How is the Learning Evaluation of the Pythagorean Theorem?: A Systematic Literature Review

Usman Aripin, Zulkardi Zulkardi, Ratu Ilma Indra Putri, Heris Hendriana

Abstract


Abstract: Mathematics learning problems, especially on the Pythagorean theorem material, cannot be studied only from one side, but need to be seen comprehensively from various integrative learning studies. This study aims to provide an overview of the evaluation of learning Pythagorean theorem material from reputable studies. This research uses the Systematic Literature Review (SRL) method. A review was conducted of 13 relevant articles published in various reputable international journals in the period 2019 to 2024. The data analysis used was carried out with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Based on the results of the review, it was found that in the Pythagorean theorem material there are still many misconceptions of understanding, with implications for the ability of abstraction that is not optimal. The quality of teaching is influenced by teachers' motivational beliefs in teaching, technology integration can help increase learning motivation, streamline learning and students are happier with teachers who use learning media, and teacher motivation in applying technology has an important role. In the realm of learning innovation, problem-based learning with a realistic mathematics approach is proven to be valid and effective and encourages active students and positive responses to the Pythagorean theorem material. Evaluation instruments must be valid, reliable, well designed to be effective in optimizing the learning process and diagnosing learning difficulties.       

 

Keywords: pythagorean theorem, learning evaluation, mathematics learning.



DOI: http://dx.doi.org/10.23960/jpmipa/v25i2.pp847-863

Full Text:

PDF

References


Adhitama, I., Sujadi, I., & Pramudya, I. (2018). Discover the pythagorean theorem using interactive multimedia learning. Journal of Physics: Conference Series, 1008(1). https://doi.org/10.1088/1742-6596/1008/1/012066

Alghadari, F., & Noor, N. A. (2020). Students depend on the Pythagorean theorem: Analysis by the three parallel design of abstraction thinking problem. Journal of Physics: Conference Series, 1657(1). https://doi.org/10.1088/1742-6596/1657/1/012005

Alok, K. (2011). Student evaluation of teaching: an instrument and a development process. International Journal of Teaching and Learning in Higher Education, 23(2), 226–235.

Arends. (2015). Larning to teach. NY: McGraw-Hill Education.

Arnellis, A., Syarifuddin, H., & Ismail, R. N. (2023). Optimizing students’ mathematical critical and creative thinking skills through the flip-a-team model with e-learning. Al-Jabar : Jurnal Pendidikan Matematika, 14(1), 133–140. https://doi.org/ 10.24042/ajpm.v14i1.16904

Backfisch, I., Lachner, A., Hische, C., Loose, F., & Scheiter, K. (2020). Professional knowledge or motivation? Investigating the role of teachers’ expertise on the quality of technology-enhanced lesson plans. Learning and Instruction, 66(December 2019), 101300. https://doi.org/10.1016/j.learninstruc.2019.101300

Borzekowski, D. L. G., Lando, A. L., Olsen, S. H., & Giffen, L. (2019). The Impact of an educational media intervention to support children’s early learning in Rwanda. International Journal of Early Childhood, 51(1), 109–126. https://doi.org/ 10.1007/s13158-019-00237-4

Cai, J., & Ding, M. (2017). On mathematical understanding: perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Education, 20(1), 5–29. https://doi.org/10.1007/s10857-015-9325-8

Casanova, J. R., Cantoria, C. C. C., & Lapinid, M. R. C. (2021). Students’ geometric thinking on triangles: much improvement is needed. Infinity Journal, 10(2), 217–234. https://doi.org/10.22460/infinity.v10i2.p217-234

Changala, M., & Mbozi, E. H. (2017). Factors contributing to institutionalisation of the aged in old people’s homes in zambia: Perspectives of the aged. South African International Conference on Education, September, 60–69.

Chi, M. T. H., & VanLehn, K. A. (2012). Seeing Deep Structure From the Interactions of Surface Features. Educational Psychologist, 47(3), 177–188. https://doi.org/ 10.1080/00461520.2012.695709

Deshpande, D. S., Riccomini, P. J., Hughes, E. M., & Raulston, T. J. (2021). Problem solving with the pythagorean theorem: a think aloud analysis of secondary students with learning disabilities. Learning Disabilities, 19(1), 23–47.

