Algebra Learning Processes Using Scientific Approach and Direct Instruction
Abstract
Algebra is one of the mathematical contents which has an essential role in the mathematics field. Nevertheless, most students still find some problems and difficulties in algebra lessons. This study describes the process of algebra learning using the framework of scientific approach and direct instruction. An observational qualitative study involved 71 students and three mathematics teachers from three different public or private senior high schools in West Java, Indonesia. The field notes were used as the instruments. The observational data were analyzed using the framework of the syntaxes of the scientific approach and directed instruction model. Results showed that performing the scientific approach and directed instruction as a learning approach and model in the process of mathematics learning, specifically in algebra learning, should fully pass away all the phases of the learning approach and model. Consequently, by learning algebra contents, such as arithmetic and geometric sequence, matrix determinant, and compound interest, students can optimize some cognitive domains in mathematics, such as communication and conceptual understanding. Particularly, the optimization of questioning activities as the second phase of the scientific approach and demonstrating knowledge and skill as the second phase of the directed instruction model is essential to cultivate and enhance students’ critical thinking in mathematics. The implications to mathematics education are discussed comprehensively
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Al-Makahleh, A. A. A. (2011). The effect of direct instruction strategy on math achievement of primary 4th and 5th grade students with learning difficulties. International Education Studies, 4(4), 199–205. https://doi.org/10.5539/ies.v4n4p199
Alenezi, A. (2023). Using project-based learning through the madrasati platform for mathematics teaching in secondary schools. International Journal of Information and Communication Technology Education, 19(1), 1–15. https://doi.org/10.4018/IJICTE.332372
Ampadu, E., & Danso, A. (2018). Constructivism in mathematics classrooms: Listening to Ghanaian teachers’ and students’ views. Africa Education Review, 15(3), 49–71. https://doi.org/10.1080/18146627.2017.1340808
Andamon, J. C., & Tan, D. A. (2018). Conceptual understanding, attitude and performance in mathematics of Grade 7 Students. International Journal of Scientific and Technology Research, 7(8), 96–105.
Asomah, R. K., Agyei, D. D., Ntow, F. D., & Benning, I. (2023). Hypothetical approach to the teaching of trigonometric concepts using cooperative learning. Education Research International, 12(1), 1–12. https://doi.org/10.1155/2023/2051776
Ayuwanti, I., Marsigit, & Siswoyo, D. (2021). Teacher-student interaction in mathematics learning. International Journal of Evaluation and Research in Education, 10(2), 660–667. https://doi.org/10.11591/ijere.v10i2.21184
Birgin, O., & Uzun Yazıcı, K. (2021). The effect of GeoGebra software–supported mathematics instruction on eighth-grade students’ conceptual understanding and retention. Journal of Computer Assisted Learning, 37(4), 925–939. https://doi.org/10.1111/jcal.12532
Boorla, V. (2013). Burhus Frederic Skinner. Journal of Pyschology Medical, 14(2), 181–183.
Bostic, J., Lesseig, K., Sherman, M., & Boston, M. (2021). Classroom observation and mathematics education research. Journal of Mathematics Teacher Education, 24(1), 5–31. https://doi.org/10.1007/s10857-019-09445-0
Chaffee, J. (2017). Thinking critically (12th ed.). Cengage Learning.
Chasanah, C., Riyadi, & Usodo, B. (2020). The effectiveness of learning models on written mathematical communication skills viewed from students’ cognitive styles. European Journal of Educational Research, 9(3), 979–994. https://doi.org/10.12973/EU-JER.9.3.979
Chau Nguyen, G. T., & Hai Pham, C. T. (2023). An empirical study of factors influencing primary school teachers’ long-term commitment to Realistic Mathematics Education. Journal on Mathematics Education, 14(1), 1–18. https://doi.org/10.22342/JME.V14I1.PP1-18
Darling-aduana, J., & Shero, M. (2023). Teaching math online : Evaluating access and rigor in an asynchronous, online algebra 1 course. Journal of Online Learning Research, 9(1), 57–82.
Das, S., & Ali, I. (2023). An investigation on the effects of attitude towards algebraic problem-solving achievement. International Journal of Evaluation and Research in Education, 12(2), 1016–1022. https://doi.org/10.11591/ijere.v12i2.23926
Dougherty, S. M., Goodman, J. S., Hill, D. V., Litke, E. G., & Page, L. C. (2015). Middle school math acceleration and equitable access to eighth-grade algebra: Evidence from the wake county public school system. Educational Evaluation and Policy Analysis, 37(1), 80–101. https://doi.org/10.3102/0162373715576076
Drijvers, P. (2004). Learning algebra in a computer algebra environment. International Journal for Technology in Mathematics Education, 11(3), 1–10.
