual reality to learn nursing skills. Nurse Education Today, 97(September 2019), 104670.1-7. https://doi.org/10.1016/j.nedt.2020.104670.

Coen, S. (2017). Geometry and Complex Variables. Routledge.

Creamer, E. G. (2021). Advancing Grounded Theory with Mixed Methods. In Advancing Grounded Theory with Mixed Methods. https://doi.org/10.4324/9780429057007.

Csapó, B. (2022). Social determinants of mathematics and science achievement in historical context. Current Opinion in Behavioral Sciences, 46(8), 1–9. https://doi.org/10.1016/j.cobeha.2022.101182

Davy Tsz Kit, N. G., Luo, W., Chan, H. M. Y., & Chu, S. K. W. (2022). Using digital story writing as a pedagogy to develop AI literacy among primary students. Computers and Education: Artificial Intelligence, 3(October 2021), 100054.1-14. https://doi.org/10.1016/j.caeai.2022.100054.

Degner, M., Moser, S., & Lewalter, D. (2022). Digital media in institutional informal learning places: A systematic literature review. Computers and Education Open, 3, 100068. https://doi.org/10.1016/j.caeo.2021.100068.

Firdausy, A. R., Setyaningsih, N., Ishabu, L. S., & Waluyo, M. (2019). The Contribution of Student Activity and Learning Facilities to Learning Independency and it’s Impact on Mathematics Learning Outcomes in Junior High School. Indonesian Journal on Learning and Advanced Education (IJOLAE), 1(2), 29–37. https://doi.org/10.23917/ijolae.v1i2.8104.

Froehlich, D. E., Rehm, M., & Rienties, B. C. (2020). Mixed Methods Social Network Analysis: an introduction of a tale of two communities. London. https://doi.org/https://doi.org/10.4324/9780429056826.

García-álvarez, J., Vázquez-Rodríguez, A., Quiroga-Carrillo, A., & Caamaño, D. P. (2022). Transversal Competencies for Employability in University Graduates: A Systematic Review from the Employers’ Perspective. Education Sciences, 12(3), 1-37. https://doi.org/10.3390/educsci12030204.

González‐pérez, L. I., & Ramírez‐montoya, M. S. (2022). Components of Education 4.0 in 21st Century Skills Frameworks: Systematic Review. Sustainability (Switzerland), 14(3), 1–31. https://doi.org/10.3390/su14031493.

Granberg, C., Palm, T., & Palmberg, B. (2021). A case study of a formative assessment practice and the effects on students’ self-regulated learning. Studies in Educational Evaluation, 68(August 2020), 1-10. https://doi.org/10.1016/j.stueduc.2020.100955.

Gunasegaram, D. R., Murphy, A. B., Barnard, A., Debroy, T., Matthews, M. J., Ladani, L., & Gu, D. (2021). Towards developing multiscale-multiphysics models and their surrogates for digital twins of metal additive manufacturing. Additive Manufacturing, 46(February), 1-17. https://doi.org/10.1016/j.addma.2021.102089.

Güneri, B., & Deveci, M. (2023). Evaluation of supplier selection in the defense industry using q-rung orthopair fuzzy set based EDAS approach. Expert Systems With Applications, 222(February), 119846.1-14. https://doi.org/10.1016/j.eswa.2023.119846.

Hainora Hamzah, Mohd Isa Hamzah, & Hafizhah Zulkifli. (2022). Systematic Literature Review on the Elements of Metacognition-Based Higher Order Thinking Skills (HOTS) Teaching and Learning Modules. Sustainability (Switzerland), 14(2), 1-15. https://doi.org/https://doi.org/10.3390/su14020813.

Haleem, A., Javaid, M., Qadri, M. A., & Suman, R. (2022). Understanding the role of digital technologies in education: A review. Sustainable Operations and Computers, 3(February), 275–285. https://doi.org/10.1016/j.susoc.2022.05.004.

Haser, Ç., Doğan, O., & Kurt Erhan, G. (2022). Tracing students’ mathematics learning loss during school closures in teachers’ self-reported practices. International Journal of Educational Development, 88(September 2021), 1-8. https://doi.org/10.1016/j.ijedudev.2021.102536.