Dodeen, H. (2013). College students ’ evaluation of effective teaching : Developing an instrument and assessing its psychometric properties. Research in Higher Education Journal, 21, 1–12.

Durksen, T. L., Klassen, R. M., & Daniels, L. M. (2017). Motivation and collaboration: The keys to a developmental framework for teachers’ professional learning. Teaching and Teacher Education, 67, 53–66. https://doi.org/10.1016/ j.tate.2017.05.011

Dwijayanti, N., Suharta, I. G. P., & Sariyasa. (2017). Bruner’s cognitive stages and their effects on the understanding of fraction concept. International Research Journal of Engineering, IT and Scientific Research, 3(4), 37–46. https://doi.org/ 10.21744/irjeis.v3i4.497

Eccles, J. S., & Roeser, R. W. (2011). Schools as developmental contexts during adolescence. Journal of Research on Adolescence, 21(1), 225–241. https://doi.org/10.1111/j.1532-7795.2010.00725.x

Farjon, D., Smits, A., & Voogt, J. (2019). Technology integration of pre-service teachers explained by attitudes and beliefs, competency, access, and experience. Computers and Education, 130, 81–93. https://doi.org/10.1016/j.compedu.2018.11.010

Güner, N. (2018). How to teach the pythagorean theorem: an analysis of lesson plans. Ankara Universitesi Egitim Bilimleri Fakultesi Dergisi, 51(1), 119–141. https://doi.org/10.30964/auebfd.405041

Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2023). Posing and solving modelling problems—extending the modelling process from a problem posing perspective. Journal Fur Mathematik-Didaktik, 44(2), 533–561. https://doi.org/10.1007/s13138-023-00223-3

Henderson, C., Turpen, C., Dancy, M., & Chapman, T. (2014). Assessment of teaching effectiveness: Lack of alignment between instructors, institutions, and research recommendations. Physical Review Special Topics - Physics Education Research, 10(1), 1–20. https://doi.org/10.1103/PhysRevSTPER.10.010106

Hendriana, H., Putra, H. D., & Hidayat, W. (2019). How to design teaching materials to improve the ability of mathematical reflective thinking of senior high school students in Indonesia? Eurasia Journal of Mathematics, Science and Technology Education, 15(12). https://doi.org/10.29333/ejmste/112033

Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. https://doi.org/10.3102/00028312042002371

Hornstra, L., Mansfield, C., van der Veen, I., Peetsma, T., & Volman, M. (2015). Motivational teacher strategies: the role of beliefs and contextual factors. Learning Environments Research, 18(3), 363–392. https://doi.org/10.1007/s10984-015-9189-y

Husna, A., Zulkardi, Z., Putri, R. I. I., Susanti, E., & Nusantara, D. S. (2024). Hypothetical learning trajectory of linear equation systems with three variables: The context of typical snacks riau islands. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika, 10(1), 12–22. https://doi.org/10.29407/jmen.v10i1.21550

Jung, E., Zhang, Y., & Chiang, J. (2019). Teachers’ mathematics education and readiness beliefs, and kindergarteners’ mathematics learning. International Journal of Education in Mathematics, Science and Technology, 7(2), 137–154. https://doi.org/10.18404/ijemst.552416

Juniati, D., & Budayasa, I. K. (2023). Geometry learning strategies with optimised technology to improve the performance of undergraduate mathematics students. World Transactions on Engineering and Technology Education, 21(1), 26–31.

Kennedy, L. M., Tipps, S., & Johnson, A. (2008). Guilding children’s learning of mathematics. Thomson Wadsworth.

Knezek, G., & Christensen, R. (2016). Extending the will, skill, tool model of technology integration: adding pedagogy as a new model construct. Journal of Computing in Higher Education, 28(3), 307–325. https://doi.org/10.1007/s12528-016-9120-2

Letchumanan, M., Mohamad, M., & Davrajoo, E. (2019). Understanding the reasons that hinder mobile e-book use of university mathematics students. Malaysian Journal of Mathematical Sciences, 13(2), 265–281.