Drijvers, P., Godino, J. D., Font, V., & Trouche, L. (2012). One episode, two lenses: A reflective analysis of student learning with computer algebra from instrumental and onto-semiotic perspectives. Educational Studies in Mathematics, 82(1), 23–49. https://doi.org/10.1007/s10649-012-9416-8
Du, X., Emmersen, J., Toft, E., & Sun, B. (2013). PBL and critical thinking disposition in Chinese medical students – A randomized cross-sectional stu. Journal of Problem Based Learning in Higher Education, 1(1), 72–83. https://doi.org/10.5278/ojs.jpblhe.v1i1.275
Ennis, R. H. (2015). Critical Thinking: A Streamlined Conception. In The Palgrave Handbook of Critical Thinking in Higher Education (pp. 31–47). https://doi.org/10.1057/9781137378057_2
Ennis, R. H. (2016). Critical thinking across the curriculum: A vision. Topoi, 37(1), 165–184. https://doi.org/10.1007/s11245-016-9401-4
Eppley, K., & Dudley-Marling, C. (2019). Does direct instruction work?: A critical assessment of direct instruction research and its theoretical perspective. Journal of Curriculum and Pedagogy, 16(1), 35–54. https://doi.org/10.1080/15505170.2018.1438321
Ewing, B. (2011). Direct instruction in mathematics: Issues for schools with high indigenous enrolments: A literature review. Australian Journal of Teacher Education, 36(5), 64–91. https://doi.org/10.14221/ajte.2011v36n12.8
Ezeugwu, J. J. O., Onuorah, J. C., Asogwa, U. D., & Ukoha, I. P. (2016). Effect of mathematics game-based instructional techniques on students’achievements and interest in algebra at basic education level. Global Journal of Pure and Applied Mathematics, 12(4), 3727–3744.
Fang, J., Rao, Y., Luo, Q., & Xu, J. (2023). Solving one-dimensional cutting stock problems with the deep reinforcement learning. Mathematics, 11(4), 1–16. https://doi.org/10.3390/math11041028
Fatah, A., Suryadi, D., Sabandar, J., & Turmudi. (2016). Open-ended approach: An effort in cultivating students’ mathematical creative thinking ability and self-esteem in mathematics. Journal on Mathematics Education, 7(1), 9–18. https://doi.org/10.22342/jme.7.1.2813.9-18
Firdaus, F. M., Wahyudin, W., & Herman, T. (2017). Improving primary students’ mathematical literacy through problem-based learning and direct instruction. Educational Research and Reviews, 12(4), 212–219. https://doi.org/10.5897/err2016.3072
Fonda, A., & Sumargiyani, S. (2018). The developing math electronic module with scientific approach using kvisoft flipbook maker pro for XI grade of senior high school students. Infinity Journal, 7(2), 109–122. https://doi.org/10.22460/infinity.v7i2.p109-122
Fung, D., & Howe, C. (2014). Group work and the learning of critical thinking in the Hong Kong secondary liberal studies curriculum. Cambridge Journal of Education, 44(2), 245–270. https://doi.org/10.1080/0305764X.2014.897685
Goos, M., Carreira, S., & Namukasa, I. K. (2023). Mathematics and interdisciplinary STEM education: recent developments and future directions. ZDM - Mathematics Education, 55(7), 1199–1217. https://doi.org/10.1007/s11858-023-01533-z
Güçler, B. (2014). The role of symbols in mathematical communication: the case of the limit notation. Research in Mathematics Education, 16(3), 251–268. https://doi.org/10.1080/14794802.2014.919872
Harel, G. (2017). The learning and teaching of linear algebra: Observations and generalizations. Journal of Mathematical Behavior, 46, 69–95. https://doi.org/10.1016/j.jmathb.2017.02.007
Hasse, C. (2017). Technological literacy for teachers. Oxford Review of Education, 43(3), 365–378. https://doi.org/10.1080/03054985.2017.1305057
Hubka, V., & Eder, W. E. (1987). A scientific approach to engineering design. Design Studies, 8(3), 123–137. https://doi.org/10.1016/0142-694X(87)90035-4