Hastasari, C., Setiawan, B., & Aw, S. (2022). Students’ communication patterns of islamic boarding schools: the case of Students in Muallimin Muhammadiyah Yogyakarta. Heliyon, 8(1), e08824.1-7. https://doi.org/10.1016/j.heliyon.2022.e08824.

Heap, V., & Waters, J. (2019). Mixed methods in criminology. In Mixed Methods in Criminology. https://doi.org/10.4324/9781315143354.

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 and Education, 153(April), 103897. https://doi.org/10.1016/j.compedu.2020.103897.

Hsieh, T., Simpkins, S. D., & Eccles, J. S. (2021). Gender by racial / ethnic intersectionality in the patterns of Adolescents ’ math motivation and their math achievement and engagement ☆. Contemporary Educational Psychology, 66(May), 101974.1-14. https://doi.org/10.1016/j.cedpsych.2021.101974.

Huu, D., Phuong, B., & Anh, N. Van. (2021). Heliyon The improvement of 10 th students ’ mathematical communication skills through learning ellipse topics. Heliyon, 7(October), e08282.1-12. https://doi.org/10.1016/j.heliyon.2021.e08282.

Hwang, G. J., Wang, S. Y., & Lai, C. L. (2021). Effects of a social regulation-based online learning framework on students’ learning achievements and behaviors in mathematics. Computers and Education, 160(1), 104031.1-5. https://doi.org/10.1016/j.compedu.2020.104031.

Ioannidis, J. P. A. (2022). Mathematical Biosciences Pre-registration of mathematical models. Mathematical Biosciences, 345(January), 108782. 1-7. https://doi.org/10.1016/j.mbs.2022.108782.

Jääskä, E., & Aaltonen, K. (2022). Teachers’ experiences of using game-based learning methods in project management higher education. Project Leadership and Society, 3(November 2021), 1-12. https://doi.org/10.1016/j.plas.2022.100041.

Khaizaar, N. I., & Hidayat, R. (2022). The Implementation of Dual Language Programme for Mathematics Education in Secondary Schools: A Systematic Literature Review. International Journal of Educational Methodology, 8(4), 669–686. https://doi.org/10.12973/ijem.8.4.669.

Khasawneh, E., Gosling, C., & Williams, B. (2021). What impact does maths anxiety have on university students? BMC Psychology, 9(1), 1–9. https://doi.org/10.1186/s40359-021-00537-2.

Lahdenperä, J., Rämö, J., & Postareff, L. (2022). Student-centred learning environments supporting undergraduate mathematics students to apply regulated learning: A mixed-methods approach. Journal of Mathematical Behavior, 66(February), 1-15. https://doi.org/10.1016/j.jmathb.2022.100949.

Lauret, D., & Bayram-Jacobs, D. (2021). Covid-19 lockdown education: The importance of structure in a suddenly changed learning environment. Education Sciences, 11(5), 1-21. https://doi.org/10.3390/educsci11050221.

Lebrasseur, A., Best, K., Lettre, J., Bussi, E., Boucher, N., Hotton, M., Beaulieu-bonneau, S., Mercier, C., Lamontagne, M., & Routhier, F. (2021). Impact of COVID-19 on people with physical disabilities : A rapid review. Disability and Health Journal, 14(1), 14. https://doi.org/10.1016/j.dhjo.2020.101014.

Lin, Q., Zhu, Y., Lu, H., Shi, K., & Niu, Z. (2021). Improving University Faculty Evaluations via multi-view Knowledge Graph. Future Generation Computer Systems, 117(4), 181–192. https://doi.org/10.1016/j.future.2020.11.021.

Lindholm, C. (2021). Social Science & Medicine Discussing mental health difficulties in a “ diagnosis free zone .” Social Science & Medicine, 289(December 2020), 1–12. https://doi.org/10.1016/j.socscimed.2021.114364.

Marginson, S. (2022). Global science and national comparisons: beyond bibliometrics and scientometrics. Comparative Education, 58(2), 125–146. https://doi.org/10.1080/03050068.2021.1981725.

Martín, A., Mike, M., Enrique, T., & Malea, O. (2021). Web of Science , and OpenCitations ’ COCI : a multidisciplinary comparison of coverage via citations. In Scientometrics (Vol. 126, Issue 1). Springer International Publishing. https://doi.org/10.1007/s11192-020-03690-4.