Li, X., Zhou, Y., & Chen, M. (2021). Validation and Implementation of Hawgent on Pythagoras Theorem. Journal of Physics: Conference Series, 2123(1). https://doi.org/10.1088/1742-6596/2123/1/012042

Lidya, A. N., & Istikomah.Endang. (2021). Powtoon-based mathematics learning media: Validation stage of the Pythagorean theorem. Mathematics Research and Education Journal, 5(1), 1–7. https://doi.org/10.25299/mrej.2021.vol5(1).9206

Llinares, S. (2021). Instructional quality of mathematics teaching and mathematics teacher education. Journal of Mathematics Teacher Education, 24(1), 1–3. https://doi.org/10.1007/s10857-021-09488-2

Lomos, C., Luyten, H., Boualam, R., Lomos, C., Luyten, H., Boualam, R., & Fischbach, A. (2021). Teachers as key actors in Implementing Information and Communications Technology ( ICT ) in Teaching and learning - findings from ICILS 2018.

Maharani, S. D., Putri, R. I. I., Syawaliyah, A. F., & Safitri, M. L. O. (2024). Interactive learning media: Literacy and numeracy Limas House Balaputera Dewa Museum in phase B. Research and Development in Education (RaDEn), 4(1), 617–629. https://doi.org/10.22219/raden.v4i1.32832

Mart, C. T. (2017). Student evaluations of teaching effectiveness in higher education. International Journal of Academic Research in Business and Social Sciences, 7(10). https://doi.org/10.6007/ijarbss/v7-i10/3358

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

Moher, D., Liberati, A., Tetzlaff, J., & Altman, D. G. (2010). Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement. International Journal of Surgery, 8(5), 336–341. https://doi.org/10.1016/j.ijsu.2010.02.007

Nurwita, F., Kusumah, Y. S., & Juandi, D. (2023). Developing learning media based on Android application for improving math problem solving skill of junior high school students on Pythagorean Theorem. AIP Conference Proceedings.

O’Keefe, L., Rafferty, J., Gunder, A., & Vignare, K. (2020). Delivering high-quality instruction online in response to COVID-19 faculty playbook with support from the (Online Learning Consortium (ed.)).

Pan, G., Shankararaman, V., Koh, K., & Gan, S. (2021). Students’ evaluation of teaching in the project-based learning programme: An instrument and a development process. International Journal of Management Education, 19(2), 100501. https://doi.org/10.1016/j.ijme.2021.100501

Pauli, C., Lipowsky, F., & Reusser, K. (2024). Capturing the subject-specific quality of mathematics instruction: How do expert judgments relate to students’ assessments of the quality of their own learning and understanding? ZDM - Mathematics Education, 0123456789. https://doi.org/10.1007/s11858-024-01561-3

Pratama, G. S., & Retnawati, H. (2018). Urgency of higher order thinking skills (HOTS) content analysis in mathematics textbook. Journal of Physics: Conference Series, 1097(1). https://doi.org/10.1088/1742-6596/1097/1/012147

Puspitarani, & Retnawati, H. (2020). Diagnosis of learning difficulties in mathematics for students resolving problems related to material in the pythagorean theorem for 8th grade students in SMP 1 Todanan and SMP Muhammadiyah 9 Todanan, academic year 2018/2019. Journal of Physics: Conference Series, 1581(1). https://doi.org/10.1088/1742-6596/1581/1/012026

Putra, I. S. (2020). Improve student’s learning using media for understanding and interest in pythagorean theorem learning. Vygotsky, 2(2), 66. https://doi.org/ 10.30736/vj.v2i2.222

Rahayu, E. G. S., Juandi, D., & Jupri, A. (2021). Didactical design for distance concept in solid geometry to develop mathematical representation ability in vocational high school. Journal of Physics: Conference Series, 1882(1). https://doi.org/10.1088/1742-6596/1882/1/012077

Rewah, V., Sulangi, V., & Salajang, S. (2021). Development of learning devices with the PBL model using the Pythagoras theorem of RME approach. Journal of Physics: Conference Series, 1968(1). https://doi.org/10.1088/1742-6596/1968/1/012050

Richland, L. E., & Begolli, K. N. (2016). Analogy and higher order thinking: learning mathematics as an example. Policy Insights from the Behavioral and Brain Sciences, 3(2), 160–168. https://doi.org/10.1177/2372732216629795

Rudi, R., Suryadi, D., & Rosjanuardi, R. (2022). Didactical transposition within reflective practice of an Indonesian mathematics teacher community: A case in proving the Pythagorean theorem topic. Southeast Asian Mathematics Education Journal, 12(1), 65–80. https://doi.org/10.46517/seamej.v12i1.132