Humble, N., Mozelius, P., & Sällvin, L. (2020). Remaking and reinforcing mathematics and technology with programming – teacher perceptions of challenges, opportunities and tools in K-12 settings. International Journal of Information and Learning Technology, 37(5), 309–321. https://doi.org/10.1108/IJILT-02-2020-0021
Ilyas, M., Meiyani, E., Ma’rufi, M., & Kaewhanam, P. (2022). Improving students’ ability in learning mathematics by using the science, technology, engineering, and mathematics (STEM) approach. Frontiers in Education, 7(October), 1–12. https://doi.org/10.3389/feduc.2022.966687
In’am, A., & Hajar, S. (2017). Learning geometry through discovery learning using a scientific approach. International Journal of Instruction, 10(1), 55–70. https://doi.org/10.12973/iji.2017.1014a
Indarti, D., Mardiyana, & Pramudya, I. (2018). Group investigation with scientific approach in mathematics learning. Journal of Physics: Conference Series, 983(1), 1–6. https://doi.org/10.1088/1742-6596/983/1/012147
Jansen, A., Berk, D., & Meikle, E. (2017). Investigating alignment between elementary mathematics teacher education and graduates’ teaching of mathematics for conceptual understanding. Harvard Educational Review, 87(2), 225–250. https://doi.org/10.17763/1943-5045-87.2.225
Jupri, A., & Gozali, S. M. (2021). Teaching and learning processes for prospective mathematics teachers: The case of absolute value equations. Mathematics Teaching-Research Journal, 13(3), 142–157.
Jupri, A., Usdiyana, D., & Sispiyati, R. (2021). Teaching and learning process for mathematization activities: The case of solving maximum and minimum problems. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(2), 100–110. https://doi.org/10.23917/jramathedu.v6i2.13263
Kaya, D., & Aydin, H. (2016). Elementary mathematics teachers’ perceptions and lived experiences on mathematical communication. Eurasia Journal of Mathematics, Science and Technology Education, 12(6), 1619–1629. https://doi.org/10.12973/eurasia.2014.1203a
Kong, S. C. (2015). An experience of a three-year study on the development of critical thinking skills in flipped secondary classrooms with pedagogical and technological support. Computers and Education, 89, 16–31. https://doi.org/10.1016/j.compedu.2015.08.017
Kosko, K. W., & Wilkins, J. L. M. (2010). Mathematical communication and its relation to the frequency of manipulative use. International Electronic Journal of Mathematics Education, 5(2), 79–90. https://doi.org/10.29333/iejme/251
Koza Çiftçi, & Yıldız, P. (2019). The effect of gender on algebra achievement: The meta-analysis of trends in international mathematics and science study (TIMSS). Turkish Journal of Computer and Mathematics Education, 10(3), 617–627. https://doi.org/10.16949/turkbilmat.568545
Krogsgaard, M. R., Brodersen, J., & Comins, J. (2011). A scientific approach to optimal treatment of cruciate ligament injuries. Acta Orthopaedica, 82(3), 9–15. https://doi.org/10.3109/17453674.2011.588864
Kwan, Y. W., & Wong, A. F. L. (2014). The constructivist classroom learning environment and its associations with critical thinking ability of secondary school students in Liberal Studies. Learning Environments Research, 17(2), 191–207. https://doi.org/10.1007/s10984-014-9158-x
Lee, S. W., & Mao, X. (2021). Algebra by the eighth grade: the association between early study of algebra I and students’ academic success. International Journal of Science and Mathematics Education, 19(6), 1271–1289. https://doi.org/10.1007/s10763-020-10116-3
Leite, W. L., Kuang, H., Jing, Z., Xing, W., Cavanaugh, C., & Huggins-Manley, A. C. (2022). The relationship between self-regulated student use of a virtual learning environment for algebra and student achievement: An examination of the role of teacher orchestration. Computer and Education, 61, 1–51.