Marzuki, Wahyudin, Cahya, E., & Juandi, D. (2021). Students’ critical thinking skills in solving mathematical problems; a systematic procedure of grounded theory study. International Journal of Instruction, 14(4), 529–548. https://doi.org/10.29333/iji.2021.14431a.

Maybury, L., Corcoran, P., & Cipcigan, L. (2022). Mathematical modelling of electric vehicle adoption: A systematic literature review. Transportation Research Part D: Transport and Environment, 107(May), 103278.1-20. https://doi.org/10.1016/j.trd.2022.103278.

Mayorova, V. I., Grishko, D. A., & Leonov, V. V. (2021). “Vivid mathematics” as a general vector of multidisciplinary STEM education for future aerospace engineers. Acta Astronautica, 178(April 2020), 72–80. https://doi.org/10.1016/j.actaastro.2020.09.003.

Moore, S., Hill, E. M., Tildesley, M. J., Dyson, L., & Keeling, M. J. (2021). Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study. The Lancet Infectious Diseases, 21(6), 793–802. https://doi.org/10.1016/S1473-3099(21)00143-2.

Nozari, H., Szmelter-jarosz, A., & Ghahremani-nahr, J. (2022). ( AIoT ) for the Smart Supply Chain ( Case Study : MDPI, 22(8), 1–18. https://doi.org/https://doi.org/10.3390/s22082931.

Oschepkov, A. A., Kidinov, A. V., Babieva, N. S., Vrublevskiy, A. S., Egorova, E. V., & Zhdanov, S. P. (2022). STEM technology-based model helps create an educational environment for developing students’ technical and creative thinking. Eurasia Journal of Mathematics, Science and Technology Education, 18(5), 1–12. https://doi.org/10.29333/ejmste/12033.

Paidican, M. A., & Arredondo, P. A. (2022). The Technological-Pedagogical Knowledge for In-Service Teachers in Primary Education: A Systematic Literature Review. Contemporary Educational Technology, 14(3), 1–15. https://doi.org/10.30935/cedtech/11813.

Palha, S., Dekker, R., Gravemeijer, K., & Hout-wolters, B. Van. (2013). The Journal of Mathematical Behavior Developing shift problems to foster geometrical proof and understanding. Journal of Mathematical Behavior, 32(2), 142–159. https://doi.org/10.1016/j.jmathb.2012.12.002.

Pincheira, N., & Alsina, Á. (2021). Teachers’ mathematics knowledge for teaching early algebra: A systematic review from the mkt perspective. Mathematics, 9(20), 1-16. https://doi.org/10.3390/math9202590.

Powell, S. R., Lembke, E. S., Ketterlin-Geller, L. R., Petscher, Y., Hwang, J., Bos, S. E., Cox, T., Hirt, S., Mason, E. N., Pruitt-Britton, T., Thomas, E., & Hopkins, S. (2021). Data-based individualization in mathematics to support middleschool teachers and their students with mathematics learning difficulty. Studies in Educational Evaluation, 69(June), 1-11. https://doi.org/10.1016/j.stueduc.2020.100897.

Richter, E., Brunner, M., & Richter, D. (2021). Teacher educators’ task perception and its relationship to professional identity and teaching practice. Teaching and Teacher Education, 101(5), 103303.1-10. https://doi.org/10.1016/j.tate.2021.103303.

Sauri, S., Gunara, S., & Cipta, F. (2022). Establishing the identity of insan kamil generation through music learning activities in pesantren. Heliyon, 8(7), e09958.1-7. https://doi.org/10.1016/j.heliyon.2022.e09958.

Schröter, S. (2020). Ditransitive constructions in Caucasian Urum – The effect of givenness on the linearization of objects. Language & Communication, 83(1), 101290.1-12. https://doi.org/10.1016/j.langsci.2020.101290.

Schukajlow, S., Blomberg, J., Rellensmann, J., & Leopold, C. (2022). The role of strategy-based motivation in mathematical problem solving: The case of learner-generated drawings. Learning and Instruction, 80(October 2021), 101561.1-9. https://doi.org/10.1016/j.learninstruc.2021.101561.