Rudi, Suryadi, D., & Rozjanuardi, R. (2020). Teacher knowledge to overcome student errors in pythagorean theorem proof: a study based on didactic mathematical knowledge framework. Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019. https://doi.org/10.4108/eai.12-10-2019.2296511

Sachdeva, S., & Eggen, P.-O. (2021). Learners’ critical thinking about learning mathematics. International Electronic Journal of Mathematics Education, 16(3), em0644. https://doi.org/10.29333/iejme/11003

Sadrina, S., Mustapha, R., & Ichsan, M. (2018). The evaluation of project-based learning in Malaysia: propose a new framework for polytechnics system. Jurnal Pendidikan Vokasi, 8(2), 143–150. https://doi.org/10.21831/jpv.v8i2.19100

Sari, N. M., Yaniawati, P., Darhim, & Kartasasmita, B. G. (2019). The effect of different ways in presenting teaching materials on students’ mathematical problem solving abilities. International Journal of Instruction, 12(4), 495–512. https://doi.org/10.29333/iji.2019.12432a

Sembiring, M. B., & Amaliah, R. (2017). Finding students’ missing concept about Pythagorean theorem n mathematics. JPMS, 12(2), 70–77.

Singh, J., Evans, E., Reed, A., Karch, L., Qualey, K., Singh, L., & Wiersma, H. (2022). Online, hybrid, and face-to-face learning through the eyes of faculty, students, administrators, and instructional designers: Lessons learned and directions for the post-vaccine and post-pandemic/covid-19 world. Journal of Educational Technology Systems, 50(3), 301–326. https://doi.org/10.1177/004 72395211063754

Swartz, M. K. (2011). The PRISMA statement: A guideline for systematic reviews and meta-analyses. Journal of Pediatric Health Care, 25(1), 1–2. https://doi.org/10.1016/j.pedhc.2010.09.006

Torres-Carrión, P. V., González-González, C. S., Aciar, S., & Rodríguez-Morales, G. (2017). Methodology for a systematic seview. 2018 IEEE Global Engineering Education Conference (EDUCON), 1364–1373. https://doi.org/10.1109/educon. 2018.8363388

Towe, M. M., & Julie, H. (2020). Developing learning trajectories with the RME of phytagorean theorem. Journal of Physics: Conference Series, 1470(1). https://doi.org/10.1088/1742-6596/1470/1/012027

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson Education UK.

Wittmann, E. C. (2021). Connecting mathematics and mathematics mducation. Department of Mathematics Technical University of Dortmund, Germany. https://doi.org/10.1007/978-3-030-61570-3

Yakar, E. A., & Yilmaz, S. (2022). Mathematical thinking processes for the pythagorean theorem of the secondary school students 1. 3(2), 87–99.

Yang, X., & Kaiser, G. (2022). The impact of mathematics teachers’ professional competence on instructional quality and students’ mathematics learning outcomes. Current Opinion in Behavioral Sciences, 48, 1–8. https://doi.org/10.1016/ j.cobeha.2022.101225

Zazkis, D., & Zazkis, R. (2016). Prospective teachers’ conceptions of proof comprehension: Revisiting a proof of the Pythagorean theorem. International Journal of Science and Mathematics Education, 14(4), 777–803. https://doi.org/10.1007/s10763-014-9595-0

Zhang, S., & Liu, Q. (2019). Investigating the relationships among teachers’ motivational beliefs, motivational regulation, and their learning engagement in online professional learning communities. Computers and Education, 134(October 2018), 145–155. https://doi.org/10.1016/j.compedu.2019.02.013

Zulfah, Astuti, Insani, S. U., Zulhendri, & Akbar, P. (2019). Development of open-ended based mathematics problem to measure high-level thinking ability. Journal of Physics: Conference Series, 1315(1), 0–8. https://doi.org/10.1088/1742-6596/1315/1/012047

Zulkardi, Putri, R. I. I., & Wijaya, A. (2020). Two decades of realistic mathematics education in Indonesia. International Reflections on the Netherlands Didactics of Mathematics: Visions on and Experiences with Realistic Mathematics Education, 325–340. https://doi.org/10.1007/978-3-030-20223-1_9


Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Jurnal Pendidikan MIPA

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

View My Stats

Creative Commons License
The copyright is reserved to The Jurnal Pendidikan MIPA that is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.