Lestari, P. D., & Mansyur, J. (2021). The influence of the online PhET simulation-assisted using direct instruction on student’s conceptual understanding of parabolic motion. Journal of Physics: Conference Series, 2126(1), 1–8. https://doi.org/10.1088/1742-6596/2126/1/012013
Lestariani, I., Sujadi, I., & Pramudya, I. (2018). Performance assessment in algebra learning process. Journal of Physics: Conference Series, 943(1), 1–5. https://doi.org/10.1088/1742-6596/943/1/012043
Litke, E. (2020a). Instructional practice in algebra: Building from existing practices to inform an incremental improvement approach. Teaching and Teacher Education, 91, 1–12. https://doi.org/10.1016/j.tate.2020.103030
Litke, E. (2020b). The nature and auality of algebra instruction: Using a content-focused observation tool as a lens for understanding and improving instructional practice. Cognition and Instruction, 38(1), 57–86. https://doi.org/10.1080/07370008.2019.1616740
Lomibao, L. S., Luna, C. A., & Namoco, R. A. (2016). The influence of mathematical communication on students’ mathematics performance and anxiety. American Journal of Educational Research, 4(5), 378–382. https://doi.org/10.12691/education-4-5-3
Loyens, S. M. M., van Meerten, J. E., Schaap, L., & Wijnia, L. (2023). Situating higher-order, critical, and critical-analytic thinking in problem- and project-based learning environments: A systematic review. In Educational Psychology Review (Vol. 35, Issue 2). Springer US. https://doi.org/10.1007/s10648-023-09757-x
Mastuti, A. G., & Prayitno, L. L. (2023). Exploring high school teacher’s design of rich algebra tasks. Jurnal Elemen, 9(1), 1–14. https://doi.org/10.29408/jel.v9i1.5851
McKenna, J. W., Shin, M., & Ciullo, S. (2015). Evaluating reading and mathematics instruction for students with learning disabilities. Learning Disability Quarterly, 38(4), 195–207. https://doi.org/10.1177/0731948714564576
McMullen, F., & Madelaine, A. (2014). Why is there so much resistance to Direct Instruction? Australian Journal of Learning Difficulties, 19(2), 137–151. https://doi.org/10.1080/19404158.2014.962065
Melaibari, S. O. M., & Ismail, N. (2023). The effect of realistic mathematics education on undergraduate freshmen students’ mathematical competencies. Applied Mathematics and Information Sciences, 17(1), 55–66. https://doi.org/10.18576/amis/170108
Moss, D. L., & Lamberg, T. (2019). Conceptions of expressions and equations in early algebra: A learning trajectory. International Journal for Mathematics Teaching and Learning, 20(2), 170–192. https://doi.org/10.4256/ijmtl.v20i2.157
NCTM. (2000). Principles and standards for school mathematics. The National Council of Teachers of Mathematics, Inc.
Neber, H., & Neuhaus, B. J. (2013). Creativity and problem-based learning (PBL): A neglected relation. In Creativity, talent and excellence (pp. 43–56). Springer. https://doi.org/10.1007/978-981-4021-93-7
Nenotaek, B., Sujadi, I., & Subanti, S. (2019). The difficulties in implementing scientific approach for mathematics learning. International Journal of Educational Research Review, 4(4), 624–636. https://doi.org/10.24331/ijere.628448
Nugraha, T., & Suparman, S. (2021). Heterogeneity of Indonesian primary school students’ mathematical critical thinking skills through problem-based learning: A meta-analysis. Al-Jabar : Jurnal Pendidikan Matematika, 12(2), 315–328. https://doi.org/10.24042/ajpm.v12i2.9645
Ojo, S. G. (2022). Effects of animated instructional packages on achievement and interest of junior secondary school student in algebra. Mathematics Teaching-Research Journal, 14(1), 99–113.
Olanoff, D., Lo, J. J., & Tobias, J. M. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on fractions. Mathematics Enthusiast, 11(2), 267–310.