Şentop Dümen, A., Koyaz, M., & Çeliker-Cenger, Y. (2022). Unfolding the material: A proposal of a multi-sensory experience oriented material exhibition medium. Materials and Design, 219(7), 1-18. https://doi.org/10.1016/j.matdes.2022.110740.

Shakmaeva, A. (2022). Regulating Math Anxiety and Improving Math Performance: A Review of Intervention Research. Przegląd Badań Edukacyjnych, 36(1), 1-23. https://doi.org/10.12775/pbe.2022.011.

Signorelli, C. M., Wang, Q., & Coecke, B. (2021). Reasoning about conscious experience with axiomatic and graphical mathematics. Consciousness and Cognition, 95(January), 103168.1-16. https://doi.org/10.1016/j.concog.2021.103168.

Sinha, T., & Kapur, M. (2021). Robust effects of the efficacy of explicit failure-driven scaffolding in problem-solving prior to instruction: A replication and extension. Learning and Instruction, 75(February), 101488.1-16. https://doi.org/10.1016/j.learninstruc.2021.101488.

Stecuła, K., & Wolniak, R. (2022). Influence of COVID-19 Pandemic on Dissemination of Innovative E-Learning Tools in Higher Education in Poland. Journal of Open Innovation: Technology, Market, and Complexity, 8(2), 1-22. https://doi.org/10.3390/joitmc8020089.

Stovner, R. B., & Klette, K. (2022). Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: A video study in lower secondary mathematics classrooms. Teaching and Teacher Education, 110, 103593. https://doi.org/10.1016/j.tate.2021.103593.

Supriyadi, E. (2022). a Bibliometrics Analysis on Mathematical Thinking in Indonesia From Scopus Online Database With Affiliation From Indonesia. Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 4(1), 82–98. https://doi.org/10.35316/alifmatika.2022.v4i1.82-98.

Suseelan, M., Chew, C. M., & Chin, H. (2022). Research on Mathematics Problem Solving in Elementary Education Conducted from 1969 to 2021: A Bibliometric Review. International Journal of Education in Mathematics, Science and Technology, 10(4), 1003–1029. https://doi.org/10.46328/ijemst.2198.

Tong, D. H., Uyen, B. P., & Quoc, N. V. A. (2021). The improvement of 10th students’ mathematical communication skills through learning ellipse topics. Heliyon, 7(11), e08282.1-12. https://doi.org/10.1016/j.heliyon.2021.e08282.

Torchinsky, A. (2018). Real Variables. CRC Press.

Tsai, C. W. (2020). Applying online competency-based learning and design-based learning to enhance the development of students’ skills in using PowerPoint and Word, self-directed learning readiness, and experience of online learning. Universal Access in the Information Society, 19(2), 283–294. https://doi.org/10.1007/s10209-018-0640-6.

Waldschläger, K., Brückner, M. Z. M., Carney Almroth, B., Hackney, C. R., Adyel, T. M., Alimi, O. S., Belontz, S. L., Cowger, W., Doyle, D., Gray, A., Kane, I., Kooi, M., Kramer, M., Lechthaler, S., Michie, L., Nordam, T., Pohl, F., Russell, C., Thit, A., … Wu, N. (2022). Learning from natural sediments to tackle microplastics challenges: A multidisciplinary perspective. Earth-Science Reviews, 228(April), 1-24. https://doi.org/10.1016/j.earscirev.2022.104021.

Watson, O. J., Barnsley, G., Toor, J., Hogan, A. B., Winskill, P., & Ghani, A. C. (2022). Global impact of the first year of COVID-19 vaccination: a mathematical modelling study. The Lancet Infectious Diseases, 22(9), 1293–1302. https://doi.org/10.1016/S1473-3099(22)00320-6.

Wijaya, T. T., Cao, Y., Weinhandl, R., & Tamur, M. (2022). A meta-analysis of the effects of E-books on students’ mathematics achievement. Heliyon, 8(6), e09432.1-9. https://doi.org/10.1016/j.heliyon.2022.e09432.

Yusop, S. R. M., Rasul, M. S., Yasin, R. M., Hashim, H. U., & Jalaludin, N. A. (2022). An Assessment Approaches and Learning Outcomes in Technical and Vocational Education: A Systematic Review Using PRISMA. Sustainability (Switzerland), 14(9), 1–18. https://doi.org/10.3390/su14095225.