Omomia, O. A., & Omomia, T. . (2014). Relevance of Skinner’s theory of reinforcement on effective school evaluation and management. European Journal of Psychological Studies, 4(4), 174–180. https://doi.org/10.13187/ejps.2014.4.174
Palhares, P. (2012). Mathematics education and ethnomathematics. A connection in need of reinforcement. REDIMAT - Journal of Research in Mathematics Education, 1(1), 79–92. https://doi.org/10.4471/redimat.2012.04
Pardimin, Arcana, N., & Supriadi, D. (2019). Developing media based on the information and communications technology to improve the effectiveness of the direct instruction method in mathematics learning. Journal for the Education of Gifted Young Scientists, 7(4), 1311–1323. https://doi.org/10.17478/jegys.562636
Pierce, R., & Stacey, K. (2001). Observations on students’ responses to learning in a CAS environment. Mathematics Education Research Journal, 13(1), 28–46. https://doi.org/10.1007/BF03217097
Rakes, C. R., Wesneski, A., & Laws, R. (2023). Building mathematics learning through inquiry using student-generated data: Lessons learned from plan-do-study-act cycles. Education Sciences, 13(9), 1–20. https://doi.org/10.3390/educsci13090919
Rapti, S., & Sapounidis, T. (2024). “Critical thinking, communication, collaboration, creativity in kindergarten with educational robotics”: A scoping review (2012–2023). Computers and Education, 210, 1–29. https://doi.org/10.1016/j.compedu.2023.104968
Reif, F. (1981). Teaching problem solving-A scientific approach. The Physics Teacher, 19(5), 310–316. https://doi.org/10.1119/1.2340790
Sanabria, J. C., & Arámburo-Lizárraga, J. (2017). Enhancing 21st century skills with AR: Using the gradual immersion method to develop collaborative creativity. Eurasia Journal of Mathematics, Science and Technology Education, 13(2), 487–501. https://doi.org/10.12973/eurasia.2017.00627a
Sanders, S. (2016). Critical and creative Thinkers in mathematics classrooms. Journal of Student Engagement: Education Matters, 6(1), 19–27. https://ro.uow.edu.au/cgi/viewcontent.cgi?article=1043&context=jseem&httpsredir=1&referer=
Schaathun, H. G. (2022). On Understanding in Mathematics. Teaching Mathematics and Its Applications, 41(4), 318–328. https://doi.org/10.1093/teamat/hrac016
Schlinger, H. D. (2011). Skinner as missionary and prophet: a review of Burrhus F. Skinner: Shaper of behaviour. Journal of Applied Behavior Analysis, 44(1), 217–225. https://doi.org/10.1901/jaba.2011.44-217
Sen, N., & Yıkmış, A. (2021). Determining the reinforcement practices of special education teachers in mathematics teaching. European Journal of Special Education Research, 6(4), 139–155. https://doi.org/10.46827/ejse.v6i4.3515
Setiyani, Putri, D. P., Ferdianto, F., & Fauji, S. H. (2020). Designing a digital teaching module based on mathematical communication in relation and function. Journal on Mathematics Education, 11(2), 223–236. https://doi.org/10.22342/jme.11.2.7320.223-236
Shan, Z. (2021). Behaviorism reinforcement learning and its application in mathematics teaching in primary and middle schools. Frontiers in Educational Research, 4(4), 93–98. https://doi.org/10.25236/fer.2021.040419
Silber-Varod, V., Eshet-Alkalai, Y., & Geri, N. (2019). Tracing research trends of 21st-century learning skills. British Journal of Educational Technology, 50(6), 1–20. https://doi.org/10.1111/bjet.12753
Siswono, T. Y. E., Hartono, S., & Kohar, A. W. (2020). Deductive or inductive? prospective teachers’ preference of proof method on an intermediate proof task. Journal on Mathematics Education, 11(3), 417–438. https://doi.org/10.22342/jme.11.3.11846.417-438
Skophammer, R., & Reed, P. A. (2014). Technological literacy courses in pre-service teacher education. Journal of Technology Studies, 40(2), 68–81. https://doi.org/10.21061/jots.v40i2.a.2
Stein, M., Kinder, D., Rolf, K., Silbert, J., & Carnine, D. W. (2018). Direct instruction mathematics. Pearson Education, Inc.
Stockard, J., Wood, T. W., Coughlin, C., & Rasplica Khoury, C. (2018). The effectiveness of direct instruction curricula: A meta-analysis of a half century of research. Review of Educational Research, 88(4), 479–507. https://doi.org/10.3102/0034654317751919
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, 1–12. https://doi.org/10.1016/j.tate.2021.103593
Sumiati, T., Septiani, N., Widodo, S., & Caturiasari, J. (2019). Building children’s learning motivation through positive reinforcement in science and math classroom. Journal of Physics: Conference Series, 1318(1), 1–5. https://doi.org/10.1088/1742-6596/1318/1/012023
Suparman, Juandi, D., Martadiputra, B. A. P., Badawi, A., Susanti, N., & Yunita. (2022). Cultivating secondary school students ’ mathematical critical thinking skills using technology-assisted problem-based learning : A meta-analysis. AIP Conference Proceedings, 070006(December), 1–7. https://doi.org/https://doi.org/10.1063/5.0102422
Suparman, Juandi, D., & Tamur, M. (2021). Problem-based learning for mathematical critical thinking skills: A meta-analysis. Journal of Hunan University (Natural Sciences), 48(2), 133–144. http://www.jonuns.com/index.php/journal/article/view/521
Susiyanti, Y., Juandi, D., & Suparman. (2022). Does project-based learning have a positive effect on student’ mathematical critical thinking skills? A meta-analysis. AIP Conference Proceedings, 2468, 1–7. https://doi.org/10.1063/5.0102486
Terry, C. L., & McGee, E. O. (2012). “I’ve come too far, I’ve worked too hard”: Reinforcement of support structures among black male mathematics students. Journal of Mathematics Education at Teachers College, 3, 43–55.
Thompson, P. W. (2020). Constructivism in mathematics education. Encyclopedia of Mathematics Education, 14(1983), 127–134.
Tunde, J., & Listiani, T. (2021). The implementation of direct instruction assisted by incomplete handout to increase conceptual understanding. Journal of Physics: Conference Series, 1806(1), 1–8. https://doi.org/10.1088/1742-6596/1806/1/012067
Veith, J. M., Bitzenbauer, P., & Girnat, B. (2022). Towards describing student learning of abstract algebra: Insights into learners’ cognitive processes from an acceptance survey. Mathematics, 10(7), 1–22. https://doi.org/10.3390/math10071138
Voogt, J., & Roblin, N. P. (2012). A comparative analysis of international frameworks for 21 st century competences: Implications for national curriculum policies. Journal of Curriculum Studies, 44(3), 299–321. https://doi.org/10.1080/00220272.2012.668938
Wang, G., Kang, Y., Li, F., Zhen, Y., Chen, X., & Huang, H. (2022). An evidence-based study on the current status of Chinese secondary school mathematics teachers’ autonomous learning capacity across demographic and contextual factors. Frontiers in Psychology, 13(October), 1–15. https://doi.org/10.3389/fpsyg.2022.1042838
Wang, Y., Pei, F., Zhai, F., & Gao, Q. (2019). Academic performance and peer relations among rural-to-urban migrant children in Beijing: Do social identity and self-efficacy matter? Asian Social Work and Policy Review, 13(3), 263–273. https://doi.org/10.1111/aswp.12179
Warwick, P., Vrikki, M., Vermunt, J. D., Mercer, N., & van Halem, N. (2016). Connecting observations of student and teacher learning: an examination of dialogic processes in Lesson Study discussions in mathematics. ZDM - Mathematics Education, 48(4), 555–569. https://doi.org/10.1007/s11858-015-0750-z
Widodo, S. A., Irfan, M., Trisniawati, T., Hidayat, W., Perbowo, K. S., Noto, M. S., & Prahmana, R. C. I. (2020). Process of algebra problem-solving in formal student. Journal of Physics: Conference Series, 1657(1), 1–10. https://doi.org/10.1088/1742-6596/1657/1/012092
Wilkie, K. J. (2016). Learning to teach upper primary school algebra: changes to teachers’ mathematical knowledge for teaching functional thinking. Mathematics Education Research Journal, 28(2), 245–275. https://doi.org/10.1007/s13394-015-0151-1
Wilkie, K. J., & Clarke, D. (2015). Pathways to professional growth: Investigating upper primary school teachers’ perspectives on learning to teach algebra. Australian Journal of Teacher Education, 40(4), 87–118. https://doi.org/10.14221/ajte.2015v40n4.6
Yaniawati, R. P., Indrawan, R., & Setiawan, G. (2019). Core model on improving mathematical communication and connection, analysis of students’ mathematical disposition. International Journal of Instruction, 12(4), 639–654. https://doi.org/10.29333/iji.2019.12441a
Yerushalmy, M. (2000). Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra. Educational Studies in Mathematics, 43, 125–147.
Yeung, W. L., & Ng, O. L. (2023). Characterizing touchscreen actions in technology-enhanced embodied learning for mathematics instruction in K-12 setting – A systematic review (2010–2023). Computers and Education, 205, 1–20. https://doi.org/10.1016/j.compedu.2023.104881
Yohannes, Juandi, D., & Tamur, M. (2021). The effect of problem-based learning model on mathematical critical thinking skills of junior high school students: A meta-analysis study. Jurnal Pengukuran Psikologi Dan Pendidikan Indonesia, 10(2), 142–157. https://doi.org/10.15408/jp3i.v10i2.17893
Yunita, Y., Juandi, D., Hasanah, A., & Suparman. (2022). Meta-analysis study: How effective is a project-based learning model on students’ mathematical problem-solving abilities? AIP Conference Proceedings, 2468, 1–7. https://doi.org/10.1063/5.0102458
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